Vignette EIEntropy

In a wide range of analyses, there is a common problem.  The data is usually not available at the desired spatial scale that researchers need.  Ecological inference allows us to recover incomplete or unavailable data by inferring individual behaviours based on the aggregated information. Sometimes, the database containing the variable of interest does not have it at the needed spatial level.  Entropy allows us to obtain the best solution according to the information that we have.  To learn more about the methodology, see Fernández-Vázquez et al. (2020)

The package estimates the variable of interest using a second data frame that provides more detailed geographical information, ensuring consistency with the aggregates available in the first database. This package contains two functions, ei_gce() and ei_gme(). The method that the function ei_gce() applies is framed between GCE (Generalized Cross entropy), minimising the distance between the two distributions \(P\) and \(Q\), being this \(Q\) the prior information we can initially have.  If the user does not have prior information can choose ei_gme() for computational reasons which will use GME (Generalized maximum entropy) since our distribution a priori will be the uniform distribution.  These two kinds of problems will be explained in the

The EIentropy package makes the process of assessing uncertainty to estimate information at the desired level of disaggregation into one function. It gathers all the steps making it easy to apply this methodology to problems of absence of data. This document introduces you to the functions ei_gme() and ei_gce(), which apply entropy to solve issues of ecological inference while providing consistent disaggregated indicators with observable aggregated data and cross moments.

Once you’ve installed it, the vignette (“EIEntropy”) will allow you to learn more. We will use the data included in this package to explore its functions.

This package is on CRAN and can be installed from within R.

1. Methodology

The problem assessed is the need to obtain a variable \(Y\) at a spatial level that is not available. This variable \(Y\) can take \(J\) values. The method aims to obtain a matrix \(P\) with dimension \(n\) x \(J\) being \(n\) the number of observations. Matrix \(P\) is compounded by the probabilities associated with each \(j\) value for each observation. Taking advantage of the information that we have, the method introduces cross-moments as a restriction to assure consistency.

Taking into account \(Y\) is the sum of \(P\) and \(U\), being \(U\) the random noise. Once we have estimated matrix \(P\) and the error term, we can obtain \(Y\) as \(Y=P+U\). The error term is built as a weighted mean of a support vector \(V\) in which weights \(W\) are estimated in the optimization.

The support vector is the component of the noise defining the flexibility of the estimation. It represents the maximum and minimum error around a value in the center. By default, \(V\) is defined as (var, 0, -var) where var represents the variance of the dependent variable. If the estimation requires more flexibility \(V\) can be defined wider–with (1,0,-1) as the recommended maximum.

We present two functions to apply ecological inference through entropy. The general case minimizes the Kullback-Leibler divergence to find the matrix of probabilities \(P\) with the minimum divergence with a prior. This case is adequate when we have prior information on the distribution of the probabilities of our variable of interest. This information refers to all existing knowledge previous to the data that can influence the expectations of the variable of interest.

$$\min_{P} \, \text{KL}(P, Q) = \sum_{i=1}^{n} \sum_{j=1}^{J} p_{ij} \log\left(\frac{p_{ij}}{q_{ij}}\right)+ \sum_{l=1}^{L} \sum_{i=1}^{n} \sum_{j=1}^{J} w_{ijl} \log\left(\frac{w_{ijl}}{wo_{ijl}}\right)\quad \text{s.t.}$$

\[ \frac{1}{n} \sum_{i=1}^{n} x_{s_{ik}} y_{ij} = \frac{1}{n} \sum_{i=1}^{n} x_{c_{ik}} (p_{ij} + u_{ij}) =\frac{1}{n} \sum_{i=1}^{n} x_{cik} [p_{ij} + w_{Lij} v_{l}]; j=1,\ldots,J \] \] \[\[ \sum_{j=1}^{J} p_{ij} = 1 \quad \text{for } i=1,\ldots,n \] \] \[\[ \sum_{l=1}^{L} w_{Lij} = 1 \quad \text{for } i=1,\ldots,n; j=1,\ldots,J \] \]

This function minimizes the distance between \(P\) and \(Q\). Being \(Q\) the prior information that we already have. If we have some information about the possible distribution of our variable of interest we can include this information here. For example, if you know your variable of interest can take two values but one of them is more common than the other you can include it in your estimation by using \(Q\).

If we don’t have any information then we will assume there is the same probability for each possibility \(j\) of our variable of interest. In this sense, we minimize the divergence with a uniform distribution.

Solving the optimization problem, we obtain estimations as \(\hat{Y}= \hat{P} + \hat{W}V\). The solution should be consistent with the restrictions. In this case, the restrictions will contain information from two data sources, dataA and dataB. If there were divergences between the two sources of data, they would be captured in the error term. This is one of the main advantages of the methodology because it allows the user to use two databases with divergences between them.

2. Data

To explore the functions we will use data included in the package. In our example, we want to obtain microdata about poverty, in terms of wealth, with an indication of location at the regional level. We have the variable of interest in one official database but without information about location. At the same time, in another database, the variable of interest is not available but the household location is.

The data can be loaded by calling the functions financial() and social().

dataA <- financial()
dataB <- social()

In this example, we aim to obtain probabilities of being poor in terms of wealth for each individual or observation in the survey with detailed information about location. With this procedure, we will have our variable of interest at the desired spatial scale. As it is known, some variables, such as education level, income, or employment status are related to wealth. Hence, we will use these variables as regressors in the example. These variables are going to be our X. We have the same variables in both data frames with the same name. For this example, the financial survey includes 100 observations for the variables Dcollege, Dunemp, total income and the variable of interest: poor_liq. They are a dummy for college, a dummy for being unemployed, the household income (in euros) and a dummy for being poor in terms of liquid assets respectively.

The data called social has the same variables but instead of the variable of interest, it has another variable with the region of each household. In this database, we have 200 observations (households).

3. Examples

3.1 Generalized Cross entropy: ei_gce()

The function ei_gce() allows the user to introduce prior information in the estimation. In this example, we keep using the databases included in this package financial and social. Once we have chosen the best function for our case note that we need to specify our function :

fn <- dataA$poor_liq ~ Dcollege+Totalincome+Dunemp

Note that the same name in both datasets for the independent variables is required.

This function’s arguments are the previously defined function, the databases used, the weights, the tolerance, the maximum number of iterations allowed and the support vector. With this function, weights can be used and included with weights. If there are no weights the function assumes a matrix of 1. Note that the weights used in this methodology are normalised so analytics and sampling weights can be used without distinction.

In this example, the variable of interest (poor_liq) is defined with a function in the argument fn (see previous section)

The arguments corresponding to the information a priori and the support vector can be included as :

q <- c(0.2,0.8) 
v <- matrix(c(1,0,-1),nrow=1)

In this example we assume a priori distribution of poverty equal to 0.2 for poor and 0.8 for non-poor. The support vector has been set to the maximum (1,0,-1). Applying the ei_gce() we can solve the estimation as:

result <- ei_gce(fn,dataA,dataB,q=q,weights = "w",v=v)
result
## $estimations
##          weights predictions_1 predictions_0 probabilities_1 probabilities_0
## 1   6.408614e-03     0.3526612    1.03997932       0.1856802       0.8143198
## 2   4.069074e-03     0.3611852    1.00659540       0.1925139       0.8074861
## 3   8.478890e-05     0.2018007    0.79389077       0.2012848       0.7987152
## 4   6.019554e-03     0.2482836    0.77140431       0.2126642       0.7873358
## 5   8.529959e-03     0.3377428    0.27358677       0.3258196       0.6741804
## 6   3.466777e-03     0.2798052    0.66129187       0.2370367       0.7629633
## 7   7.143169e-03     0.3733840    0.52415554       0.2796025       0.7203975
## 8   6.728993e-03     0.3756344    1.09117708       0.1809317       0.8190683
## 9   9.459067e-03     0.2877814    0.78702116       0.2166944       0.7833056
## 10  1.952733e-03     0.2226752    0.75146695       0.2117173       0.7882827
## 11  6.884772e-03     0.3555312    1.03582456       0.1868151       0.8131849
## 12  1.046638e-03     0.2106771    0.72337741       0.2144218       0.7855782
## 13  6.632154e-03     0.4639106    0.85053121       0.2368135       0.7631865
## 14  5.694566e-03     0.2609696    0.81452272       0.2076120       0.7923880
## 15  8.199805e-03     0.4555912    0.36432259       0.3283205       0.6716795
## 16  7.974757e-03     0.3397106    0.72431237       0.2364912       0.7635088
## 17  1.016052e-05     0.2003965    0.80005099       0.2000560       0.7999440
## 18  1.077733e-03     0.2337937    0.75041296       0.2137528       0.7862472
## 19  4.555596e-03     0.3224837    1.00715977       0.1862268       0.8137732
## 20  1.797040e-03     0.2095780    0.72479111       0.2139996       0.7860004
## 21  7.726297e-03     0.3498615    0.14997501       0.3584095       0.6415905
## 22  7.537852e-03     0.4983089    1.18914834       0.1841440       0.8158560
## 23  5.078895e-04     0.2066423    0.80453438       0.2003420       0.7996580
## 24  8.673474e-03     0.4659097    1.04261104       0.2039921       0.7960079
## 25  6.743411e-03     0.2848000    0.32400748       0.3043771       0.6956229
## 26  2.597985e-03     0.2216336    0.59251985       0.2391501       0.7608499
## 27  7.946911e-03     0.2965673    0.85155155       0.2073982       0.7926018
## 28  3.132542e-03     0.2671697    0.66162186       0.2347626       0.7652374
## 29  1.413325e-03     0.2339130    0.85377483       0.1967876       0.8032124
## 30  1.952905e-03     0.2747870    0.80538222       0.2114290       0.7885710
## 31  7.786354e-03     0.3641713    1.03627013       0.1881235       0.8118765
## 32  6.412179e-03     0.3141028    0.23559225       0.3302812       0.6697188
## 33  8.813903e-03     0.2427698    0.40473956       0.2792660       0.7207340
## 34  3.104395e-03     0.2259749    0.69449306       0.2219212       0.7780788
## 35  1.494452e-03     0.2359713    0.85715421       0.1965743       0.8034257
## 36  1.979537e-03     0.2505294    0.73628529       0.2189597       0.7810403
## 37  1.781772e-03     0.2445111    0.68548055       0.2266515       0.7733485
## 38  8.631740e-04     0.2199829    0.80551695       0.2023531       0.7976469
## 39  2.624354e-03     0.2540498    0.79849383       0.2091165       0.7908835
## 40  7.278409e-03     0.3803848    1.09029772       0.1818259       0.8181741
## 41  9.198636e-03     0.3721894    0.29280984       0.3279855       0.6720145
## 42  8.939710e-04     0.2045391    0.78882755       0.2025561       0.7974439
## 43  5.755561e-03     0.3538831    0.43337648       0.2940743       0.7059257
## 44  9.197598e-03     0.4221829    0.13263798       0.3767581       0.6232419
## 45  7.835590e-03     0.2497892    0.72658450       0.2204847       0.7795153
## 46  7.304276e-03     0.3784180    1.08466672       0.1824422       0.8175578
## 47  2.825585e-03     0.2473003    0.76871006       0.2129502       0.7870498
## 48  5.701607e-03     0.2950633    0.28273923       0.3156210       0.6843790
## 49  9.403839e-03     0.3027989    0.53329222       0.2647413       0.7352587
## 50  8.874280e-03     0.2153520    0.60381911       0.2360101       0.7639899
## 51  5.856153e-03     0.3093848    0.29888952       0.3146391       0.6853609
## 52  7.506319e-04     0.2278652    0.79982179       0.2045744       0.7954256
## 53  2.829871e-03     0.3079285    0.93203077       0.1960680       0.8039320
## 54  1.403796e-03     0.2254491    0.72701196       0.2162915       0.7837085
## 55  2.256222e-03     0.2659105    0.85121088       0.2023972       0.7976028
## 56  8.706739e-03     0.3780882    1.05008290       0.1880874       0.8119126
## 57  6.495227e-04     0.2271737    0.80808595       0.2031082       0.7968918
## 58  7.423215e-03     0.4947906    0.60169178       0.2880435       0.7119565
## 59  9.409367e-03     0.2688901    0.43967038       0.2769284       0.7230716
## 60  3.467645e-03     0.2922539    0.95545377       0.1897663       0.8102337
## 61  4.891585e-03     0.2119124    0.70263851       0.2181418       0.7818582
## 62  5.191919e-05     0.2009450    0.80117419       0.1999628       0.8000372
## 63  6.960881e-04     0.2251791    0.84905269       0.1961436       0.8038564
## 64  3.234067e-03     0.3093491    0.66643422       0.2413431       0.7586569
## 65  8.095405e-03     0.5170827    1.21099845       0.1834243       0.8165757
## 66  2.123864e-03     0.2349545    0.67860615       0.2262012       0.7737988
## 67  3.309518e-03     0.2716568    0.65532966       0.2366639       0.7633361
## 68  5.300329e-03     0.3787056    0.74454595       0.2398998       0.7601002
## 69  7.890242e-03     0.4749215    0.74281574       0.2580209       0.7419791
## 70  5.248723e-03     0.3735130    0.73513441       0.2406247       0.7593753
## 71  9.625057e-04     0.2301381    0.78463504       0.2074481       0.7925519
## 72  3.609097e-03     0.3434140    0.98412877       0.1933175       0.8066825
## 73  5.617329e-03     0.3155370    0.34811668       0.3048609       0.6951391
## 74  9.237887e-03     0.3340911    0.19039502       0.3451287       0.6548713
## 75  9.275353e-03     0.2707651    0.74512726       0.2208981       0.7791019
## 76  7.561670e-04     0.2153829    0.82142421       0.1990213       0.8009787
## 77  1.374263e-03     0.2227906    0.82514861       0.1996176       0.8003824
## 78  2.232129e-03     0.2006943    0.74323505       0.2094332       0.7905668
## 79  7.759625e-03     0.2454837    0.71683753       0.2214161       0.7785839
## 80  3.268253e-03     0.2485843    0.49296628       0.2626450       0.7373550
## 81  5.423895e-03     0.3468515    0.46127656       0.2870675       0.7129325
## 82  3.519797e-03     0.2595236    0.86757856       0.1986919       0.8013081
## 83  3.686690e-03     0.2955618    0.95862538       0.1897817       0.8102183
## 84  8.770650e-03     0.4690099    1.04597156       0.2039524       0.7960476
## 85  4.499834e-03     0.2341002    0.42601309       0.2733101       0.7266899
## 86  6.913635e-03     0.4683562    0.59760543       0.2836355       0.7163645
## 87  7.423989e-03     0.3468818    0.77757893       0.2284887       0.7715113
## 88  9.184997e-03     0.4987431    1.10650907       0.1986493       0.8013507
## 89  9.934938e-04     0.2367018    0.87195615       0.1943118       0.8056882
## 90  7.108557e-03     0.4622404    0.54914224       0.2917684       0.7082316
## 91  6.307975e-03     0.3911718    1.13991627       0.1753216       0.8246784
## 92  5.444530e-03     0.3998260    1.18037638       0.1699324       0.8300676
## 93  5.708904e-03     0.3052747    0.93315246       0.1954563       0.8045437
## 94  7.141561e-03     0.3061271    0.33806639       0.3052852       0.6947148
## 95  7.903713e-03     0.2472353    0.47049796       0.2667997       0.7332003
## 96  5.645807e-03     0.3552547    1.06499349       0.1820116       0.8179884
## 97  3.539554e-03     0.3141657    0.90981346       0.2007132       0.7992868
## 98  2.396317e-03     0.2912799    0.91136892       0.1967303       0.8032697
## 99  3.785424e-03     0.2417960    0.52237233       0.2557632       0.7442368
## 100 6.899727e-03     0.3156277    0.72045937       0.2329166       0.7670834
## 101 1.963958e-03     0.2087034    0.71289891       0.2158593       0.7841407
## 102 4.301069e-03     0.3645696    0.67341825       0.2500181       0.7499819
## 103 8.824290e-03     0.3261669   -0.03881251       0.4082048       0.5917952
## 104 9.245072e-03     0.4464166    1.21046119       0.1720583       0.8279417
## 105 7.604964e-03     0.3329462    0.36007955       0.3055547       0.6944453
## 106 7.759268e-04     0.2027814    0.76416679       0.2063128       0.7936872
## 107 6.426895e-03     0.4162794    0.51408413       0.2897314       0.7102686
## 108 5.150249e-03     0.3031295    0.37982774       0.2957041       0.7042959
## 109 5.158771e-03     0.2891811    0.74918109       0.2233589       0.7766411
## 110 7.247160e-03     0.4980240    0.63910815       0.2815973       0.7184027
## 111 7.664692e-03     0.3025904    0.27356754       0.3191574       0.6808426
## 112 4.033598e-03     0.2334386    0.78399010       0.2081005       0.7918995
## 113 8.610544e-03     0.3053493    0.18321237       0.3414836       0.6585164
## 114 9.173485e-03     0.2940720    0.81201873       0.2135588       0.7864412
## 115 2.312141e-03     0.2691141    0.85671036       0.2020226       0.7979774
## 116 5.785912e-03     0.4188237    1.06871442       0.1916173       0.8083827
## 117 3.133029e-03     0.2956236    0.88240503       0.2021624       0.7978376
## 118 3.027803e-04     0.2084002    0.79234649       0.2026119       0.7973881
## 119 6.494774e-04     0.2093135    0.75999868       0.2080793       0.7919207
## 120 2.627321e-03     0.2861652    0.88500640       0.2001890       0.7998110
## 121 6.300118e-03     0.3336324    0.99310646       0.1902779       0.8097221
## 122 5.009005e-03     0.3685685    0.58307821       0.2674109       0.7325891
## 123 8.546357e-03     0.3704561    0.77785852       0.2325978       0.7674022
## 124 5.935042e-03     0.3940190    1.15535834       0.1732020       0.8267980
## 125 5.670056e-05     0.2014143    0.80063612       0.2001262       0.7998738
## 126 1.956694e-04     0.2032467    0.80358449       0.1999452       0.8000548
## 127 3.491569e-03     0.2794290    0.65760766       0.2376250       0.7623750
## 128 6.018842e-03     0.2627353    0.62510304       0.2404979       0.7595021
## 129 2.453778e-03     0.2259674    0.80548388       0.2033363       0.7966637
## 130 3.330195e-03     0.2683302    0.79726813       0.2117010       0.7882990
## 131 4.568058e-04     0.2111221    0.80439055       0.2010932       0.7989068
## 132 1.878873e-03     0.2477050    0.82329167       0.2039826       0.7960174
## 133 7.274750e-03     0.3405975    0.98709349       0.1923777       0.8076223
## 134 8.055270e-03     0.2745838    0.53634544       0.2590232       0.7409768
## 135 7.918719e-03     0.4353217    0.61834072       0.2733463       0.7266537
## 136 1.613960e-03     0.2144844    0.79665876       0.2029013       0.7970987
## 137 4.043005e-03     0.2879625    0.81027751       0.2128218       0.7871782
## 138 2.836492e-03     0.2538897    0.65611859       0.2334166       0.7665834
## 139 8.648536e-03     0.4846480    0.68513474       0.2704146       0.7295854
## 140 7.121030e-03     0.3961932    0.93421757       0.2103945       0.7896055
## 141 7.015624e-03     0.5058364    0.69956868       0.2718862       0.7281138
## 142 2.042604e-03     0.2551071    0.74232019       0.2187118       0.7812882
## 143 7.276373e-03     0.3018862    0.31256601       0.3101411       0.6898589
## 144 8.504937e-03     0.5003336    1.35088013       0.1555554       0.8444446
## 145 9.535921e-03     0.5385621    0.75287924       0.2685723       0.7314277
## 146 8.545091e-03     0.2764052    0.12028652       0.3523898       0.6476102
## 147 2.254398e-03     0.2121143    0.70556433       0.2176782       0.7823218
## 148 5.514651e-03     0.2562337    0.63694474       0.2372313       0.7627687
## 149 6.254560e-03     0.3619402    1.06753869       0.1826486       0.8173514
## 150 6.128050e-03     0.4379638    0.62340439       0.2729012       0.7270988
## 151 1.952048e-03     0.2101247    0.71743948       0.2153307       0.7846693
## 152 8.239200e-03     0.4406327    0.59736423       0.2783196       0.7216804
## 153 4.212187e-03     0.2279876    0.43988768       0.2693878       0.7306122
## 154 6.562633e-03     0.2531823    0.26134605       0.3127073       0.6872927
## 155 8.529452e-05     0.2030006    0.79954935       0.2005601       0.7994399
## 156 4.627415e-03     0.2576408    0.47604039       0.2676041       0.7323959
## 157 7.506022e-03     0.2401970    0.70922982       0.2218173       0.7781827
## 158 5.802968e-03     0.2936117    0.26531464       0.3193805       0.6806195
## 159 8.889093e-03     0.2602357    0.44721693       0.2738143       0.7261857
## 160 3.338891e-03     0.2617620    0.51924880       0.2599626       0.7400374
## 161 5.739428e-03     0.2712092    0.39425265       0.2867068       0.7132932
## 162 9.051019e-03     0.2815232    0.78083149       0.2166774       0.7833226
## 163 7.187216e-03     0.4751212    0.82312417       0.2437179       0.7562821
## 164 2.371262e-03     0.2282200    0.56049334       0.2461808       0.7538192
## 165 5.791201e-03     0.2845418    0.69915869       0.2312005       0.7687995
## 166 5.959915e-03     0.3025625    0.91951367       0.1972349       0.8027651
## 167 8.379680e-03     0.3201382    0.64428357       0.2472515       0.7527485
## 168 8.564844e-03     0.4032622    0.17058495       0.3633409       0.6366591
## 169 1.064177e-03     0.2397631    0.80037867       0.2064403       0.7935597
## 170 6.110630e-03     0.2528938    0.59245418       0.2446785       0.7553215
## 171 1.771706e-03     0.2798718    0.78408124       0.2158507       0.7841493
## 172 3.746941e-03     0.3272598    0.64516408       0.2483730       0.7516270
## 173 8.344937e-03     0.4199695    0.52340535       0.2886073       0.7113927
## 174 8.671874e-03     0.2596263    0.45848872       0.2714455       0.7285545
## 175 5.165876e-03     0.3075600    0.55592095       0.2613064       0.7386936
## 176 6.250491e-03     0.3127140    0.45204052       0.2825430       0.7174570
## 177 5.663535e-03     0.4123456    0.80308309       0.2357036       0.7642964
## 178 8.189466e-03     0.2759854    0.15405783       0.3433981       0.6566019
## 179 5.172787e-03     0.3452574    0.66206765       0.2485639       0.7514361
## 180 2.048906e-03     0.2901851    0.77536258       0.2190730       0.7809270
## 181 6.680525e-03     0.3810045    0.37593491       0.3113022       0.6886978
## 182 4.062967e-03     0.2784500    0.59382459       0.2489797       0.7510203
## 183 8.424910e-03     0.4398690    0.28689916       0.3424716       0.6575284
## 184 7.709358e-03     0.3922657    0.26015467       0.3394052       0.6605948
## 185 2.544983e-03     0.2403428    0.64941468       0.2322429       0.7677571
## 186 5.364966e-03     0.4269838    0.70328495       0.2561229       0.7438771
## 187 5.934410e-04     0.2193280    0.79261670       0.2043554       0.7956446
## 188 5.020772e-05     0.2020039    0.80257121       0.1999080       0.8000920
## 189 2.873655e-03     0.3291788    0.77215338       0.2263324       0.7736676
## 190 5.514606e-03     0.2547930    0.37431759       0.2878637       0.7121363
## 191 2.057597e-03     0.2227030    0.74558140       0.2127063       0.7872937
## 192 8.173496e-03     0.2669813    0.50831713       0.2630116       0.7369884
## 193 2.086392e-03     0.2521224    0.72960624       0.2203666       0.7796334
## 194 3.212343e-03     0.2666968    0.89458238       0.1954817       0.8045183
## 195 7.999160e-03     0.3703026    0.41959045       0.3000417       0.6999583
## 196 9.251449e-07     0.2000123    0.79998171       0.2000050       0.7999950
## 197 2.268155e-03     0.2405407    0.78202127       0.2096044       0.7903956
## 198 7.367501e-03     0.3409921    0.76424679       0.2297589       0.7702411
## 199 2.263759e-03     0.2265856    0.57070106       0.2440073       0.7559927
## 200 3.956566e-03     0.3566956    1.00071089       0.1927522       0.8072478
##          errors_1      errors_0
## 1    1.669810e-01  2.256595e-01
## 2    1.686714e-01  1.991093e-01
## 3    5.159031e-04 -4.824456e-03
## 4    3.561938e-02 -1.593148e-02
## 5    1.192317e-02 -4.005936e-01
## 6    4.276853e-02 -1.016715e-01
## 7    9.378146e-02 -1.962420e-01
## 8    1.947027e-01  2.721088e-01
## 9    7.108698e-02  3.715604e-03
## 10   1.095793e-02 -3.681577e-02
## 11   1.687161e-01  2.226396e-01
## 12  -3.744729e-03 -6.220075e-02
## 13   2.270971e-01  8.734476e-02
## 14   5.335760e-02  2.213468e-02
## 15   1.272707e-01 -3.073569e-01
## 16   1.032194e-01 -3.919645e-02
## 17   3.404876e-04  1.070271e-04
## 18   2.004089e-02 -3.583426e-02
## 19   1.362569e-01  1.933865e-01
## 20  -4.421543e-03 -6.120934e-02
## 21  -8.547965e-03 -4.916155e-01
## 22   3.141649e-01  3.732923e-01
## 23   6.300331e-03  4.876363e-03
## 24   2.619176e-01  2.466031e-01
## 25  -1.957708e-02 -3.716154e-01
## 26  -1.751655e-02 -1.683300e-01
## 27   8.916904e-02  5.894978e-02
## 28   3.240708e-02 -1.036155e-01
## 29   3.712536e-02  5.056246e-02
## 30   6.335803e-02  1.681119e-02
## 31   1.760478e-01  2.243937e-01
## 32  -1.617845e-02 -4.341265e-01
## 33  -3.649623e-02 -3.159944e-01
## 34   4.053699e-03 -8.358571e-02
## 35   3.939703e-02  5.372847e-02
## 36   3.156971e-02 -4.475502e-02
## 37   1.785960e-02 -8.786797e-02
## 38   1.762980e-02  7.870039e-03
## 39   4.493328e-02  7.610342e-03
## 40   1.985589e-01  2.721236e-01
## 41   4.420394e-02 -3.792047e-01
## 42   1.983003e-03 -8.616400e-03
## 43   5.980881e-02 -2.725492e-01
## 44   4.542486e-02 -4.906039e-01
## 45   2.930445e-02 -5.293077e-02
## 46   1.959758e-01  2.671089e-01
## 47   3.435014e-02 -1.833975e-02
## 48  -2.055770e-02 -4.016397e-01
## 49   3.805753e-02 -2.019664e-01
## 50  -2.065807e-02 -1.601708e-01
## 51  -5.254278e-03 -3.864714e-01
## 52   2.329081e-02  4.396221e-03
## 53   1.118605e-01  1.280988e-01
## 54   9.157626e-03 -5.669652e-02
## 55   6.351329e-02  5.360805e-02
## 56   1.900008e-01  2.381703e-01
## 57   2.406550e-02  1.119412e-02
## 58   2.067472e-01 -1.102648e-01
## 59  -8.038289e-03 -2.834013e-01
## 60   1.024877e-01  1.452200e-01
## 61  -6.229375e-03 -7.921971e-02
## 62   9.821428e-04  1.137020e-03
## 63   2.903555e-02  4.519628e-02
## 64   6.800602e-02 -9.222271e-02
## 65   3.336584e-01  3.944227e-01
## 66   8.753335e-03 -9.519264e-02
## 67   3.499288e-02 -1.080064e-01
## 68   1.388058e-01 -1.555427e-02
## 69   2.169006e-01  8.366844e-04
## 70   1.328882e-01 -2.424088e-02
## 71   2.269006e-02 -7.916899e-03
## 72   1.500966e-01  1.774462e-01
## 73   1.067611e-02 -3.470224e-01
## 74  -1.103761e-02 -4.644763e-01
## 75   4.986696e-02 -3.397460e-02
## 76   1.636157e-02  2.044549e-02
## 77   2.317298e-02  2.476625e-02
## 78  -8.738872e-03 -4.733180e-02
## 79   2.406756e-02 -6.174635e-02
## 80  -1.406064e-02 -2.443887e-01
## 81   5.978399e-02 -2.516559e-01
## 82   6.083168e-02  6.627050e-02
## 83   1.057801e-01  1.484071e-01
## 84   2.650575e-01  2.499240e-01
## 85  -3.920990e-02 -3.006768e-01
## 86   1.847207e-01 -1.187591e-01
## 87   1.183930e-01  6.067645e-03
## 88   3.000939e-01  3.051583e-01
## 89   4.238995e-02  6.626796e-02
## 90   1.704720e-01 -1.590894e-01
## 91   2.158503e-01  3.152379e-01
## 92   2.298936e-01  3.503088e-01
## 93   1.098184e-01  1.286088e-01
## 94   8.418825e-04 -3.566484e-01
## 95  -1.956444e-02 -2.627024e-01
## 96   1.732431e-01  2.470051e-01
## 97   1.134525e-01  1.105267e-01
## 98   9.454955e-02  1.080992e-01
## 99  -1.396728e-02 -2.218644e-01
## 100  8.271109e-02 -4.662401e-02
## 101 -7.155890e-03 -7.124179e-02
## 102  1.145515e-01 -7.656362e-02
## 103 -8.203790e-02 -6.306077e-01
## 104  2.743583e-01  3.825194e-01
## 105  2.739151e-02 -3.343657e-01
## 106 -3.531368e-03 -2.952046e-02
## 107  1.265481e-01 -1.961845e-01
## 108  7.425400e-03 -3.244682e-01
## 109  6.582218e-02 -2.746003e-02
## 110  2.164267e-01 -7.929454e-02
## 111 -1.656696e-02 -4.072751e-01
## 112  2.533811e-02 -7.909438e-03
## 113 -3.613434e-02 -4.753040e-01
## 114  8.051320e-02  2.557757e-02
## 115  6.709150e-02  5.873300e-02
## 116  2.272063e-01  2.603318e-01
## 117  9.346121e-02  8.456744e-02
## 118  5.788276e-03 -5.041632e-03
## 119  1.234150e-03 -3.192199e-02
## 120  8.597619e-02  8.519541e-02
## 121  1.433545e-01  1.833844e-01
## 122  1.011576e-01 -1.495109e-01
## 123  1.378583e-01  1.045633e-02
## 124  2.208170e-01  3.285603e-01
## 125  1.288115e-03  7.623374e-04
## 126  3.301463e-03  3.529715e-03
## 127  4.180397e-02 -1.047673e-01
## 128  2.223747e-02 -1.343991e-01
## 129  2.263117e-02  8.820135e-03
## 130  5.662917e-02  8.969157e-03
## 131  1.002890e-02  5.483702e-03
## 132  4.372239e-02  2.727425e-02
## 133  1.482198e-01  1.794712e-01
## 134  1.556060e-02 -2.046313e-01
## 135  1.619754e-01 -1.083130e-01
## 136  1.158314e-02 -4.399418e-04
## 137  7.514075e-02  2.309929e-02
## 138  2.047307e-02 -1.104648e-01
## 139  2.142335e-01 -4.445071e-02
## 140  1.857988e-01  1.446121e-01
## 141  2.339502e-01 -2.854512e-02
## 142  3.639523e-02 -3.896799e-02
## 143 -8.254948e-03 -3.772929e-01
## 144  3.447782e-01  5.064356e-01
## 145  2.699898e-01  2.145156e-02
## 146 -7.598455e-02 -5.273237e-01
## 147 -5.563841e-03 -7.675751e-02
## 148  1.900240e-02 -1.258239e-01
## 149  1.792917e-01  2.501873e-01
## 150  1.650626e-01 -1.036944e-01
## 151 -5.206043e-03 -6.722982e-02
## 152  1.623131e-01 -1.243162e-01
## 153 -4.140015e-02 -2.907246e-01
## 154 -5.952496e-02 -4.259466e-01
## 155  2.440506e-03  1.094046e-04
## 156 -9.963320e-03 -2.563555e-01
## 157  1.837966e-02 -6.895286e-02
## 158 -2.576878e-02 -4.153049e-01
## 159 -1.357867e-02 -2.789687e-01
## 160  1.799375e-03 -2.207886e-01
## 161 -1.549752e-02 -3.190406e-01
## 162  6.484579e-02 -2.491135e-03
## 163  2.314033e-01  6.684205e-02
## 164 -1.796080e-02 -1.933258e-01
## 165  5.334131e-02 -6.964084e-02
## 166  1.053276e-01  1.167486e-01
## 167  7.288674e-02 -1.084649e-01
## 168  3.992137e-02 -4.660742e-01
## 169  3.332289e-02  6.818926e-03
## 170  8.215303e-03 -1.628673e-01
## 171  6.402109e-02 -6.807999e-05
## 172  7.888682e-02 -1.064630e-01
## 173  1.313622e-01 -1.879873e-01
## 174 -1.181920e-02 -2.700658e-01
## 175  4.625360e-02 -1.827727e-01
## 176  3.017096e-02 -2.654164e-01
## 177  1.766420e-01  3.878666e-02
## 178 -6.741271e-02 -5.025440e-01
## 179  9.669354e-02 -8.936845e-02
## 180  7.111207e-02 -5.564414e-03
## 181  6.970230e-02 -3.127629e-01
## 182  2.947025e-02 -1.571957e-01
## 183  9.739743e-02 -3.706292e-01
## 184  5.286048e-02 -4.004401e-01
## 185  8.099941e-03 -1.183424e-01
## 186  1.708608e-01 -4.059210e-02
## 187  1.497253e-02 -3.027878e-03
## 188  2.095865e-03  2.479219e-03
## 189  1.028464e-01 -1.514197e-03
## 190 -3.307066e-02 -3.378188e-01
## 191  9.996759e-03 -4.171234e-02
## 192  3.969631e-03 -2.286712e-01
## 193  3.175584e-02 -5.002716e-02
## 194  7.121516e-02  9.006407e-02
## 195  7.026087e-02 -2.803678e-01
## 196  7.376057e-06 -1.332560e-05
## 197  3.093626e-02 -8.374312e-03
## 198  1.112331e-01 -5.994262e-03
## 199 -1.742168e-02 -1.852916e-01
## 200  1.639433e-01  1.934631e-01
## 
## $values
## $values$divergencekl
## [1] -10.87511
## 
## $values$iterations
## [1] 66
## 
## $values$message
## [1] "relative convergence (4)"
## 
## $values$q
##        [,1] [,2]
##   [1,]  0.2  0.8
##   [2,]  0.2  0.8
##   [3,]  0.2  0.8
##   [4,]  0.2  0.8
##   [5,]  0.2  0.8
##   [6,]  0.2  0.8
##   [7,]  0.2  0.8
##   [8,]  0.2  0.8
##   [9,]  0.2  0.8
##  [10,]  0.2  0.8
##  [11,]  0.2  0.8
##  [12,]  0.2  0.8
##  [13,]  0.2  0.8
##  [14,]  0.2  0.8
##  [15,]  0.2  0.8
##  [16,]  0.2  0.8
##  [17,]  0.2  0.8
##  [18,]  0.2  0.8
##  [19,]  0.2  0.8
##  [20,]  0.2  0.8
##  [21,]  0.2  0.8
##  [22,]  0.2  0.8
##  [23,]  0.2  0.8
##  [24,]  0.2  0.8
##  [25,]  0.2  0.8
##  [26,]  0.2  0.8
##  [27,]  0.2  0.8
##  [28,]  0.2  0.8
##  [29,]  0.2  0.8
##  [30,]  0.2  0.8
##  [31,]  0.2  0.8
##  [32,]  0.2  0.8
##  [33,]  0.2  0.8
##  [34,]  0.2  0.8
##  [35,]  0.2  0.8
##  [36,]  0.2  0.8
##  [37,]  0.2  0.8
##  [38,]  0.2  0.8
##  [39,]  0.2  0.8
##  [40,]  0.2  0.8
##  [41,]  0.2  0.8
##  [42,]  0.2  0.8
##  [43,]  0.2  0.8
##  [44,]  0.2  0.8
##  [45,]  0.2  0.8
##  [46,]  0.2  0.8
##  [47,]  0.2  0.8
##  [48,]  0.2  0.8
##  [49,]  0.2  0.8
##  [50,]  0.2  0.8
##  [51,]  0.2  0.8
##  [52,]  0.2  0.8
##  [53,]  0.2  0.8
##  [54,]  0.2  0.8
##  [55,]  0.2  0.8
##  [56,]  0.2  0.8
##  [57,]  0.2  0.8
##  [58,]  0.2  0.8
##  [59,]  0.2  0.8
##  [60,]  0.2  0.8
##  [61,]  0.2  0.8
##  [62,]  0.2  0.8
##  [63,]  0.2  0.8
##  [64,]  0.2  0.8
##  [65,]  0.2  0.8
##  [66,]  0.2  0.8
##  [67,]  0.2  0.8
##  [68,]  0.2  0.8
##  [69,]  0.2  0.8
##  [70,]  0.2  0.8
##  [71,]  0.2  0.8
##  [72,]  0.2  0.8
##  [73,]  0.2  0.8
##  [74,]  0.2  0.8
##  [75,]  0.2  0.8
##  [76,]  0.2  0.8
##  [77,]  0.2  0.8
##  [78,]  0.2  0.8
##  [79,]  0.2  0.8
##  [80,]  0.2  0.8
##  [81,]  0.2  0.8
##  [82,]  0.2  0.8
##  [83,]  0.2  0.8
##  [84,]  0.2  0.8
##  [85,]  0.2  0.8
##  [86,]  0.2  0.8
##  [87,]  0.2  0.8
##  [88,]  0.2  0.8
##  [89,]  0.2  0.8
##  [90,]  0.2  0.8
##  [91,]  0.2  0.8
##  [92,]  0.2  0.8
##  [93,]  0.2  0.8
##  [94,]  0.2  0.8
##  [95,]  0.2  0.8
##  [96,]  0.2  0.8
##  [97,]  0.2  0.8
##  [98,]  0.2  0.8
##  [99,]  0.2  0.8
## [100,]  0.2  0.8
## [101,]  0.2  0.8
## [102,]  0.2  0.8
## [103,]  0.2  0.8
## [104,]  0.2  0.8
## [105,]  0.2  0.8
## [106,]  0.2  0.8
## [107,]  0.2  0.8
## [108,]  0.2  0.8
## [109,]  0.2  0.8
## [110,]  0.2  0.8
## [111,]  0.2  0.8
## [112,]  0.2  0.8
## [113,]  0.2  0.8
## [114,]  0.2  0.8
## [115,]  0.2  0.8
## [116,]  0.2  0.8
## [117,]  0.2  0.8
## [118,]  0.2  0.8
## [119,]  0.2  0.8
## [120,]  0.2  0.8
## [121,]  0.2  0.8
## [122,]  0.2  0.8
## [123,]  0.2  0.8
## [124,]  0.2  0.8
## [125,]  0.2  0.8
## [126,]  0.2  0.8
## [127,]  0.2  0.8
## [128,]  0.2  0.8
## [129,]  0.2  0.8
## [130,]  0.2  0.8
## [131,]  0.2  0.8
## [132,]  0.2  0.8
## [133,]  0.2  0.8
## [134,]  0.2  0.8
## [135,]  0.2  0.8
## [136,]  0.2  0.8
## [137,]  0.2  0.8
## [138,]  0.2  0.8
## [139,]  0.2  0.8
## [140,]  0.2  0.8
## [141,]  0.2  0.8
## [142,]  0.2  0.8
## [143,]  0.2  0.8
## [144,]  0.2  0.8
## [145,]  0.2  0.8
## [146,]  0.2  0.8
## [147,]  0.2  0.8
## [148,]  0.2  0.8
## [149,]  0.2  0.8
## [150,]  0.2  0.8
## [151,]  0.2  0.8
## [152,]  0.2  0.8
## [153,]  0.2  0.8
## [154,]  0.2  0.8
## [155,]  0.2  0.8
## [156,]  0.2  0.8
## [157,]  0.2  0.8
## [158,]  0.2  0.8
## [159,]  0.2  0.8
## [160,]  0.2  0.8
## [161,]  0.2  0.8
## [162,]  0.2  0.8
## [163,]  0.2  0.8
## [164,]  0.2  0.8
## [165,]  0.2  0.8
## [166,]  0.2  0.8
## [167,]  0.2  0.8
## [168,]  0.2  0.8
## [169,]  0.2  0.8
## [170,]  0.2  0.8
## [171,]  0.2  0.8
## [172,]  0.2  0.8
## [173,]  0.2  0.8
## [174,]  0.2  0.8
## [175,]  0.2  0.8
## [176,]  0.2  0.8
## [177,]  0.2  0.8
## [178,]  0.2  0.8
## [179,]  0.2  0.8
## [180,]  0.2  0.8
## [181,]  0.2  0.8
## [182,]  0.2  0.8
## [183,]  0.2  0.8
## [184,]  0.2  0.8
## [185,]  0.2  0.8
## [186,]  0.2  0.8
## [187,]  0.2  0.8
## [188,]  0.2  0.8
## [189,]  0.2  0.8
## [190,]  0.2  0.8
## [191,]  0.2  0.8
## [192,]  0.2  0.8
## [193,]  0.2  0.8
## [194,]  0.2  0.8
## [195,]  0.2  0.8
## [196,]  0.2  0.8
## [197,]  0.2  0.8
## [198,]  0.2  0.8
## [199,]  0.2  0.8
## [200,]  0.2  0.8
## 
## 
## $tol
## [1] 1e-10
## 
## $v
##      [,1] [,2] [,3]
## [1,]    1    0   -1
## 
## $lambda
##   (Intercept)  Dcollege   Totalincome      Dunemp
## 1    57.03564  8.987007 -0.0001201035  -0.8332262
## 0    28.58571 75.368523 -0.0002268384 -25.0246657
## 
## $checkrestrictions
## $checkrestrictions$g1
##        [,1]
##   [1,]    0
##   [2,]    0
##   [3,]    0
##   [4,]    0
##   [5,]    0
##   [6,]    0
##   [7,]    0
##   [8,]    0
##   [9,]    0
##  [10,]    0
##  [11,]    0
##  [12,]    0
##  [13,]    0
##  [14,]    0
##  [15,]    0
##  [16,]    0
##  [17,]    0
##  [18,]    0
##  [19,]    0
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##  [21,]    0
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##  [93,]    0
##  [94,]    0
##  [95,]    0
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## [100,]    0
## [101,]    0
## [102,]    0
## [103,]    0
## [104,]    0
## [105,]    0
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## [108,]    0
## [109,]    0
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## [111,]    0
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## [114,]    0
## [115,]    0
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## [117,]    0
## [118,]    0
## [119,]    0
## [120,]    0
## [121,]    0
## [122,]    0
## [123,]    0
## [124,]    0
## [125,]    0
## [126,]    0
## [127,]    0
## [128,]    0
## [129,]    0
## [130,]    0
## [131,]    0
## [132,]    0
## [133,]    0
## [134,]    0
## [135,]    0
## [136,]    0
## [137,]    0
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## [139,]    0
## [140,]    0
## [141,]    0
## [142,]    0
## [143,]    0
## [144,]    0
## [145,]    0
## [146,]    0
## [147,]    0
## [148,]    0
## [149,]    0
## [150,]    0
## [151,]    0
## [152,]    0
## [153,]    0
## [154,]    0
## [155,]    0
## [156,]    0
## [157,]    0
## [158,]    0
## [159,]    0
## [160,]    0
## [161,]    0
## [162,]    0
## [163,]    0
## [164,]    0
## [165,]    0
## [166,]    0
## [167,]    0
## [168,]    0
## [169,]    0
## [170,]    0
## [171,]    0
## [172,]    0
## [173,]    0
## [174,]    0
## [175,]    0
## [176,]    0
## [177,]    0
## [178,]    0
## [179,]    0
## [180,]    0
## [181,]    0
## [182,]    0
## [183,]    0
## [184,]    0
## [185,]    0
## [186,]    0
## [187,]    0
## [188,]    0
## [189,]    0
## [190,]    0
## [191,]    0
## [192,]    0
## [193,]    0
## [194,]    0
## [195,]    0
## [196,]    0
## [197,]    0
## [198,]    0
## [199,]    0
## [200,]    0
## 
## $checkrestrictions$g2
##        [,1] [,2]
##   [1,]    0    0
##   [2,]    0    0
##   [3,]    0    0
##   [4,]    0    0
##   [5,]    0    0
##   [6,]    0    0
##   [7,]    0    0
##   [8,]    0    0
##   [9,]    0    0
##  [10,]    0    0
##  [11,]    0    0
##  [12,]    0    0
##  [13,]    0    0
##  [14,]    0    0
##  [15,]    0    0
##  [16,]    0    0
##  [17,]    0    0
##  [18,]    0    0
##  [19,]    0    0
##  [20,]    0    0
##  [21,]    0    0
##  [22,]    0    0
##  [23,]    0    0
##  [24,]    0    0
##  [25,]    0    0
##  [26,]    0    0
##  [27,]    0    0
##  [28,]    0    0
##  [29,]    0    0
##  [30,]    0    0
##  [31,]    0    0
##  [32,]    0    0
##  [33,]    0    0
##  [34,]    0    0
##  [35,]    0    0
##  [36,]    0    0
##  [37,]    0    0
##  [38,]    0    0
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##  [40,]    0    0
##  [41,]    0    0
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##  [50,]    0    0
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##  [52,]    0    0
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##  [54,]    0    0
##  [55,]    0    0
##  [56,]    0    0
##  [57,]    0    0
##  [58,]    0    0
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##  [61,]    0    0
##  [62,]    0    0
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##  [64,]    0    0
##  [65,]    0    0
##  [66,]    0    0
##  [67,]    0    0
##  [68,]    0    0
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##  [70,]    0    0
##  [71,]    0    0
##  [72,]    0    0
##  [73,]    0    0
##  [74,]    0    0
##  [75,]    0    0
##  [76,]    0    0
##  [77,]    0    0
##  [78,]    0    0
##  [79,]    0    0
##  [80,]    0    0
##  [81,]    0    0
##  [82,]    0    0
##  [83,]    0    0
##  [84,]    0    0
##  [85,]    0    0
##  [86,]    0    0
##  [87,]    0    0
##  [88,]    0    0
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##  [90,]    0    0
##  [91,]    0    0
##  [92,]    0    0
##  [93,]    0    0
##  [94,]    0    0
##  [95,]    0    0
##  [96,]    0    0
##  [97,]    0    0
##  [98,]    0    0
##  [99,]    0    0
## [100,]    0    0
## [101,]    0    0
## [102,]    0    0
## [103,]    0    0
## [104,]    0    0
## [105,]    0    0
## [106,]    0    0
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## [109,]    0    0
## [110,]    0    0
## [111,]    0    0
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## [114,]    0    0
## [115,]    0    0
## [116,]    0    0
## [117,]    0    0
## [118,]    0    0
## [119,]    0    0
## [120,]    0    0
## [121,]    0    0
## [122,]    0    0
## [123,]    0    0
## [124,]    0    0
## [125,]    0    0
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## [127,]    0    0
## [128,]    0    0
## [129,]    0    0
## [130,]    0    0
## [131,]    0    0
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## [133,]    0    0
## [134,]    0    0
## [135,]    0    0
## [136,]    0    0
## [137,]    0    0
## [138,]    0    0
## [139,]    0    0
## [140,]    0    0
## [141,]    0    0
## [142,]    0    0
## [143,]    0    0
## [144,]    0    0
## [145,]    0    0
## [146,]    0    0
## [147,]    0    0
## [148,]    0    0
## [149,]    0    0
## [150,]    0    0
## [151,]    0    0
## [152,]    0    0
## [153,]    0    0
## [154,]    0    0
## [155,]    0    0
## [156,]    0    0
## [157,]    0    0
## [158,]    0    0
## [159,]    0    0
## [160,]    0    0
## [161,]    0    0
## [162,]    0    0
## [163,]    0    0
## [164,]    0    0
## [165,]    0    0
## [166,]    0    0
## [167,]    0    0
## [168,]    0    0
## [169,]    0    0
## [170,]    0    0
## [171,]    0    0
## [172,]    0    0
## [173,]    0    0
## [174,]    0    0
## [175,]    0    0
## [176,]    0    0
## [177,]    0    0
## [178,]    0    0
## [179,]    0    0
## [180,]    0    0
## [181,]    0    0
## [182,]    0    0
## [183,]    0    0
## [184,]    0    0
## [185,]    0    0
## [186,]    0    0
## [187,]    0    0
## [188,]    0    0
## [189,]    0    0
## [190,]    0    0
## [191,]    0    0
## [192,]    0    0
## [193,]    0    0
## [194,]    0    0
## [195,]    0    0
## [196,]    0    0
## [197,]    0    0
## [198,]    0    0
## [199,]    0    0
## [200,]    0    0
## 
## $checkrestrictions$g3
##             y_factor1 y_factor0
## (Intercept)         0         0
## Dcollege            0         0
## Totalincome         0         0
## Dunemp              0         0
## 
## 
## $cross_moments_A
##             1          0         
## (Intercept)       0.34       0.66
## Dcollege          0.17       0.44
## Totalincome  103036.63  189594.78
## Dunemp            0.16       0.29
## 
## $cross_moments_B
##             1          0         
## (Intercept)       0.34       0.66
## Dcollege          0.17       0.44
## Totalincome  103036.63  189594.78
## Dunemp            0.16       0.29
## 
## $J
## [1] 2
## 
## $fn
## dataA$poor_liq ~ Dcollege + Totalincome + Dunemp
## 
## attr(,"class")
## [1] "kl"

The function will produce a data frame called estimations with the following information:

The function provides information about the optimization process, in concrete:

Lagrange multipliers \(\lambda\) associated to each independent variables are also provided in the form of a data frame. In addition, it provides an object with the restrictions checked which should be approximately zero. Being g1 the restriction related to the unit probability constraint, g2 to the error unit sum constraint, and g3 to the consistency restriction that implies that the difference between the cross moment in both datasets must be zero. The restriction g3 can be checked thoroughly with the objects separately which are to be provided in the output as cross moments A (the cross moments in dataA) and cross moments B (the cross moments in dataB).

To make the results more visual, this package includes a personalized summary function, providing the means for each category \(j\) for the predictions, the probabilities and the error.

suppressPackageStartupMessages(library(dplyr))
summary(result)
## Iterations[1] 66
## Kullback-Leibler divergence value[1] -10.87511
## [1] "mean_estimations"
##       weights predictions_1 predictions_0 probabilities_1 probabilities_0
## 1 0.006608031     0.3377783     0.6622217       0.2507808       0.7492192
##     errors_1    errors_0
## 1 0.08699743 -0.08699743
## [1] "lambda"
##   (Intercept)  Dcollege   Totalincome      Dunemp
## 1    57.03564  8.987007 -0.0001201035  -0.8332262
## 0    28.58571 75.368523 -0.0002268384 -25.0246657

Graphs included are generated with the plot function, showing the averages of the predictions for each territorial unit and the 95% confidence interval associated with each of them.

plot(x=result,dataB$reg)

Notes: Arguments tol and iter can be defined by the user. The default tolerance has been set in 1e-10 while the maximum number or iterations by default is settled in 1000.

3.2 Without prior information

Suppose we do not have prior information about our variable of interest. In that case, the process starting point will be the uniform distribution as we do not have the information to think one characteristic is more likely than the other.

The function ei_gce() will include by default the uniform distribution as \(Q\) if the user does not specify any other. This would be:

result2 <- ei_gce(fn,dataA,dataB,weights= "w")
result2
## $estimations
##          weights predictions_1 predictions_0 probabilities_1 probabilities_0
## 1   6.408614e-03    0.37714125     1.0373453      0.17143080       0.8285692
## 2   4.069074e-03    0.46516838     0.9465387      0.26050109       0.7394989
## 3   8.478890e-05    0.49554427     0.4949818      0.50026475       0.4997352
## 4   6.019554e-03    0.29425456     0.7815640      0.27116773       0.7288323
## 5   8.529959e-03    0.24792086     0.3351759      0.45651989       0.5434801
## 6   3.466777e-03    0.37076597     0.4876873      0.44458711       0.5554129
## 7   7.143169e-03    0.25980107     0.5065021      0.38173083       0.6182692
## 8   6.728993e-03    0.36038533     1.0624024      0.14987220       0.8501278
## 9   9.459067e-03    0.24653141     0.9526972      0.16596553       0.8340345
## 10  1.952733e-03    0.42547709     0.5404905      0.44585291       0.5541471
## 11  6.884772e-03    0.36676136     1.0476604      0.16115983       0.8388402
## 12  1.046638e-03    0.42656461     0.4268691      0.49985561       0.5001444
## 13  6.632154e-03    0.45686702     0.9334005      0.26416701       0.7358330
## 14  5.694566e-03    0.34661343     0.8392470      0.26618187       0.7338181
## 15  8.199805e-03    0.29044879     0.3979352      0.44769091       0.5523091
## 16  7.974757e-03    0.34208516     0.8763006      0.24538694       0.7546131
## 17  1.016052e-05    0.50008404     0.5008871      0.49962202       0.5003780
## 18  1.077733e-03    0.47310069     0.4945723      0.48988963       0.5101104
## 19  4.555596e-03    0.43194367     0.9691883      0.23344952       0.7665505
## 20  1.797040e-03    0.40140327     0.4763705      0.46452977       0.5354702
## 21  7.726297e-03    0.36613331     0.2079584      0.57897919       0.4210208
## 22  7.537852e-03    0.33716479     1.0938416      0.12177907       0.8782209
## 23  5.078895e-04    0.48835958     0.5396067      0.47587229       0.5241277
## 24  8.673474e-03    0.34928903     1.0777078      0.13630039       0.8636996
## 25  6.743411e-03    0.28645585     0.2974432      0.49452584       0.5054742
## 26  2.597985e-03    0.34630227     0.3301959      0.50785849       0.4921415
## 27  7.946911e-03    0.32381881     0.9735060      0.18622722       0.8137728
## 28  3.132542e-03    0.37158327     0.4640120      0.45608396       0.5439160
## 29  1.413325e-03    0.50486840     0.6852096      0.41406952       0.5859305
## 30  1.952905e-03    0.50803523     0.6558099      0.42980542       0.5701946
## 31  7.786354e-03    0.34741236     1.0685414      0.14103857       0.8589614
## 32  6.412179e-03    0.36399171     0.2144078      0.57461752       0.4253825
## 33  8.813903e-03    0.14764168     0.4589503      0.34574856       0.6542514
## 34  3.104395e-03    0.35538687     0.5085653      0.42745368       0.5725463
## 35  1.494452e-03    0.50471084     0.6952247      0.40910466       0.5908953
## 36  1.979537e-03    0.43997262     0.5224387      0.46116813       0.5388319
## 37  1.781772e-03    0.42523291     0.4282943      0.49854806       0.5014519
## 38  8.631740e-04    0.49491102     0.5728497      0.46325832       0.5367417
## 39  2.624354e-03    0.46497183     0.6798734      0.39816837       0.6018316
## 40  7.278409e-03    0.34905418     1.0741074      0.13836260       0.8616374
## 41  9.198636e-03    0.21786461     0.3741713      0.42227208       0.5777279
## 42  8.939710e-04    0.45949760     0.5303565      0.46664821       0.5333518
## 43  5.755561e-03    0.32270787     0.3367562      0.49312040       0.5068796
## 44  9.197598e-03    0.32806665     0.2496263      0.53913535       0.4608646
## 45  7.835590e-03    0.20378551     0.7852619      0.22815796       0.7718420
## 46  7.304276e-03    0.34955434     1.0730092      0.13921843       0.8607816
## 47  2.825585e-03    0.43352583     0.6371530      0.40405005       0.5959499
## 48  5.701607e-03    0.36363400     0.2181770      0.57250290       0.4274971
## 49  9.403839e-03    0.14601797     0.6247015      0.27122818       0.7287718
## 50  8.874280e-03    0.08319604     0.6259964      0.23775918       0.7622408
## 51  5.856153e-03    0.35220680     0.2339843      0.55886956       0.4411304
## 52  7.506319e-04    0.50195984     0.5572225      0.47395691       0.5260431
## 53  2.829871e-03    0.51333910     0.8552131      0.33161744       0.6683826
## 54  1.403796e-03    0.42963844     0.4600167      0.48563963       0.5143604
## 55  2.256222e-03    0.50956486     0.7420473      0.38819982       0.6118002
## 56  8.706739e-03    0.32821719     1.0912941      0.11983046       0.8801695
## 57  6.495227e-04    0.51007566     0.5661375      0.47355883       0.5264412
## 58  7.423215e-03    0.46620774     0.7547749      0.36198157       0.6380184
## 59  9.409367e-03    0.12397261     0.5121636      0.30905232       0.6909477
## 60  3.467645e-03    0.47043120     0.8983506      0.28929940       0.7107006
## 61  4.891585e-03    0.25236016     0.5896630      0.34011455       0.6598855
## 62  5.191919e-05    0.49955438     0.5055161      0.49719380       0.5028062
## 63  6.960881e-04    0.52499287     0.6371782      0.44671371       0.5532863
## 64  3.234067e-03    0.43693106     0.5181213      0.46176054       0.5382395
## 65  8.095405e-03    0.32338768     1.1079813      0.10778777       0.8922122
## 66  2.123864e-03    0.38804726     0.4229340      0.48337200       0.5166280
## 67  3.309518e-03    0.36617689     0.4653322      0.45286639       0.5471336
## 68  5.300329e-03    0.45370052     0.7757856      0.34578402       0.6542160
## 69  7.890242e-03    0.43151836     0.9045737      0.26894812       0.7310519
## 70  5.248723e-03    0.44718763     0.7585647      0.35144311       0.6485569
## 71  9.625057e-04    0.48690886     0.5426170      0.47377134       0.5262287
## 72  3.609097e-03    0.48364078     0.9192295      0.28373016       0.7162698
## 73  5.617329e-03    0.34034003     0.2579076      0.54093438       0.4590656
## 74  9.237887e-03    0.26393393     0.3105135      0.47674372       0.5232563
## 75  9.275353e-03    0.20156879     0.8823507      0.18190526       0.8180947
## 76  7.561670e-04    0.49760860     0.5883611      0.45717689       0.5428231
## 77  1.374263e-03    0.48128816     0.6314624      0.42902088       0.5709791
## 78  2.232129e-03    0.37084550     0.5174122      0.43073033       0.5692697
## 79  7.759625e-03    0.19416138     0.7630443      0.23377581       0.7662242
## 80  3.268253e-03    0.35954595     0.2702605      0.54401485       0.4559852
## 81  5.423895e-03    0.32883027     0.3491396      0.49009389       0.5099061
## 82  3.519797e-03    0.44627564     0.8133954      0.32337015       0.6766299
## 83  3.686690e-03    0.46329523     0.9091087      0.28031363       0.7196864
## 84  8.770650e-03    0.34686168     1.0804290      0.13370219       0.8662978
## 85  4.499834e-03    0.32020854     0.2749703      0.52248058       0.4775194
## 86  6.913635e-03    0.45482457     0.7095721      0.37906307       0.6209369
## 87  7.423989e-03    0.38267173     0.9137446      0.24307454       0.7569255
## 88  9.184997e-03    0.32784976     1.1020921      0.11311844       0.8868816
## 89  9.934938e-04    0.53182183     0.6919862      0.42330355       0.5766964
## 90  7.108557e-03    0.41232918     0.6358960      0.39477027       0.6052297
## 91  6.307975e-03    0.35899760     1.0677309      0.14614703       0.8538530
## 92  5.444530e-03    0.36801098     1.0605664      0.15404711       0.8459529
## 93  5.708904e-03    0.40224861     0.9639683      0.22381773       0.7761823
## 94  7.141561e-03    0.26731227     0.3222444      0.47266687       0.5273331
## 95  7.903713e-03    0.16503977     0.4725605      0.34873889       0.6512611
## 96  5.645807e-03    0.39114729     1.0268658      0.18329921       0.8167008
## 97  3.539554e-03    0.49407716     0.8675386      0.31638400       0.6836160
## 98  2.396317e-03    0.52472961     0.8185412      0.35610946       0.6438905
## 99  3.785424e-03    0.31833636     0.3185355      0.49990197       0.5000980
## 100 6.899727e-03    0.34665495     0.8118087      0.27989298       0.7201070
## 101 1.963958e-03    0.38847654     0.4653266      0.46355677       0.5364432
## 102 4.301069e-03    0.46970567     0.6283352      0.42510995       0.5748901
## 103 8.824290e-03    0.44210578     0.1264227      0.65781858       0.3421814
## 104 9.245072e-03    0.29598217     1.1344334      0.08099393       0.9190061
## 105 7.604964e-03    0.24465134     0.3562680      0.44460827       0.5553917
## 106 7.759268e-04    0.45320405     0.4823024      0.48628343       0.5137166
## 107 6.426895e-03    0.36017770     0.5030301      0.43233607       0.5676639
## 108 5.150249e-03    0.34234848     0.2619044      0.53989153       0.4601085
## 109 5.158771e-03    0.38924139     0.7550982      0.32689679       0.6731032
## 110 7.247160e-03    0.48560880     0.7937026      0.35114912       0.6488509
## 111 7.664692e-03    0.27774103     0.3016060      0.48809770       0.5119023
## 112 4.033598e-03    0.35902332     0.7016212      0.33886187       0.6611381
## 113 8.610544e-03    0.29051865     0.2822042      0.50415282       0.4958472
## 114 9.173485e-03    0.27410838     0.9733603      0.16627370       0.8337263
## 115 2.312141e-03    0.51128192     0.7527716      0.38361563       0.6163844
## 116 5.785912e-03    0.40348498     1.0217407      0.19141205       0.8085879
## 117 3.133029e-03    0.50150724     0.8249308      0.34222256       0.6577774
## 118 3.027803e-04    0.49290501     0.5075815      0.49309179       0.5069082
## 119 6.494774e-04    0.46052427     0.4682541      0.49635504       0.5036450
## 120 2.627321e-03    0.51441103     0.8032533      0.35933654       0.6406635
## 121 6.300118e-03    0.38606931     1.0151756      0.18797894       0.8120211
## 122 5.009005e-03    0.39456016     0.5113977      0.44484480       0.5551552
## 123 8.546357e-03    0.36682710     0.9593040      0.21165629       0.7883437
## 124 5.935042e-03    0.36343500     1.0640665      0.15011602       0.8498840
## 125 5.670056e-05    0.49996438     0.5053768      0.49745234       0.5025477
## 126 1.956694e-04    0.49743772     0.5190521      0.48982517       0.5101748
## 127 3.491569e-03    0.36763750     0.4826404      0.44545031       0.5545497
## 128 6.018842e-03    0.25616411     0.5745524      0.34884899       0.6511510
## 129 2.453778e-03    0.42789201     0.6552214      0.39282715       0.6071729
## 130 3.330195e-03    0.45417305     0.7229733      0.37220846       0.6277915
## 131 4.568058e-04    0.49890141     0.5417206      0.47983381       0.5201662
## 132 1.878873e-03    0.49715241     0.6752413      0.41533263       0.5846674
## 133 7.274750e-03    0.36343791     1.0385279      0.16518574       0.8348143
## 134 8.055270e-03    0.17014299     0.5542960      0.31464697       0.6853530
## 135 7.918719e-03    0.35004369     0.7405532      0.31614416       0.6838558
## 136 1.613960e-03    0.44481836     0.5890183      0.43212130       0.5678787
## 137 4.043005e-03    0.45292971     0.7853299      0.34062783       0.6593722
## 138 2.836492e-03    0.36867919     0.4335517      0.46904473       0.5309553
## 139 8.648536e-03    0.40487932     0.8830264      0.26894496       0.7310550
## 140 7.121030e-03    0.40200465     1.0056064      0.20009289       0.7999071
## 141 7.015624e-03    0.50187230     0.8437294      0.33252515       0.6674748
## 142 2.042604e-03    0.44644732     0.5396343      0.45614015       0.5438598
## 143 7.276373e-03    0.27335984     0.3110208      0.48123851       0.5187615
## 144 8.504937e-03    0.28247517     1.1493785      0.06658550       0.9334145
## 145 9.535921e-03    0.40889049     0.9714828      0.22238905       0.7776110
## 146 8.545091e-03    0.32920843     0.2406706      0.54424966       0.4557503
## 147 2.254398e-03    0.37776176     0.4714298      0.45556209       0.5444379
## 148 5.514651e-03    0.27258801     0.5631967      0.36208360       0.6379164
## 149 6.254560e-03    0.37577593     1.0434209      0.16731376       0.8326862
## 150 6.128050e-03    0.46189360     0.6907313      0.39148614       0.6085139
## 151 1.952048e-03    0.39256313     0.4730384      0.46188233       0.5381177
## 152 8.239200e-03    0.33030142     0.7244077      0.31481580       0.6851842
## 153 4.212187e-03    0.32458168     0.2727708      0.52573386       0.4742661
## 154 6.562633e-03    0.32256037     0.2521837      0.53513537       0.4648646
## 155 8.529452e-05    0.49978515     0.5056391      0.49724449       0.5027555
## 156 4.627415e-03    0.30253610     0.3171597      0.49277405       0.5072260
## 157 7.506022e-03    0.19114462     0.7362700      0.24439886       0.7556011
## 158 5.802968e-03    0.36849401     0.2110728      0.57850615       0.4214939
## 159 8.889093e-03    0.13810196     0.4959950      0.32384848       0.6761515
## 160 3.338891e-03    0.35704129     0.2980884      0.52889689       0.4711031
## 161 5.739428e-03    0.29183905     0.3035596      0.49417589       0.5058241
## 162 9.051019e-03    0.24618977     0.9294581      0.17769374       0.8223063
## 163 7.187216e-03    0.44810276     0.9357911      0.25904136       0.7409586
## 164 2.371262e-03    0.37102330     0.2899472      0.53968911       0.4603109
## 165 5.791201e-03    0.33183351     0.7032194      0.32554578       0.6744542
## 166 5.959915e-03    0.39382659     0.9629482      0.22086087       0.7791391
## 167 8.379680e-03    0.25726600     0.7659295      0.26171938       0.7382806
## 168 8.564844e-03    0.32893640     0.2510774      0.53882508       0.4611749
## 169 1.064177e-03    0.50320864     0.5820375      0.46280363       0.5371964
## 170 6.110630e-03    0.23336254     0.5255237      0.35980767       0.6401923
## 171 1.771706e-03    0.52165766     0.6221197      0.45237445       0.5476256
## 172 3.746941e-03    0.42731665     0.5216065      0.45558329       0.5444167
## 173 8.344937e-03    0.25568851     0.5881502      0.34243333       0.6575667
## 174 8.671874e-03    0.14356028     0.4964644      0.32654345       0.6734566
## 175 5.165876e-03    0.29467774     0.4293383      0.43492991       0.5650701
## 176 6.250491e-03    0.26256158     0.3704982      0.44683128       0.5531687
## 177 5.663535e-03    0.47401131     0.8621297      0.31031897       0.6896810
## 178 8.189466e-03    0.32238324     0.2483320      0.53700277       0.4629972
## 179 5.172787e-03    0.37674556     0.6194582      0.38587109       0.6141289
## 180 2.048906e-03    0.51888456     0.6288527      0.44784838       0.5521516
## 181 6.680525e-03    0.31019463     0.3270606      0.49169947       0.5083005
## 182 4.062967e-03    0.32344524     0.4156342      0.45557096       0.5444290
## 183 8.424910e-03    0.28920352     0.3299449      0.47986599       0.5201340
## 184 7.709358e-03    0.31518486     0.2788500      0.51806096       0.4819390
## 185 2.544983e-03    0.36650207     0.4030769      0.48246229       0.5175377
## 186 5.364966e-03    0.50714408     0.7578390      0.37916478       0.6208352
## 187 5.934410e-04    0.49408196     0.5305317      0.48283973       0.5171603
## 188 5.020772e-05    0.50207164     0.5088920      0.49678951       0.5032105
## 189 2.873655e-03    0.52784565     0.6870685      0.42385754       0.5761425
## 190 5.514606e-03    0.30662476     0.2813498      0.51258088       0.4874191
## 191 2.057597e-03    0.41814279     0.5359942      0.44449887       0.5555011
## 192 8.173496e-03    0.15968125     0.5246355      0.32242309       0.6775769
## 193 2.086392e-03    0.43346769     0.5171342      0.46058870       0.5394113
## 194 3.212343e-03    0.46856269     0.8320486      0.32370141       0.6762986
## 195 7.999160e-03    0.22223376     0.4232661      0.40126814       0.5987319
## 196 9.251449e-07    0.49996937     0.5000287      0.49997206       0.5000279
## 197 2.268155e-03    0.45362675     0.6246519      0.41936308       0.5806369
## 198 7.367501e-03    0.37636981     0.8968114      0.24939839       0.7506016
## 199 2.263759e-03    0.37305021     0.2949578      0.53817011       0.4618299
## 200 3.956566e-03    0.46982353     0.9399072      0.26622578       0.7337742
##          errors_1      errors_0
## 1    2.057104e-01  2.087761e-01
## 2    2.046673e-01  2.070398e-01
## 3   -4.720487e-03 -4.753428e-03
## 4    2.308683e-02  5.273171e-02
## 5   -2.085990e-01 -2.083042e-01
## 6   -7.382114e-02 -6.772560e-02
## 7   -1.219298e-01 -1.117670e-01
## 8    2.105131e-01  2.122746e-01
## 9    8.056588e-02  1.186627e-01
## 10  -2.037582e-02 -1.365657e-02
## 11   2.056015e-01  2.088203e-01
## 12  -7.329100e-02 -7.327534e-02
## 13   1.927000e-01  1.975675e-01
## 14   8.043156e-02  1.054288e-01
## 15  -1.572421e-01 -1.543739e-01
## 16   9.669821e-02  1.216876e-01
## 17   4.620245e-04  5.090774e-04
## 18  -1.678894e-02 -1.553809e-02
## 19   1.984941e-01  2.026378e-01
## 20  -6.312650e-02 -5.909976e-02
## 21  -2.128459e-01 -2.130624e-01
## 22   2.153857e-01  2.156207e-01
## 23   1.248730e-02  1.547897e-02
## 24   2.129886e-01  2.140081e-01
## 25  -2.080700e-01 -2.080310e-01
## 26  -1.615562e-01 -1.619456e-01
## 27   1.375916e-01  1.597333e-01
## 28  -8.450068e-02 -7.990403e-02
## 29   9.079888e-02  9.927907e-02
## 30   7.822981e-02  8.561535e-02
## 31   2.063738e-01  2.095800e-01
## 32  -2.106258e-01 -2.109747e-01
## 33  -1.981069e-01 -1.953012e-01
## 34  -7.206681e-02 -6.398106e-02
## 35   9.560617e-02  1.043293e-01
## 36  -2.119550e-02 -1.639318e-02
## 37  -7.331516e-02 -7.315760e-02
## 38   3.165269e-02  3.610801e-02
## 39   6.680346e-02  7.804174e-02
## 40   2.106916e-01  2.124700e-01
## 41  -2.044075e-01 -2.035567e-01
## 42  -7.150611e-03 -2.995334e-03
## 43  -1.704125e-01 -1.701234e-01
## 44  -2.110687e-01 -2.112383e-01
## 45  -2.437245e-02  1.341985e-02
## 46   2.103359e-01  2.122277e-01
## 47   2.947577e-02  4.120303e-02
## 48  -2.088689e-01 -2.093201e-01
## 49  -1.252102e-01 -1.040704e-01
## 50  -1.545631e-01 -1.362445e-01
## 51  -2.066628e-01 -2.071462e-01
## 52   2.800293e-02  3.117940e-02
## 53   1.817217e-01  1.868306e-01
## 54  -5.600119e-02 -5.434367e-02
## 55   1.213650e-01  1.302471e-01
## 56   2.083867e-01  2.111246e-01
## 57   3.651684e-02  3.969632e-02
## 58   1.042262e-01  1.167564e-01
## 59  -1.850797e-01 -1.787841e-01
## 60   1.811318e-01  1.876500e-01
## 61  -8.775439e-02 -7.022242e-02
## 62   2.360581e-03  2.709862e-03
## 63   7.827916e-02  8.389189e-02
## 64  -2.482948e-02 -2.011813e-02
## 65   2.155999e-01  2.157690e-01
## 66  -9.532473e-02 -9.369402e-02
## 67  -8.668950e-02 -8.180145e-02
## 68   1.079165e-01  1.215697e-01
## 69   1.625702e-01  1.735218e-01
## 70   9.574452e-02  1.100079e-01
## 71   1.313751e-02  1.638838e-02
## 72   1.999106e-01  2.029597e-01
## 73  -2.005943e-01 -2.011580e-01
## 74  -2.128098e-01 -2.127428e-01
## 75   1.966353e-02  6.425598e-02
## 76   4.043171e-02  4.553799e-02
## 77   5.226728e-02  6.048331e-02
## 78  -5.988483e-02 -5.185747e-02
## 79  -3.961444e-02 -3.179883e-03
## 80  -1.844689e-01 -1.857247e-01
## 81  -1.612636e-01 -1.607665e-01
## 82   1.229055e-01  1.367655e-01
## 83   1.829816e-01  1.894223e-01
## 84   2.131595e-01  2.141312e-01
## 85  -2.022720e-01 -2.025491e-01
## 86   7.576150e-02  8.863520e-02
## 87   1.395972e-01  1.568191e-01
## 88   2.147313e-01  2.152105e-01
## 89   1.085183e-01  1.152898e-01
## 90   1.755891e-02  3.066622e-02
## 91   2.128506e-01  2.138780e-01
## 92   2.139639e-01  2.146135e-01
## 93   1.784309e-01  1.877860e-01
## 94  -2.053546e-01 -2.050887e-01
## 95  -1.836991e-01 -1.787007e-01
## 96   2.078481e-01  2.101650e-01
## 97   1.776932e-01  1.839226e-01
## 98   1.686202e-01  1.746507e-01
## 99  -1.815656e-01 -1.815625e-01
## 100  6.676197e-02  9.170167e-02
## 101 -7.508023e-02 -7.111658e-02
## 102  4.459572e-02  5.344515e-02
## 103 -2.157128e-01 -2.157587e-01
## 104  2.149882e-01  2.154274e-01
## 105 -1.999569e-01 -1.991238e-01
## 106 -3.307938e-02 -3.141418e-02
## 107 -7.215837e-02 -6.463382e-02
## 108 -1.975430e-01 -1.982041e-01
## 109  6.234460e-02  8.199501e-02
## 110  1.344597e-01  1.448517e-01
## 111 -2.103567e-01 -2.102963e-01
## 112  2.016145e-02  4.048309e-02
## 113 -2.136342e-01 -2.136430e-01
## 114  1.078347e-01  1.396340e-01
## 115  1.276663e-01  1.363872e-01
## 116  2.120729e-01  2.131528e-01
## 117  1.592847e-01  1.671534e-01
## 118 -1.867798e-04  6.732463e-04
## 119 -3.583076e-02 -3.539085e-02
## 120  1.550745e-01  1.625898e-01
## 121  1.980904e-01  2.031546e-01
## 122 -5.028463e-02 -4.375748e-02
## 123  1.551708e-01  1.709603e-01
## 124  2.133190e-01  2.141825e-01
## 125  2.512032e-03  2.829127e-03
## 126  7.612545e-03  8.877262e-03
## 127 -7.781280e-02 -7.190929e-02
## 128 -9.268488e-02 -7.659865e-02
## 129  3.506486e-02  4.804852e-02
## 130  8.196459e-02  9.518179e-02
## 131  1.906760e-02  2.155438e-02
## 132  8.181978e-02  9.057391e-02
## 133  1.982522e-01  2.037136e-01
## 134 -1.445040e-01 -1.310570e-01
## 135  3.389953e-02  5.669736e-02
## 136  1.269706e-02  2.113961e-02
## 137  1.123019e-01  1.259577e-01
## 138 -1.003655e-01 -9.740352e-02
## 139  1.359344e-01  1.519713e-01
## 140  2.019118e-01  2.056993e-01
## 141  1.693471e-01  1.762546e-01
## 142 -9.692835e-03 -4.225555e-03
## 143 -2.078787e-01 -2.077407e-01
## 144  2.158897e-01  2.159640e-01
## 145  1.865014e-01  1.938718e-01
## 146 -2.150412e-01 -2.150798e-01
## 147 -7.780032e-02 -7.300813e-02
## 148 -8.949558e-02 -7.471968e-02
## 149  2.084622e-01  2.107346e-01
## 150  7.040746e-02  8.221743e-02
## 151 -6.931920e-02 -6.507926e-02
## 152  1.548562e-02  3.922351e-02
## 153 -2.011522e-01 -2.014953e-01
## 154 -2.125750e-01 -2.126809e-01
## 155  2.540660e-03  2.883625e-03
## 156 -1.902379e-01 -1.900663e-01
## 157 -5.325424e-02 -1.933118e-02
## 158 -2.100121e-01 -2.104210e-01
## 159 -1.857465e-01 -1.801565e-01
## 160 -1.718556e-01 -1.730147e-01
## 161 -2.023368e-01 -2.022645e-01
## 162  6.849603e-02  1.071519e-01
## 163  1.890614e-01  1.948324e-01
## 164 -1.686658e-01 -1.703637e-01
## 165  6.287725e-03  2.876523e-02
## 166  1.729657e-01  1.838091e-01
## 167 -4.453383e-03  2.764886e-02
## 168 -2.098887e-01 -2.100975e-01
## 169  4.040500e-02  4.484118e-02
## 170 -1.264451e-01 -1.146687e-01
## 171  6.928322e-02  7.449418e-02
## 172 -2.826664e-02 -2.281019e-02
## 173 -8.674482e-02 -6.941650e-02
## 174 -1.829832e-01 -1.769921e-01
## 175 -1.402522e-01 -1.357318e-01
## 176 -1.842697e-01 -1.826705e-01
## 177  1.636923e-01  1.724487e-01
## 178 -2.146195e-01 -2.146653e-01
## 179 -9.125533e-03  5.329327e-03
## 180  7.103619e-02  7.670110e-02
## 181 -1.815048e-01 -1.812400e-01
## 182 -1.321257e-01 -1.287948e-01
## 183 -1.906625e-01 -1.901891e-01
## 184 -2.028761e-01 -2.030891e-01
## 185 -1.159602e-01 -1.144608e-01
## 186  1.279793e-01  1.370038e-01
## 187  1.124223e-02  1.337146e-02
## 188  5.282130e-03  5.681506e-03
## 189  1.039881e-01  1.109260e-01
## 190 -2.059561e-01 -2.060693e-01
## 191 -2.635608e-02 -1.950693e-02
## 192 -1.627418e-01 -1.529414e-01
## 193 -2.712101e-02 -2.227712e-02
## 194  1.448613e-01  1.557500e-01
## 195 -1.790344e-01 -1.754657e-01
## 196 -2.691493e-06  7.862666e-07
## 197  3.426368e-02  4.401497e-02
## 198  1.269714e-01  1.462098e-01
## 199 -1.651199e-01 -1.668721e-01
## 200  2.035978e-01  2.061330e-01
## 
## $values
## $values$divergencekl
## [1] -184.3254
## 
## $values$iterations
## [1] 94
## 
## $values$message
## [1] "relative convergence (4)"
## 
## $values$q
##        [,1] [,2]
##   [1,]  0.5  0.5
##   [2,]  0.5  0.5
##   [3,]  0.5  0.5
##   [4,]  0.5  0.5
##   [5,]  0.5  0.5
##   [6,]  0.5  0.5
##   [7,]  0.5  0.5
##   [8,]  0.5  0.5
##   [9,]  0.5  0.5
##  [10,]  0.5  0.5
##  [11,]  0.5  0.5
##  [12,]  0.5  0.5
##  [13,]  0.5  0.5
##  [14,]  0.5  0.5
##  [15,]  0.5  0.5
##  [16,]  0.5  0.5
##  [17,]  0.5  0.5
##  [18,]  0.5  0.5
##  [19,]  0.5  0.5
##  [20,]  0.5  0.5
##  [21,]  0.5  0.5
##  [22,]  0.5  0.5
##  [23,]  0.5  0.5
##  [24,]  0.5  0.5
##  [25,]  0.5  0.5
##  [26,]  0.5  0.5
##  [27,]  0.5  0.5
##  [28,]  0.5  0.5
##  [29,]  0.5  0.5
##  [30,]  0.5  0.5
##  [31,]  0.5  0.5
##  [32,]  0.5  0.5
##  [33,]  0.5  0.5
##  [34,]  0.5  0.5
##  [35,]  0.5  0.5
##  [36,]  0.5  0.5
##  [37,]  0.5  0.5
##  [38,]  0.5  0.5
##  [39,]  0.5  0.5
##  [40,]  0.5  0.5
##  [41,]  0.5  0.5
##  [42,]  0.5  0.5
##  [43,]  0.5  0.5
##  [44,]  0.5  0.5
##  [45,]  0.5  0.5
##  [46,]  0.5  0.5
##  [47,]  0.5  0.5
##  [48,]  0.5  0.5
##  [49,]  0.5  0.5
##  [50,]  0.5  0.5
##  [51,]  0.5  0.5
##  [52,]  0.5  0.5
##  [53,]  0.5  0.5
##  [54,]  0.5  0.5
##  [55,]  0.5  0.5
##  [56,]  0.5  0.5
##  [57,]  0.5  0.5
##  [58,]  0.5  0.5
##  [59,]  0.5  0.5
##  [60,]  0.5  0.5
##  [61,]  0.5  0.5
##  [62,]  0.5  0.5
##  [63,]  0.5  0.5
##  [64,]  0.5  0.5
##  [65,]  0.5  0.5
##  [66,]  0.5  0.5
##  [67,]  0.5  0.5
##  [68,]  0.5  0.5
##  [69,]  0.5  0.5
##  [70,]  0.5  0.5
##  [71,]  0.5  0.5
##  [72,]  0.5  0.5
##  [73,]  0.5  0.5
##  [74,]  0.5  0.5
##  [75,]  0.5  0.5
##  [76,]  0.5  0.5
##  [77,]  0.5  0.5
##  [78,]  0.5  0.5
##  [79,]  0.5  0.5
##  [80,]  0.5  0.5
##  [81,]  0.5  0.5
##  [82,]  0.5  0.5
##  [83,]  0.5  0.5
##  [84,]  0.5  0.5
##  [85,]  0.5  0.5
##  [86,]  0.5  0.5
##  [87,]  0.5  0.5
##  [88,]  0.5  0.5
##  [89,]  0.5  0.5
##  [90,]  0.5  0.5
##  [91,]  0.5  0.5
##  [92,]  0.5  0.5
##  [93,]  0.5  0.5
##  [94,]  0.5  0.5
##  [95,]  0.5  0.5
##  [96,]  0.5  0.5
##  [97,]  0.5  0.5
##  [98,]  0.5  0.5
##  [99,]  0.5  0.5
## [100,]  0.5  0.5
## [101,]  0.5  0.5
## [102,]  0.5  0.5
## [103,]  0.5  0.5
## [104,]  0.5  0.5
## [105,]  0.5  0.5
## [106,]  0.5  0.5
## [107,]  0.5  0.5
## [108,]  0.5  0.5
## [109,]  0.5  0.5
## [110,]  0.5  0.5
## [111,]  0.5  0.5
## [112,]  0.5  0.5
## [113,]  0.5  0.5
## [114,]  0.5  0.5
## [115,]  0.5  0.5
## [116,]  0.5  0.5
## [117,]  0.5  0.5
## [118,]  0.5  0.5
## [119,]  0.5  0.5
## [120,]  0.5  0.5
## [121,]  0.5  0.5
## [122,]  0.5  0.5
## [123,]  0.5  0.5
## [124,]  0.5  0.5
## [125,]  0.5  0.5
## [126,]  0.5  0.5
## [127,]  0.5  0.5
## [128,]  0.5  0.5
## [129,]  0.5  0.5
## [130,]  0.5  0.5
## [131,]  0.5  0.5
## [132,]  0.5  0.5
## [133,]  0.5  0.5
## [134,]  0.5  0.5
## [135,]  0.5  0.5
## [136,]  0.5  0.5
## [137,]  0.5  0.5
## [138,]  0.5  0.5
## [139,]  0.5  0.5
## [140,]  0.5  0.5
## [141,]  0.5  0.5
## [142,]  0.5  0.5
## [143,]  0.5  0.5
## [144,]  0.5  0.5
## [145,]  0.5  0.5
## [146,]  0.5  0.5
## [147,]  0.5  0.5
## [148,]  0.5  0.5
## [149,]  0.5  0.5
## [150,]  0.5  0.5
## [151,]  0.5  0.5
## [152,]  0.5  0.5
## [153,]  0.5  0.5
## [154,]  0.5  0.5
## [155,]  0.5  0.5
## [156,]  0.5  0.5
## [157,]  0.5  0.5
## [158,]  0.5  0.5
## [159,]  0.5  0.5
## [160,]  0.5  0.5
## [161,]  0.5  0.5
## [162,]  0.5  0.5
## [163,]  0.5  0.5
## [164,]  0.5  0.5
## [165,]  0.5  0.5
## [166,]  0.5  0.5
## [167,]  0.5  0.5
## [168,]  0.5  0.5
## [169,]  0.5  0.5
## [170,]  0.5  0.5
## [171,]  0.5  0.5
## [172,]  0.5  0.5
## [173,]  0.5  0.5
## [174,]  0.5  0.5
## [175,]  0.5  0.5
## [176,]  0.5  0.5
## [177,]  0.5  0.5
## [178,]  0.5  0.5
## [179,]  0.5  0.5
## [180,]  0.5  0.5
## [181,]  0.5  0.5
## [182,]  0.5  0.5
## [183,]  0.5  0.5
## [184,]  0.5  0.5
## [185,]  0.5  0.5
## [186,]  0.5  0.5
## [187,]  0.5  0.5
## [188,]  0.5  0.5
## [189,]  0.5  0.5
## [190,]  0.5  0.5
## [191,]  0.5  0.5
## [192,]  0.5  0.5
## [193,]  0.5  0.5
## [194,]  0.5  0.5
## [195,]  0.5  0.5
## [196,]  0.5  0.5
## [197,]  0.5  0.5
## [198,]  0.5  0.5
## [199,]  0.5  0.5
## [200,]  0.5  0.5
## 
## 
## $tol
## [1] 1e-10
## 
## $v
##           [,1] [,2]       [,3]
## [1,] 0.2160606    0 -0.2160606
## 
## $lambda
##   (Intercept) Dcollege  Totalincome    Dunemp
## 1    1925.469  2117.91 -0.008238330 -485.6138
## 0    2092.312  2267.59 -0.008558383 -539.4989
## 
## $checkrestrictions
## $checkrestrictions$g1
##        [,1]
##   [1,]    0
##   [2,]    0
##   [3,]    0
##   [4,]    0
##   [5,]    0
##   [6,]    0
##   [7,]    0
##   [8,]    0
##   [9,]    0
##  [10,]    0
##  [11,]    0
##  [12,]    0
##  [13,]    0
##  [14,]    0
##  [15,]    0
##  [16,]    0
##  [17,]    0
##  [18,]    0
##  [19,]    0
##  [20,]    0
##  [21,]    0
##  [22,]    0
##  [23,]    0
##  [24,]    0
##  [25,]    0
##  [26,]    0
##  [27,]    0
##  [28,]    0
##  [29,]    0
##  [30,]    0
##  [31,]    0
##  [32,]    0
##  [33,]    0
##  [34,]    0
##  [35,]    0
##  [36,]    0
##  [37,]    0
##  [38,]    0
##  [39,]    0
##  [40,]    0
##  [41,]    0
##  [42,]    0
##  [43,]    0
##  [44,]    0
##  [45,]    0
##  [46,]    0
##  [47,]    0
##  [48,]    0
##  [49,]    0
##  [50,]    0
##  [51,]    0
##  [52,]    0
##  [53,]    0
##  [54,]    0
##  [55,]    0
##  [56,]    0
##  [57,]    0
##  [58,]    0
##  [59,]    0
##  [60,]    0
##  [61,]    0
##  [62,]    0
##  [63,]    0
##  [64,]    0
##  [65,]    0
##  [66,]    0
##  [67,]    0
##  [68,]    0
##  [69,]    0
##  [70,]    0
##  [71,]    0
##  [72,]    0
##  [73,]    0
##  [74,]    0
##  [75,]    0
##  [76,]    0
##  [77,]    0
##  [78,]    0
##  [79,]    0
##  [80,]    0
##  [81,]    0
##  [82,]    0
##  [83,]    0
##  [84,]    0
##  [85,]    0
##  [86,]    0
##  [87,]    0
##  [88,]    0
##  [89,]    0
##  [90,]    0
##  [91,]    0
##  [92,]    0
##  [93,]    0
##  [94,]    0
##  [95,]    0
##  [96,]    0
##  [97,]    0
##  [98,]    0
##  [99,]    0
## [100,]    0
## [101,]    0
## [102,]    0
## [103,]    0
## [104,]    0
## [105,]    0
## [106,]    0
## [107,]    0
## [108,]    0
## [109,]    0
## [110,]    0
## [111,]    0
## [112,]    0
## [113,]    0
## [114,]    0
## [115,]    0
## [116,]    0
## [117,]    0
## [118,]    0
## [119,]    0
## [120,]    0
## [121,]    0
## [122,]    0
## [123,]    0
## [124,]    0
## [125,]    0
## [126,]    0
## [127,]    0
## [128,]    0
## [129,]    0
## [130,]    0
## [131,]    0
## [132,]    0
## [133,]    0
## [134,]    0
## [135,]    0
## [136,]    0
## [137,]    0
## [138,]    0
## [139,]    0
## [140,]    0
## [141,]    0
## [142,]    0
## [143,]    0
## [144,]    0
## [145,]    0
## [146,]    0
## [147,]    0
## [148,]    0
## [149,]    0
## [150,]    0
## [151,]    0
## [152,]    0
## [153,]    0
## [154,]    0
## [155,]    0
## [156,]    0
## [157,]    0
## [158,]    0
## [159,]    0
## [160,]    0
## [161,]    0
## [162,]    0
## [163,]    0
## [164,]    0
## [165,]    0
## [166,]    0
## [167,]    0
## [168,]    0
## [169,]    0
## [170,]    0
## [171,]    0
## [172,]    0
## [173,]    0
## [174,]    0
## [175,]    0
## [176,]    0
## [177,]    0
## [178,]    0
## [179,]    0
## [180,]    0
## [181,]    0
## [182,]    0
## [183,]    0
## [184,]    0
## [185,]    0
## [186,]    0
## [187,]    0
## [188,]    0
## [189,]    0
## [190,]    0
## [191,]    0
## [192,]    0
## [193,]    0
## [194,]    0
## [195,]    0
## [196,]    0
## [197,]    0
## [198,]    0
## [199,]    0
## [200,]    0
## 
## $checkrestrictions$g2
##        [,1] [,2]
##   [1,]    0    0
##   [2,]    0    0
##   [3,]    0    0
##   [4,]    0    0
##   [5,]    0    0
##   [6,]    0    0
##   [7,]    0    0
##   [8,]    0    0
##   [9,]    0    0
##  [10,]    0    0
##  [11,]    0    0
##  [12,]    0    0
##  [13,]    0    0
##  [14,]    0    0
##  [15,]    0    0
##  [16,]    0    0
##  [17,]    0    0
##  [18,]    0    0
##  [19,]    0    0
##  [20,]    0    0
##  [21,]    0    0
##  [22,]    0    0
##  [23,]    0    0
##  [24,]    0    0
##  [25,]    0    0
##  [26,]    0    0
##  [27,]    0    0
##  [28,]    0    0
##  [29,]    0    0
##  [30,]    0    0
##  [31,]    0    0
##  [32,]    0    0
##  [33,]    0    0
##  [34,]    0    0
##  [35,]    0    0
##  [36,]    0    0
##  [37,]    0    0
##  [38,]    0    0
##  [39,]    0    0
##  [40,]    0    0
##  [41,]    0    0
##  [42,]    0    0
##  [43,]    0    0
##  [44,]    0    0
##  [45,]    0    0
##  [46,]    0    0
##  [47,]    0    0
##  [48,]    0    0
##  [49,]    0    0
##  [50,]    0    0
##  [51,]    0    0
##  [52,]    0    0
##  [53,]    0    0
##  [54,]    0    0
##  [55,]    0    0
##  [56,]    0    0
##  [57,]    0    0
##  [58,]    0    0
##  [59,]    0    0
##  [60,]    0    0
##  [61,]    0    0
##  [62,]    0    0
##  [63,]    0    0
##  [64,]    0    0
##  [65,]    0    0
##  [66,]    0    0
##  [67,]    0    0
##  [68,]    0    0
##  [69,]    0    0
##  [70,]    0    0
##  [71,]    0    0
##  [72,]    0    0
##  [73,]    0    0
##  [74,]    0    0
##  [75,]    0    0
##  [76,]    0    0
##  [77,]    0    0
##  [78,]    0    0
##  [79,]    0    0
##  [80,]    0    0
##  [81,]    0    0
##  [82,]    0    0
##  [83,]    0    0
##  [84,]    0    0
##  [85,]    0    0
##  [86,]    0    0
##  [87,]    0    0
##  [88,]    0    0
##  [89,]    0    0
##  [90,]    0    0
##  [91,]    0    0
##  [92,]    0    0
##  [93,]    0    0
##  [94,]    0    0
##  [95,]    0    0
##  [96,]    0    0
##  [97,]    0    0
##  [98,]    0    0
##  [99,]    0    0
## [100,]    0    0
## [101,]    0    0
## [102,]    0    0
## [103,]    0    0
## [104,]    0    0
## [105,]    0    0
## [106,]    0    0
## [107,]    0    0
## [108,]    0    0
## [109,]    0    0
## [110,]    0    0
## [111,]    0    0
## [112,]    0    0
## [113,]    0    0
## [114,]    0    0
## [115,]    0    0
## [116,]    0    0
## [117,]    0    0
## [118,]    0    0
## [119,]    0    0
## [120,]    0    0
## [121,]    0    0
## [122,]    0    0
## [123,]    0    0
## [124,]    0    0
## [125,]    0    0
## [126,]    0    0
## [127,]    0    0
## [128,]    0    0
## [129,]    0    0
## [130,]    0    0
## [131,]    0    0
## [132,]    0    0
## [133,]    0    0
## [134,]    0    0
## [135,]    0    0
## [136,]    0    0
## [137,]    0    0
## [138,]    0    0
## [139,]    0    0
## [140,]    0    0
## [141,]    0    0
## [142,]    0    0
## [143,]    0    0
## [144,]    0    0
## [145,]    0    0
## [146,]    0    0
## [147,]    0    0
## [148,]    0    0
## [149,]    0    0
## [150,]    0    0
## [151,]    0    0
## [152,]    0    0
## [153,]    0    0
## [154,]    0    0
## [155,]    0    0
## [156,]    0    0
## [157,]    0    0
## [158,]    0    0
## [159,]    0    0
## [160,]    0    0
## [161,]    0    0
## [162,]    0    0
## [163,]    0    0
## [164,]    0    0
## [165,]    0    0
## [166,]    0    0
## [167,]    0    0
## [168,]    0    0
## [169,]    0    0
## [170,]    0    0
## [171,]    0    0
## [172,]    0    0
## [173,]    0    0
## [174,]    0    0
## [175,]    0    0
## [176,]    0    0
## [177,]    0    0
## [178,]    0    0
## [179,]    0    0
## [180,]    0    0
## [181,]    0    0
## [182,]    0    0
## [183,]    0    0
## [184,]    0    0
## [185,]    0    0
## [186,]    0    0
## [187,]    0    0
## [188,]    0    0
## [189,]    0    0
## [190,]    0    0
## [191,]    0    0
## [192,]    0    0
## [193,]    0    0
## [194,]    0    0
## [195,]    0    0
## [196,]    0    0
## [197,]    0    0
## [198,]    0    0
## [199,]    0    0
## [200,]    0    0
## 
## $checkrestrictions$g3
##             y_factor1 y_factor0
## (Intercept)     0.000     0.000
## Dcollege        0.000     0.000
## Totalincome    -0.155     0.029
## Dunemp          0.000     0.000
## 
## 
## $cross_moments_A
##             1          0         
## (Intercept)       0.34       0.66
## Dcollege          0.17       0.44
## Totalincome  103036.63  189594.78
## Dunemp            0.16       0.29
## 
## $cross_moments_B
##             1          0         
## (Intercept)       0.34       0.66
## Dcollege          0.17       0.44
## Totalincome  103036.79  189594.75
## Dunemp            0.16       0.29
## 
## $J
## [1] 2
## 
## $fn
## dataA$poor_liq ~ Dcollege + Totalincome + Dunemp
## 
## attr(,"class")
## [1] "kl"

The summary and the plot options are the same as in the previous case.

3.2.1 Another option when we do not have prior information: ei_gme()

In the case the user does not have prior information the function ei_gme() is also available. This function is provided for cases where the user may prefer using GME (Generalized maximum entropy). Specifically, if the user has a big volume of data because it is a more efficient function in computational terms than ei_gce() with the uniform distribution as prior. Both functions should provide the same result.

ei_gme() applies the Shannon entropy function to the optimization. It is adequate when you cannot assume anything about the distribution of \(Y\). So the starting point is the uniform distribution.

Using the same example, our variable of interest is the poverty rate in terms of wealth and our independent variables are the income and dummies for unemployment and college studies. In this case, we need to define the function

result3 <- ei_gme (fn,dataA,dataB,weights="w")

The function will produce the same output as ei_gce(), see the previous section for further details.

result3
## $estimations
##          weights predictions_1 predictions_0 probabilities_1 probabilities_0
## 1   6.408614e-03    0.37714100     1.0373456      0.17143056       0.8285694
## 2   4.069074e-03    0.46516844     0.9465387      0.26050116       0.7394988
## 3   8.478890e-05    0.49554426     0.4949818      0.50026475       0.4997352
## 4   6.019554e-03    0.29425398     0.7815639      0.27116751       0.7288325
## 5   8.529959e-03    0.24791986     0.3351769      0.45651891       0.5434811
## 6   3.466777e-03    0.37076550     0.4876877      0.44458668       0.5554133
## 7   7.143169e-03    0.25980016     0.5065030      0.38172997       0.6182700
## 8   6.728993e-03    0.36038509     1.0624027      0.14987197       0.8501280
## 9   9.459067e-03    0.24653071     0.9526971      0.16596528       0.8340347
## 10  1.952733e-03    0.42547701     0.5404902      0.44585302       0.5541470
## 11  6.884772e-03    0.36676112     1.0476607      0.16115959       0.8388404
## 12  1.046638e-03    0.42656444     0.4268691      0.49985549       0.5001445
## 13  6.632154e-03    0.45686631     0.9334013      0.26416625       0.7358337
## 14  5.694566e-03    0.34661296     0.8392470      0.26618165       0.7338183
## 15  8.199805e-03    0.29044842     0.3979353      0.44769069       0.5523093
## 16  7.974757e-03    0.34208495     0.8762999      0.24538724       0.7546128
## 17  1.016052e-05    0.50008404     0.5008871      0.49962202       0.5003780
## 18  1.077733e-03    0.47310062     0.4945723      0.48988960       0.5101104
## 19  4.555596e-03    0.43194344     0.9691885      0.23344930       0.7665507
## 20  1.797040e-03    0.40140320     0.4763702      0.46452988       0.5354701
## 21  7.726297e-03    0.36613320     0.2079584      0.57897910       0.4210209
## 22  7.537852e-03    0.33716485     1.0938415      0.12177914       0.8782209
## 23  5.078895e-04    0.48835953     0.5396067      0.47587226       0.5241277
## 24  8.673474e-03    0.34928915     1.0777076      0.13630052       0.8636995
## 25  6.743411e-03    0.28645508     0.2974439      0.49452509       0.5054749
## 26  2.597985e-03    0.34630193     0.3301962      0.50785821       0.4921418
## 27  7.946911e-03    0.32381835     0.9735062      0.18622698       0.8137730
## 28  3.132542e-03    0.37158284     0.4640124      0.45608357       0.5439164
## 29  1.413325e-03    0.50486829     0.6852096      0.41406943       0.5859306
## 30  1.952905e-03    0.50803501     0.6558103      0.42980514       0.5701949
## 31  7.786354e-03    0.34741212     1.0685416      0.14103834       0.8589617
## 32  6.412179e-03    0.36399162     0.2144079      0.57461746       0.4253825
## 33  8.813903e-03    0.14764207     0.4589496      0.34574908       0.6542509
## 34  3.104395e-03    0.35538676     0.5085648      0.42745386       0.5725461
## 35  1.494452e-03    0.50471073     0.6952247      0.40910457       0.5908954
## 36  1.979537e-03    0.43997236     0.5224390      0.46116787       0.5388321
## 37  1.781772e-03    0.42523278     0.4282943      0.49854802       0.5014520
## 38  8.631740e-04    0.49491100     0.5728496      0.46325836       0.5367416
## 39  2.624354e-03    0.46497177     0.6798731      0.39816848       0.6018315
## 40  7.278409e-03    0.34905395     1.0741076      0.13836237       0.8616376
## 41  9.198636e-03    0.21786352     0.3741723      0.42227101       0.5777290
## 42  8.939710e-04    0.45949750     0.5303564      0.46664817       0.5333518
## 43  5.755561e-03    0.32270764     0.3367562      0.49312027       0.5068797
## 44  9.197598e-03    0.32806646     0.2496265      0.53913519       0.4608648
## 45  7.835590e-03    0.20378477     0.7852617      0.22815772       0.7718423
## 46  7.304276e-03    0.34955410     1.0730095      0.13921821       0.8607818
## 47  2.825585e-03    0.43352574     0.6371526      0.40405019       0.5959498
## 48  5.701607e-03    0.36363393     0.2181771      0.57250285       0.4274972
## 49  9.403839e-03    0.14601780     0.6247003      0.27122861       0.7287714
## 50  8.874280e-03    0.08319548     0.6259962      0.23775894       0.7622411
## 51  5.856153e-03    0.35220670     0.2339843      0.55886949       0.4411305
## 52  7.506319e-04    0.50195976     0.5572226      0.47395680       0.5260432
## 53  2.829871e-03    0.51333914     0.8552131      0.33161750       0.6683825
## 54  1.403796e-03    0.42963824     0.4600169      0.48563946       0.5143605
## 55  2.256222e-03    0.50956487     0.7420472      0.38819990       0.6118001
## 56  8.706739e-03    0.32821696     1.0912943      0.11983024       0.8801698
## 57  6.495227e-04    0.51007559     0.5661376      0.47355873       0.5264413
## 58  7.423215e-03    0.46620740     0.7547751      0.36198130       0.6380187
## 59  9.409367e-03    0.12397287     0.5121628      0.30905282       0.6909472
## 60  3.467645e-03    0.47043100     0.8983508      0.28929920       0.7107008
## 61  4.891585e-03    0.25235968     0.5896629      0.34011437       0.6598856
## 62  5.191919e-05    0.49955438     0.5055161      0.49719380       0.5028062
## 63  6.960881e-04    0.52499283     0.6371783      0.44671365       0.5532863
## 64  3.234067e-03    0.43693087     0.5181214      0.46176043       0.5382396
## 65  8.095405e-03    0.32338775     1.1079812      0.10778784       0.8922122
## 66  2.123864e-03    0.38804696     0.4229342      0.48337175       0.5166283
## 67  3.309518e-03    0.36617643     0.4653326      0.45286598       0.5471340
## 68  5.300329e-03    0.45369992     0.7757864      0.34578335       0.6542166
## 69  7.890242e-03    0.43151755     0.9045747      0.26894725       0.7310527
## 70  5.248723e-03    0.44718704     0.7585655      0.35144245       0.6485576
## 71  9.625057e-04    0.48690874     0.5426172      0.47377121       0.5262288
## 72  3.609097e-03    0.48364084     0.9192295      0.28373023       0.7162698
## 73  5.617329e-03    0.34033991     0.2579077      0.54093430       0.4590657
## 74  9.237887e-03    0.26393288     0.3105145      0.47674268       0.5232573
## 75  9.275353e-03    0.20156798     0.8823505      0.18190501       0.8180950
## 76  7.561670e-04    0.49760854     0.5883611      0.45717684       0.5428232
## 77  1.374263e-03    0.48128804     0.6314625      0.42902081       0.5709792
## 78  2.232129e-03    0.37084525     0.5174121      0.43073025       0.5692698
## 79  7.759625e-03    0.19416064     0.7630441      0.23377557       0.7662244
## 80  3.268253e-03    0.35954585     0.2702604      0.54401482       0.4559852
## 81  5.423895e-03    0.32883003     0.3491396      0.49009377       0.5099062
## 82  3.519797e-03    0.44627539     0.8133955      0.32336997       0.6766300
## 83  3.686690e-03    0.46329502     0.9091089      0.28031343       0.7196866
## 84  8.770650e-03    0.34686180     1.0804289      0.13370232       0.8662977
## 85  4.499834e-03    0.32020803     0.2749708      0.52248010       0.4775199
## 86  6.913635e-03    0.45482424     0.7095723      0.37906282       0.6209372
## 87  7.423989e-03    0.38267169     0.9137441      0.24307479       0.7569252
## 88  9.184997e-03    0.32784987     1.1020920      0.11311855       0.8868814
## 89  9.934938e-04    0.53182177     0.6919863      0.42330347       0.5766965
## 90  7.108557e-03    0.41232879     0.6358961      0.39477003       0.6052300
## 91  6.307975e-03    0.35899737     1.0677312      0.14614680       0.8538532
## 92  5.444530e-03    0.36801075     1.0605667      0.15404688       0.8459531
## 93  5.708904e-03    0.40224834     0.9639685      0.22381750       0.7761825
## 94  7.141561e-03    0.26731143     0.3222452      0.47266606       0.5273339
## 95  7.903713e-03    0.16504002     0.4725597      0.34873935       0.6512606
## 96  5.645807e-03    0.39114706     1.0268661      0.18329898       0.8167010
## 97  3.539554e-03    0.49407722     0.8675384      0.31638410       0.6836159
## 98  2.396317e-03    0.52472964     0.8185411      0.35610951       0.6438905
## 99  3.785424e-03    0.31833590     0.3185359      0.49990155       0.5000984
## 100 6.899727e-03    0.34665472     0.8118079      0.27989326       0.7201067
## 101 1.963958e-03    0.38847647     0.4653263      0.46355690       0.5364431
## 102 4.301069e-03    0.46970545     0.6283353      0.42510979       0.5748902
## 103 8.824290e-03    0.44210574     0.1264228      0.65781855       0.3421815
## 104 9.245072e-03    0.29598198     1.1344336      0.08099374       0.9190063
## 105 7.604964e-03    0.24465042     0.3562688      0.44460738       0.5553926
## 106 7.759268e-04    0.45320401     0.4823022      0.48628348       0.5137165
## 107 6.426895e-03    0.36017732     0.5030302      0.43233587       0.5676641
## 108 5.150249e-03    0.34234836     0.2619044      0.53989146       0.4601085
## 109 5.158771e-03    0.38924124     0.7550976      0.32689702       0.6731030
## 110 7.247160e-03    0.48560850     0.7937028      0.35114885       0.6488512
## 111 7.664692e-03    0.27774016     0.3016068      0.48809683       0.5119032
## 112 4.033598e-03    0.35902292     0.7016212      0.33886170       0.6611383
## 113 8.610544e-03    0.29051769     0.2822052      0.50415187       0.4958481
## 114 9.173485e-03    0.27410778     0.9733603      0.16627345       0.8337265
## 115 2.312141e-03    0.51128193     0.7527714      0.38361570       0.6163843
## 116 5.785912e-03    0.40348506     1.0217406      0.19141214       0.8085879
## 117 3.133029e-03    0.50150728     0.8249307      0.34222266       0.6577773
## 118 3.027803e-04    0.49290497     0.5075815      0.49309175       0.5069082
## 119 6.494774e-04    0.46052418     0.4682542      0.49635496       0.5036450
## 120 2.627321e-03    0.51441106     0.8032531      0.35933661       0.6406634
## 121 6.300118e-03    0.38606905     1.0151758      0.18797870       0.8120213
## 122 5.009005e-03    0.39455986     0.5113978      0.44484464       0.5551554
## 123 8.546357e-03    0.36682709     0.9593036      0.21165655       0.7883435
## 124 5.935042e-03    0.36343477     1.0640667      0.15011579       0.8498842
## 125 5.670056e-05    0.49996437     0.5053768      0.49745235       0.5025477
## 126 1.956694e-04    0.49743770     0.5190521      0.48982516       0.5101748
## 127 3.491569e-03    0.36763703     0.4826408      0.44544988       0.5545501
## 128 6.018842e-03    0.25616395     0.5745515      0.34884931       0.6511507
## 129 2.453778e-03    0.42789177     0.6552214      0.39282704       0.6071730
## 130 3.330195e-03    0.45417300     0.7229730      0.37220860       0.6277914
## 131 4.568058e-04    0.49890140     0.5417205      0.47983383       0.5201662
## 132 1.878873e-03    0.49715239     0.6752411      0.41533270       0.5846673
## 133 7.274750e-03    0.36343765     1.0385281      0.16518550       0.8348145
## 134 8.055270e-03    0.17014297     0.5542951      0.31464738       0.6853526
## 135 7.918719e-03    0.35004282     0.7405543      0.31614325       0.6838568
## 136 1.613960e-03    0.44481819     0.5890183      0.43212122       0.5678788
## 137 4.043005e-03    0.45292968     0.7853295      0.34062799       0.6593720
## 138 2.836492e-03    0.36867880     0.4335521      0.46904439       0.5309556
## 139 8.648536e-03    0.40487846     0.8830274      0.26894402       0.7310560
## 140 7.121030e-03    0.40200478     1.0056062      0.20009305       0.7999069
## 141 7.015624e-03    0.50187202     0.8437297      0.33252488       0.6674751
## 142 2.042604e-03    0.44644705     0.5396346      0.45613989       0.5438601
## 143 7.276373e-03    0.27335900     0.3110216      0.48123769       0.5187623
## 144 8.504937e-03    0.28247500     1.1493787      0.06658533       0.9334147
## 145 9.535921e-03    0.40888960     0.9714838      0.22238811       0.7776119
## 146 8.545091e-03    0.32920752     0.2406715      0.54424876       0.4557512
## 147 2.254398e-03    0.37776169     0.4714294      0.45556223       0.5444378
## 148 5.514651e-03    0.27258786     0.5631959      0.36208390       0.6379161
## 149 6.254560e-03    0.37577569     1.0434211      0.16731353       0.8326865
## 150 6.128050e-03    0.46189330     0.6907315      0.39148591       0.6085141
## 151 1.952048e-03    0.39256306     0.4730381      0.46188246       0.5381175
## 152 8.239200e-03    0.33030051     0.7244088      0.31481486       0.6851851
## 153 4.212187e-03    0.32458121     0.2727712      0.52573342       0.4742666
## 154 6.562633e-03    0.32255966     0.2521844      0.53513468       0.4648653
## 155 8.529452e-05    0.49978514     0.5056392      0.49724448       0.5027555
## 156 4.627415e-03    0.30253554     0.3171601      0.49277353       0.5072265
## 157 7.506022e-03    0.19114391     0.7362697      0.24439862       0.7556014
## 158 5.802968e-03    0.36849394     0.2110729      0.57850610       0.4214939
## 159 8.889093e-03    0.13810223     0.4959942      0.32384897       0.6761510
## 160 3.338891e-03    0.35704116     0.2980883      0.52889685       0.4711032
## 161 5.739428e-03    0.29183838     0.3035602      0.49417525       0.5058248
## 162 9.051019e-03    0.24618906     0.9294580      0.17769349       0.8223065
## 163 7.187216e-03    0.44810200     0.9357919      0.25904055       0.7409594
## 164 2.371262e-03    0.37102321     0.2899472      0.53968910       0.4603109
## 165 5.791201e-03    0.33183326     0.7032186      0.32554605       0.6744539
## 166 5.959915e-03    0.39382630     0.9629484      0.22086063       0.7791394
## 167 8.379680e-03    0.25726560     0.7659283      0.26171973       0.7382803
## 168 8.564844e-03    0.32893623     0.2510775      0.53882493       0.4611751
## 169 1.064177e-03    0.50320852     0.5820377      0.46280348       0.5371965
## 170 6.110630e-03    0.23336248     0.5255228      0.35980801       0.6401920
## 171 1.771706e-03    0.52165759     0.6221198      0.45237437       0.5476256
## 172 3.746941e-03    0.42731642     0.5216066      0.45558316       0.5444168
## 173 8.344937e-03    0.25568751     0.5881512      0.34243236       0.6575676
## 174 8.671874e-03    0.14356052     0.4964636      0.32654393       0.6734561
## 175 5.165876e-03    0.29467706     0.4293389      0.43492929       0.5650707
## 176 6.250491e-03    0.26256080     0.3704989      0.44683054       0.5531695
## 177 5.663535e-03    0.47401068     0.8621305      0.31031827       0.6896817
## 178 8.189466e-03    0.32238236     0.2483328      0.53700190       0.4629981
## 179 5.172787e-03    0.37674492     0.6194590      0.38587044       0.6141296
## 180 2.048906e-03    0.51888448     0.6288528      0.44784828       0.5521517
## 181 6.680525e-03    0.31019439     0.3270606      0.49169932       0.5083007
## 182 4.062967e-03    0.32344469     0.4156347      0.45557047       0.5444295
## 183 8.424910e-03    0.28920324     0.3299450      0.47986579       0.5201342
## 184 7.709358e-03    0.31518467     0.2788501      0.51806082       0.4819392
## 185 2.544983e-03    0.36650172     0.4030771      0.48246199       0.5175380
## 186 5.364966e-03    0.50714385     0.7578392      0.37916456       0.6208354
## 187 5.934410e-04    0.49408188     0.5305318      0.48283964       0.5171604
## 188 5.020772e-05    0.50207164     0.5088920      0.49678951       0.5032105
## 189 2.873655e-03    0.52784553     0.6870686      0.42385741       0.5761426
## 190 5.514606e-03    0.30662414     0.2813504      0.51258028       0.4874197
## 191 2.057597e-03    0.41814271     0.5359939      0.44449899       0.5555010
## 192 8.173496e-03    0.15968134     0.5246346      0.32242353       0.6775765
## 193 2.086392e-03    0.43346741     0.5171345      0.46058843       0.5394116
## 194 3.212343e-03    0.46856248     0.8320487      0.32370124       0.6762988
## 195 7.999160e-03    0.22223277     0.4232671      0.40126720       0.5987328
## 196 9.251449e-07    0.49996937     0.5000287      0.49997206       0.5000279
## 197 2.268155e-03    0.45362669     0.6246516      0.41936319       0.5806368
## 198 7.367501e-03    0.37636973     0.8968109      0.24939865       0.7506013
## 199 2.263759e-03    0.37305012     0.2949577      0.53817009       0.4618299
## 200 3.956566e-03    0.46982359     0.9399072      0.26622585       0.7337742
##          errors_1      errors_0
## 1    2.057104e-01  2.087761e-01
## 2    2.046673e-01  2.070398e-01
## 3   -4.720492e-03 -4.753433e-03
## 4    2.308647e-02  5.273141e-02
## 5   -2.085990e-01 -2.083042e-01
## 6   -7.382118e-02 -6.772559e-02
## 7   -1.219298e-01 -1.117670e-01
## 8    2.105131e-01  2.122746e-01
## 9    8.056542e-02  1.186624e-01
## 10  -2.037601e-02 -1.365677e-02
## 11   2.056015e-01  2.088203e-01
## 12  -7.329105e-02 -7.327537e-02
## 13   1.927001e-01  1.975676e-01
## 14   8.043131e-02  1.054286e-01
## 15  -1.572423e-01 -1.543740e-01
## 16   9.669772e-02  1.216871e-01
## 17   4.620248e-04  5.090779e-04
## 18  -1.678897e-02 -1.553812e-02
## 19   1.984941e-01  2.026378e-01
## 20  -6.312668e-02 -5.909996e-02
## 21  -2.128459e-01 -2.130625e-01
## 22   2.153857e-01  2.156207e-01
## 23   1.248727e-02  1.547896e-02
## 24   2.129886e-01  2.140081e-01
## 25  -2.080700e-01 -2.080310e-01
## 26  -1.615563e-01 -1.619456e-01
## 27   1.375914e-01  1.597331e-01
## 28  -8.450073e-02 -7.990404e-02
## 29   9.079887e-02  9.927906e-02
## 30   7.822987e-02  8.561544e-02
## 31   2.063738e-01  2.095800e-01
## 32  -2.106258e-01 -2.109747e-01
## 33  -1.981070e-01 -1.953013e-01
## 34  -7.206710e-02 -6.398138e-02
## 35   9.560616e-02  1.043293e-01
## 36  -2.119551e-02 -1.639315e-02
## 37  -7.331524e-02 -7.315768e-02
## 38   3.165264e-02  3.610795e-02
## 39   6.680329e-02  7.804157e-02
## 40   2.106916e-01  2.124700e-01
## 41  -2.044075e-01 -2.035567e-01
## 42  -7.150672e-03 -2.995391e-03
## 43  -1.704126e-01 -1.701235e-01
## 44  -2.110687e-01 -2.112383e-01
## 45  -2.437296e-02  1.341938e-02
## 46   2.103359e-01  2.122277e-01
## 47   2.947555e-02  4.120279e-02
## 48  -2.088689e-01 -2.093201e-01
## 49  -1.252108e-01 -1.040711e-01
## 50  -1.545635e-01 -1.362448e-01
## 51  -2.066628e-01 -2.071462e-01
## 52   2.800295e-02  3.117943e-02
## 53   1.817216e-01  1.868306e-01
## 54  -5.600122e-02 -5.434368e-02
## 55   1.213650e-01  1.302471e-01
## 56   2.083867e-01  2.111246e-01
## 57   3.651686e-02  3.969636e-02
## 58   1.042261e-01  1.167564e-01
## 59  -1.850800e-01 -1.787844e-01
## 60   1.811318e-01  1.876500e-01
## 61  -8.775469e-02 -7.022273e-02
## 62   2.360579e-03  2.709861e-03
## 63   7.827917e-02  8.389191e-02
## 64  -2.482957e-02 -2.011820e-02
## 65   2.155999e-01  2.157690e-01
## 66  -9.532478e-02 -9.369404e-02
## 67  -8.668955e-02 -8.180145e-02
## 68   1.079166e-01  1.215698e-01
## 69   1.625703e-01  1.735219e-01
## 70   9.574459e-02  1.100080e-01
## 71   1.313752e-02  1.638841e-02
## 72   1.999106e-01  2.029597e-01
## 73  -2.005944e-01 -2.011580e-01
## 74  -2.128098e-01 -2.127428e-01
## 75   1.966296e-02  6.425551e-02
## 76   4.043169e-02  4.553798e-02
## 77   5.226723e-02  6.048327e-02
## 78  -5.988499e-02 -5.185763e-02
## 79  -3.961493e-02 -3.180358e-03
## 80  -1.844690e-01 -1.857248e-01
## 81  -1.612637e-01 -1.607666e-01
## 82   1.229054e-01  1.367655e-01
## 83   1.829816e-01  1.894223e-01
## 84   2.131595e-01  2.141312e-01
## 85  -2.022721e-01 -2.025491e-01
## 86   7.576142e-02  8.863514e-02
## 87   1.395969e-01  1.568188e-01
## 88   2.147313e-01  2.152105e-01
## 89   1.085183e-01  1.152898e-01
## 90   1.755876e-02  3.066611e-02
## 91   2.128506e-01  2.138780e-01
## 92   2.139639e-01  2.146135e-01
## 93   1.784308e-01  1.877860e-01
## 94  -2.053546e-01 -2.050887e-01
## 95  -1.836993e-01 -1.787009e-01
## 96   2.078481e-01  2.101650e-01
## 97   1.776931e-01  1.839225e-01
## 98   1.686201e-01  1.746506e-01
## 99  -1.815657e-01 -1.815625e-01
## 100  6.676146e-02  9.170119e-02
## 101 -7.508043e-02 -7.111679e-02
## 102  4.459566e-02  5.344510e-02
## 103 -2.157128e-01 -2.157587e-01
## 104  2.149882e-01  2.154274e-01
## 105 -1.999570e-01 -1.991238e-01
## 106 -3.307947e-02 -3.141428e-02
## 107 -7.215855e-02 -6.463398e-02
## 108 -1.975431e-01 -1.982041e-01
## 109  6.234423e-02  8.199463e-02
## 110  1.344596e-01  1.448517e-01
## 111 -2.103567e-01 -2.102963e-01
## 112  2.016121e-02  4.048288e-02
## 113 -2.136342e-01 -2.136430e-01
## 114  1.078343e-01  1.396337e-01
## 115  1.276662e-01  1.363871e-01
## 116  2.120729e-01  2.131528e-01
## 117  1.592846e-01  1.671533e-01
## 118 -1.867789e-04  6.732522e-04
## 119 -3.583079e-02 -3.539087e-02
## 120  1.550744e-01  1.625898e-01
## 121  1.980903e-01  2.031546e-01
## 122 -5.028477e-02 -4.375760e-02
## 123  1.551705e-01  1.709601e-01
## 124  2.133190e-01  2.141825e-01
## 125  2.512029e-03  2.829124e-03
## 126  7.612538e-03  8.877257e-03
## 127 -7.781284e-02 -7.190928e-02
## 128 -9.268536e-02 -7.659921e-02
## 129  3.506474e-02  4.804841e-02
## 130  8.196439e-02  9.518159e-02
## 131  1.906758e-02  2.155435e-02
## 132  8.181969e-02  9.057382e-02
## 133  1.982521e-01  2.037136e-01
## 134 -1.445044e-01 -1.310576e-01
## 135  3.389958e-02  5.669753e-02
## 136  1.269697e-02  2.113953e-02
## 137  1.123017e-01  1.259575e-01
## 138 -1.003656e-01 -9.740354e-02
## 139  1.359344e-01  1.519715e-01
## 140  2.019117e-01  2.056993e-01
## 141  1.693471e-01  1.762546e-01
## 142 -9.692835e-03 -4.225522e-03
## 143 -2.078787e-01 -2.077407e-01
## 144  2.158897e-01  2.159640e-01
## 145  1.865015e-01  1.938719e-01
## 146 -2.150412e-01 -2.150798e-01
## 147 -7.780054e-02 -7.300837e-02
## 148 -8.949604e-02 -7.472020e-02
## 149  2.084622e-01  2.107346e-01
## 150  7.040738e-02  8.221738e-02
## 151 -6.931940e-02 -6.507947e-02
## 152  1.548565e-02  3.922368e-02
## 153 -2.011522e-01 -2.014954e-01
## 154 -2.125750e-01 -2.126809e-01
## 155  2.540662e-03  2.883628e-03
## 156 -1.902380e-01 -1.900663e-01
## 157 -5.325471e-02 -1.933165e-02
## 158 -2.100122e-01 -2.104210e-01
## 159 -1.857467e-01 -1.801568e-01
## 160 -1.718557e-01 -1.730148e-01
## 161 -2.023369e-01 -2.022645e-01
## 162  6.849557e-02  1.071515e-01
## 163  1.890615e-01  1.948325e-01
## 164 -1.686659e-01 -1.703637e-01
## 165  6.287213e-03  2.876469e-02
## 166  1.729657e-01  1.838091e-01
## 167 -4.454133e-03  2.764807e-02
## 168 -2.098887e-01 -2.100975e-01
## 169  4.040504e-02  4.484123e-02
## 170 -1.264455e-01 -1.146692e-01
## 171  6.928322e-02  7.449420e-02
## 172 -2.826674e-02 -2.281027e-02
## 173 -8.674485e-02 -6.941641e-02
## 174 -1.829834e-01 -1.769924e-01
## 175 -1.402522e-01 -1.357318e-01
## 176 -1.842697e-01 -1.826705e-01
## 177  1.636924e-01  1.724487e-01
## 178 -2.146195e-01 -2.146653e-01
## 179 -9.125522e-03  5.329423e-03
## 180  7.103619e-02  7.670112e-02
## 181 -1.815049e-01 -1.812400e-01
## 182 -1.321258e-01 -1.287948e-01
## 183 -1.906626e-01 -1.901892e-01
## 184 -2.028761e-01 -2.030891e-01
## 185 -1.159603e-01 -1.144609e-01
## 186  1.279793e-01  1.370038e-01
## 187  1.124224e-02  1.337148e-02
## 188  5.282129e-03  5.681505e-03
## 189  1.039881e-01  1.109260e-01
## 190 -2.059561e-01 -2.060693e-01
## 191 -2.635628e-02 -1.950714e-02
## 192 -1.627422e-01 -1.529419e-01
## 193 -2.712102e-02 -2.227710e-02
## 194  1.448612e-01  1.557500e-01
## 195 -1.790344e-01 -1.754657e-01
## 196 -2.691577e-06  7.861760e-07
## 197  3.426350e-02  4.401479e-02
## 198  1.269711e-01  1.462095e-01
## 199 -1.651200e-01 -1.668722e-01
## 200  2.035977e-01  2.061330e-01
## 
## $values
## $values$entropy
## [1] 393.749
## 
## $values$iterations
## [1] 96
## 
## $values$message
## [1] "relative convergence (4)"
## 
## 
## $tol
## [1] 1e-10
## 
## $v
##           [,1] [,2]       [,3]
## [1,] 0.2160606    0 -0.2160606
## 
## $lambda
##   (Intercept) Dcollege  Totalincome    Dunemp
## 1    1925.471 2117.909 -0.008238336 -485.6150
## 0    2092.314 2267.589 -0.008558389 -539.5005
## 
## $checkrestrictions
## $checkrestrictions$g1
##        [,1]
##   [1,]    0
##   [2,]    0
##   [3,]    0
##   [4,]    0
##   [5,]    0
##   [6,]    0
##   [7,]    0
##   [8,]    0
##   [9,]    0
##  [10,]    0
##  [11,]    0
##  [12,]    0
##  [13,]    0
##  [14,]    0
##  [15,]    0
##  [16,]    0
##  [17,]    0
##  [18,]    0
##  [19,]    0
##  [20,]    0
##  [21,]    0
##  [22,]    0
##  [23,]    0
##  [24,]    0
##  [25,]    0
##  [26,]    0
##  [27,]    0
##  [28,]    0
##  [29,]    0
##  [30,]    0
##  [31,]    0
##  [32,]    0
##  [33,]    0
##  [34,]    0
##  [35,]    0
##  [36,]    0
##  [37,]    0
##  [38,]    0
##  [39,]    0
##  [40,]    0
##  [41,]    0
##  [42,]    0
##  [43,]    0
##  [44,]    0
##  [45,]    0
##  [46,]    0
##  [47,]    0
##  [48,]    0
##  [49,]    0
##  [50,]    0
##  [51,]    0
##  [52,]    0
##  [53,]    0
##  [54,]    0
##  [55,]    0
##  [56,]    0
##  [57,]    0
##  [58,]    0
##  [59,]    0
##  [60,]    0
##  [61,]    0
##  [62,]    0
##  [63,]    0
##  [64,]    0
##  [65,]    0
##  [66,]    0
##  [67,]    0
##  [68,]    0
##  [69,]    0
##  [70,]    0
##  [71,]    0
##  [72,]    0
##  [73,]    0
##  [74,]    0
##  [75,]    0
##  [76,]    0
##  [77,]    0
##  [78,]    0
##  [79,]    0
##  [80,]    0
##  [81,]    0
##  [82,]    0
##  [83,]    0
##  [84,]    0
##  [85,]    0
##  [86,]    0
##  [87,]    0
##  [88,]    0
##  [89,]    0
##  [90,]    0
##  [91,]    0
##  [92,]    0
##  [93,]    0
##  [94,]    0
##  [95,]    0
##  [96,]    0
##  [97,]    0
##  [98,]    0
##  [99,]    0
## [100,]    0
## [101,]    0
## [102,]    0
## [103,]    0
## [104,]    0
## [105,]    0
## [106,]    0
## [107,]    0
## [108,]    0
## [109,]    0
## [110,]    0
## [111,]    0
## [112,]    0
## [113,]    0
## [114,]    0
## [115,]    0
## [116,]    0
## [117,]    0
## [118,]    0
## [119,]    0
## [120,]    0
## [121,]    0
## [122,]    0
## [123,]    0
## [124,]    0
## [125,]    0
## [126,]    0
## [127,]    0
## [128,]    0
## [129,]    0
## [130,]    0
## [131,]    0
## [132,]    0
## [133,]    0
## [134,]    0
## [135,]    0
## [136,]    0
## [137,]    0
## [138,]    0
## [139,]    0
## [140,]    0
## [141,]    0
## [142,]    0
## [143,]    0
## [144,]    0
## [145,]    0
## [146,]    0
## [147,]    0
## [148,]    0
## [149,]    0
## [150,]    0
## [151,]    0
## [152,]    0
## [153,]    0
## [154,]    0
## [155,]    0
## [156,]    0
## [157,]    0
## [158,]    0
## [159,]    0
## [160,]    0
## [161,]    0
## [162,]    0
## [163,]    0
## [164,]    0
## [165,]    0
## [166,]    0
## [167,]    0
## [168,]    0
## [169,]    0
## [170,]    0
## [171,]    0
## [172,]    0
## [173,]    0
## [174,]    0
## [175,]    0
## [176,]    0
## [177,]    0
## [178,]    0
## [179,]    0
## [180,]    0
## [181,]    0
## [182,]    0
## [183,]    0
## [184,]    0
## [185,]    0
## [186,]    0
## [187,]    0
## [188,]    0
## [189,]    0
## [190,]    0
## [191,]    0
## [192,]    0
## [193,]    0
## [194,]    0
## [195,]    0
## [196,]    0
## [197,]    0
## [198,]    0
## [199,]    0
## [200,]    0
## 
## $checkrestrictions$g2
##        [,1] [,2]
##   [1,]    0    0
##   [2,]    0    0
##   [3,]    0    0
##   [4,]    0    0
##   [5,]    0    0
##   [6,]    0    0
##   [7,]    0    0
##   [8,]    0    0
##   [9,]    0    0
##  [10,]    0    0
##  [11,]    0    0
##  [12,]    0    0
##  [13,]    0    0
##  [14,]    0    0
##  [15,]    0    0
##  [16,]    0    0
##  [17,]    0    0
##  [18,]    0    0
##  [19,]    0    0
##  [20,]    0    0
##  [21,]    0    0
##  [22,]    0    0
##  [23,]    0    0
##  [24,]    0    0
##  [25,]    0    0
##  [26,]    0    0
##  [27,]    0    0
##  [28,]    0    0
##  [29,]    0    0
##  [30,]    0    0
##  [31,]    0    0
##  [32,]    0    0
##  [33,]    0    0
##  [34,]    0    0
##  [35,]    0    0
##  [36,]    0    0
##  [37,]    0    0
##  [38,]    0    0
##  [39,]    0    0
##  [40,]    0    0
##  [41,]    0    0
##  [42,]    0    0
##  [43,]    0    0
##  [44,]    0    0
##  [45,]    0    0
##  [46,]    0    0
##  [47,]    0    0
##  [48,]    0    0
##  [49,]    0    0
##  [50,]    0    0
##  [51,]    0    0
##  [52,]    0    0
##  [53,]    0    0
##  [54,]    0    0
##  [55,]    0    0
##  [56,]    0    0
##  [57,]    0    0
##  [58,]    0    0
##  [59,]    0    0
##  [60,]    0    0
##  [61,]    0    0
##  [62,]    0    0
##  [63,]    0    0
##  [64,]    0    0
##  [65,]    0    0
##  [66,]    0    0
##  [67,]    0    0
##  [68,]    0    0
##  [69,]    0    0
##  [70,]    0    0
##  [71,]    0    0
##  [72,]    0    0
##  [73,]    0    0
##  [74,]    0    0
##  [75,]    0    0
##  [76,]    0    0
##  [77,]    0    0
##  [78,]    0    0
##  [79,]    0    0
##  [80,]    0    0
##  [81,]    0    0
##  [82,]    0    0
##  [83,]    0    0
##  [84,]    0    0
##  [85,]    0    0
##  [86,]    0    0
##  [87,]    0    0
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## 
## $checkrestrictions$g3
##                  1    0
## (Intercept)  0.000 0.00
## Dcollege     0.000 0.00
## Totalincome -0.031 0.01
## Dunemp       0.000 0.00
## 
## 
## $cross_moments_A
##             1          0         
## (Intercept)       0.34       0.66
## Dcollege          0.17       0.44
## Totalincome  103036.63  189594.78
## Dunemp            0.16       0.29
## 
## $cross_moments_B
##             1          0         
## (Intercept)       0.34       0.66
## Dcollege          0.17       0.44
## Totalincome  103036.67  189594.77
## Dunemp            0.16       0.29
## 
## $J
## [1] 2
## 
## $fn
## dataA$poor_liq ~ Dcollege + Totalincome + Dunemp
## 
## $divergencekl
## [1] 13.52074
## 
## attr(,"class")
## [1] "shannon"

To make the results more visual, this package includes a personalized summary function which will resume the main results, providing the means for each category \(j\) for the predictions, the probabilities and the error.

summary(object=result3)
## Iterations[1] 96
## Entropy value[1] 393.749
## [1] 13.52074
## [1] "mean_estimations"
##       weights predictions_1 predictions_0 probabilities_1 probabilities_0
## 1 0.006608031     0.3377784     0.6622217       0.3420553       0.6579447
##       errors_1    errors_0
## 1 -0.004276907 0.004276958
## [1] "lambda"
##   (Intercept) Dcollege  Totalincome    Dunemp
## 1    1925.471 2117.909 -0.008238336 -485.6150
## 0    2092.314 2267.589 -0.008558389 -539.5005

Graphs are generated with the plot function, showing the averages of the predictions for each territorial unit and the 95% confidence interval associated with each of them.

plot(x=result3, reg=dataB$reg)   

References

Fernandez-Vazquez, E., Díaz-Dapena, A., Rubiera-Morollon, F., Viñuela, A., (2020) Spatial Disaggregation of Social Indicators: An Info-Metrics Approach. Social Indicators Research, 152(2), 809–821. https://doi.org/10.1007/s11205-020-02455-z.