# Summary of Bayesian Models as HTML Table

#### Daniel Lüdecke

#### 2023-04-02

    ## Loading 'brms' package (version 2.19.0). Useful instructions
    ## can be found by typing help('brms'). A more detailed introduction
    ## to the package is available through vignette('brms_overview').

    ##
    ## Attaching package: 'brms'

    ## The following objects are masked from 'package:rstanarm':
    ##
    ##     dirichlet, exponential, get_y, lasso, ngrps

    ## The following object is masked from 'package:stats':
    ##
    ##     ar

This vignette shows examples for using `tab_model()` to create HTML tables for mixed models. Basically, `tab_model()` behaves in a very similar way for mixed models as for other, simple regression models, as shown in this vignette.

    # load required packages
    library(sjPlot)
    library(brms)

    # sample models
    zinb <- read.csv("http://stats.idre.ucla.edu/stat/data/fish.csv")
    set.seed(123)
    m1 <- brm(bf(
        count ~ persons + child + camper + (1 | persons),
        zi ~ child + camper + (1 | persons)
      ),
      data = zinb,
      family = zero_inflated_poisson()
    )

    data(epilepsy)
    set.seed(123)
    epilepsy$visit <- as.numeric(epilepsy$visit)
    epilepsy$Base2 <- sample(epilepsy$Base, nrow(epilepsy), replace = TRUE)
    f1 <- bf(Base ~ zAge + count + (1 |ID| patient))
    f2 <- bf(Base2 ~ zAge + Trt + (1 |ID| patient))
    m2 <- brm(f1 + f2 + set_rescor(FALSE), data = epilepsy)

## Bayesian models summaries as HTML table

For Bayesian regression models, some of the differences to the table output from simple models or mixed models of `tab_models()` are the use of Highest Density Intervals instead of confidence intervals, the Bayes-R-squared values, and a different “point estimate” (which is, by default, the median from the posterior draws).

    tab_model(m1)

| count
--- | ---
Predictors | Incidence Rate Ratios | CI (95%)
Count Model
Intercept | 0.42 | 0.22 – 0.88
persons | 2.32 | 1.86 – 2.93
child | 0.32 | 0.26 – 0.38
camper | 2.08 | 1.73 – 2.53
Zero-Inflated Model
Intercept | 0.52 | 0.11 – 2.21
child | 6.44 | 3.46 – 12.95
camper | 0.43 | 0.21 – 0.87
Random Effects
σ2 | 5.57
τ00 | 33.61
ICC | 0.14
N persons | 4
Observations | 250
Marginal R2 / Conditional R2 | 0.186 / 0.248

## Multivariate response models

For multivariate response models, like mediator-analysis-models, it is recommended to print just one model in the table, as each regression is displayed as own “model” in the output.

    tab_model(m2)

| Base | Base2
--- | --- | ---
Predictors | Estimates | CI (95%) | Estimates | CI (95%)
Intercept | 28.61 | 11.35 – 34.20 | 26.61 | 11.24 – 29.03
z Age | -4.85 | -5.42 – -1.76 | 1.21 | -0.31 – 2.15
count | 0.00 | -0.00 – 0.00 |  |
Trt: Trt 1 |  |  | -0.32 | -4.36 – 1.43
Random Effects
σ2 | 54.98
τ00 | 3.90
ICC | 0.96
N patient | 59
Observations | 236

## Show two Credible Interval-column

To show a second CI-column, use `show.ci50 = TRUE`.

    tab_model(m2, show.ci50 = TRUE)

| Base | Base2
--- | --- | ---
Predictors | Estimates | CI (50%) | CI (95%) | Estimates | CI (50%) | CI (95%)
Intercept | 28.61 | 24.07 – 30.23 | 11.35 – 34.20 | 26.61 | 21.53 – 28.45 | 11.24 – 29.03
z Age | -4.85 | -5.17 – -3.89 | -5.42 – -1.76 | 1.21 | 0.74 – 1.54 | -0.31 – 2.15
count | 0.00 | -0.00 – 0.00 | -0.00 – 0.00 |  |  |
Trt: Trt 1 |  |  |  | -0.32 | -1.91 – 0.69 | -4.36 – 1.43
Random Effects
σ2 | 55.75
τ00 | 4.73
ICC | 0.96
N patient | 59
Observations | 236

## Mixing multivariate and univariate response models

When both multivariate and univariate response models are displayed in one table, a column Response is added for the multivariate response model, to indicate the different outcomes.

    tab_model(m1, m2)

| count | Base,Base 2
--- | --- | ---
Predictors | Incidence Rate Ratios | CI (95%) | Estimates | CI (95%) | Response
Intercept | 0.42 | 0.22 – 0.88 | 28.61 | 11.35 – 34.20 | Base
Intercept | 0.42 | 0.22 – 0.88 | 26.61 | 11.24 – 29.03 | Base2
persons | 2.32 | 1.86 – 2.93 |  |  |
child | 0.32 | 0.26 – 0.38 |  |  |
camper | 2.08 | 1.73 – 2.53 |  |  |
z Age |  |  | -4.85 | -5.42 – -1.76 | Base
count |  |  | 0.00 | -0.00 – 0.00 | Base
z Age |  |  | 1.21 | -0.31 – 2.15 | Base2
Trt: Trt 1 |  |  | -0.32 | -4.36 – 1.43 | Base2
Zero-Inflated Model
Intercept | 0.52 | 0.11 – 2.21 |  |  |
child | 6.44 | 3.46 – 12.95 |  |  |
camper | 0.43 | 0.21 – 0.87 |  |  |
Random Effects
σ2 | 5.37 | 54.04
τ00 | 33.71 | 4.37
ICC | 0.14 | 0.96
N | 4 persons | 59 patient
Observations | 250 | 236
Marginal R2 / Conditional R2 | 0.186 / 0.248 | NA