---
title: "Basic Regressions with mverse"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Basic Regressions with mverse}
  %\VignetteEncoding{UTF-8}
  %\VignetteEngine{knitr::rmarkdown}
references:
  - id: multiverse
    title: "multiverse: R package for creating explorable multiverse analysis"
    type: entry
    URL: https://mucollective.github.io/multiverse/
    accessed:
      year: 2020
    author:
    - given: Abhraneel
      family: Sarma
    - given: Matthew
      family: Kay
  - id: boston
    title: Hedonic prices and the demand for clean air
    author: 
    - family: Harrison Jr
      given: David
    - family: Rubinfeld
      given: Daniel L
    container-title: Journal of environmental economics and management
    type: article-journal
    volume: 5
    number: 1
    pages: 81-102
    issued:
      year: 1978
    publisher: Elsevier
---



```{r setup, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE, fig.width=7
)
Sys.setenv(LANG="en")
```
This vignette describes the workflow of linear regression modeling in the multiverse with the following functions:

 * `formula_branch()`, `add_formula_branch`: create branches for regression formulas and add them to a `mverse` object.
 * `lm_mverse()`: fit a simple linear model with the given formula branches and family branches.
 * `summary()`: provide a summary of the fitted models in different branches. 
 * `spec_curve()`: display the specification curve of a model.


```{r load, warning=FALSE, message=FALSE}
library(tidyverse)
library(mverse)
```

We will use the Boston housing dataset {@boston} as an example. This dataset has 506 observations on 14 variables. This dataset is extensively used in regression analyses and algorithm benchmarks. The objective is to predict the median value of a home (`medv`) with the feature variables.

```{r}
glimpse(MASS::Boston) # using kable for displaying data in html
```


## Simple Linear Regression with `mverse`

In order to perform a linear regression in the multiverse, we create a formula branch with all the models we wish to explore, add it the `mverse` object, and execute `lm` on each universe by calling `lm_mverse`.

Create a multiverse with `mverse`.

```{r lm}
mv <- create_multiverse(MASS::Boston)
```

We can explore models of the median value of home prices `medv` on different combinations of the following explanatory variables: proportion of adults without some high school education and proportion of male workers classified as laborers (`lstat`), average number of rooms per dwelling (`rm`), per capita crime rate (`crim`), and property tax (`tax`).

Create the models with `formula_branch()`

```{r}
formulas <- formula_branch(medv ~ log(lstat) * rm,
                           medv ~ log(lstat) * tax,
                           medv ~ log(lstat) * tax * rm)
```

Add the models to the multiverse `mv`.

```{r}
mv <- mv %>% add_formula_branch(formulas)
```

Fit `lm()` across `mv` using `lm_mverse()`.

```{r}
lm_mverse(mv)
```


By default, `summary` will give the estimates of parameters for each model. You can also output other information by changing the `output` parameter.


```{r summary_lm}
summary(mv)
```

Changing `output` to `df` yields the degrees of freedom table.  

```{r}
summary(mv, output = "df")
```

Other options include F (`output = "f"`) statistics 

```{r}
summary(mv, output = "f")
```

and $R^2$ (`output = "r"`).

```{r}
# output R-squared by `r.squared` or "r"
summary(mv, output = "r")
```


Finally, we can display how the effect of number of rooms in a dwelling `log(lstat)` using `spec_curve`.  

```{r}
spec_curve(mv, var = "log(lstat)") 
```

