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README.Rmd
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README.Rmd
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---
output: github_document
---
<!-- README.md is generated from README.Rmd. Please edit that file -->
```{r, include = FALSE}
knitr::opts_chunk$set(
collapse = TRUE,
comment = "#>",
fig.path = "man/figures/README-",
out.width = "100%"
)
```
# ivgets
<!-- badges: start -->
[](https://github.com/jkurle/ivgets/actions)
[](https://app.codecov.io/gh/jkurle/ivgets?branch=master)
[](https://cran.r-project.org/package=ivgets)
<!-- badges: end -->
The _ivgets_ package provides general-to-specific modeling functionality for
two-stage least squares (2SLS or TSLS) models. There are two main uses. Starting
from a generalized unrestricted model (GUM), the algorithm searches over the set
of exogenous regressors to find a specification that can explain the data while
trying to be as parsimonious as possible. Second, the package can perform
indicator saturation methods to detect outliers and structural breaks in the
data.
## Installation
You can install the released version of ivgets from [CRAN](https://CRAN.R-project.org) with:
``` r
install.packages("ivgets")
```
And the development version from [GitHub](https://github.com/) with:
``` r
# install.packages("devtools")
devtools::install_github("jkurle/ivgets")
```
## Dependencies
The _ivgets_ package relies heavily on two packages. The estimation of 2SLS
models is based on the [ivreg](https://zeileis.github.io/ivreg/) package and
model selection uses the [gets](http://www.sucarrat.net/R/gets/) package.
### Versions
_ivgets_ avoids specifying minimum or maximum versions of the dependencies in
the `DESCRIPTION` file if possible. This is to avoid forcing users to update
their packages and potentially break existing code.
## Example
### Setup
Suppose we want to model the potential effect of some regressors $x_{1}$ to
$x_{11}$ on a dependent variable $y$. We are worried that $x_{11}$ could be
endogenous, so we use a 2SLS model to estimate the parameters. For the exogenous
regressors $x_{1}$ to $x_{10}$ we are unsure whether they are relevant but our
theory tells us that they might be relevant. So we want to include all of them
in the original model and then use model selection to determine which regressors
are actually relevant. Furthermore suppose we are concerned that the sample
might contain outlying observations and that these outliers are biasing our
results.
Formally, our structural equation is
$$
y_{i} = \beta_{1} x_{1i} + \beta_{2}
x_{2i} + ... + \beta_{11} x_{11i} + u_{i} = x_{i}^{\prime} \beta + u_{i}
$$.
The first stage can be written as
$$x_{i} = \Pi^{\prime} z_{i} + r_{i}$$,
where $z_{i}$ includes all the exogenous regressors $x_{1}$ to $x_{10}$ and the
excluded instruments $z_{11}$ and $z_{12}$.
### Indicator Saturation
Since we are concerned about outliers, we first do impulse indicator saturation
to detect observations with unusually large errors. We still include all our
potentially relevant exogenous regressors in the model.
```{r eval = TRUE}
library(ivgets)
# we specify "-1" in the formula because x1 is already an intercept in our data frame
fml <- y ~ -1+x1+x2+x3+x4+x5+x6+x7+x8+x9+x10+x11 | -1+x1+x2+x3+x4+x5+x6+x7+x8+x9+x10+z11+z12
base <- ivreg(formula = fml, data = artificial2sls_contaminated)
# do impulse indicator saturation
indicators <- isat(base, iis = TRUE, t.pval = 1/100, print.searchinfo = FALSE)
print(indicators$final)
```
For the selection of indicators, we use a significance level, `t.pval`, of
1/100. The data set has 100 observations and we select over 100 impulse
indicators. So we expect to falsely retain one indicator on average. As the
output shows, the algorithm has retained four indicators: iis9, iis11, iis43,
iis73. Since this is artificial data, we know which observations were outliers.
In this case, all of the retained indicators correspond to actual outlying
observations 9, 11, 43, and 73. The algorithm has only missed one additional
outlier, which was observation 78.
The object `indicators` is a list with two entries. The first entry,
`$selection`, stores the information related to the search, such as the number
of estimations and all terminal models. The second entry, `$final`, is an object
of class `"ivreg"` and is the model result of the final model.
### General-to-Specific Theory Modeling
Now that we have identified (some of the) outliers, we still want to find out
which of our theoretical exogenous regressors are actually relevant. As before,
we can simply pass the final model from the previous step to the `gets()`
method. Since we do not want to select over the impulse indicators again, we
need to specify this accordingly in the function call. The names of the
indicators are conveniently saved in the `$selection$ISnames` entry.
```{r eval = TRUE}
selection <- gets(indicators$final, keep_exog = indicators$selection$ISnames, print.searchinfo = FALSE)
print(selection$final)
```
As before, the returned object is a list with entry `$selection`, which stores information about the search, and `$final`, which is an `"ivreg"` model object of the final model. There is an additional third entry named `$keep` that
specifies the names of all regressors in the second stage that were not selected over. This can be used as a check that the selection was done correctly.
```{r eval = TRUE}
# as specified, the impulse indicators and the endogenous regressor, x11, were not selected over
print(selection$keep)
```
The final model has only retained the exogenous theory variables $x_{1}$ and $x_{2}$, which is the correct selection. The data generating process only contained the variables $x_{1}$, $x_{2}$, and $x_{11}$. Their true parameters were `c(6, -5, 3)`, so the estimates are quite close.