distreg

The distreg package is a collection of functions built for distribution regression. That is, one can estimate the distribution of (Y) conditional on (X) using a model for a binary outcome. For example, [ F_{Y|X}(y|x) = \Lambda(x'\beta) ] where (\Lambda) is some known link function, such as logit.

This package was formerly called TempleMetrics. For the time being, we are just hosting the package on Github, but it should work just fine for you. The main methods are:

• distreg – a function to implement distribution regression as in Foresi and Peracchi (1995) doi:10.2307/2291056 and Chernozhukov, Fernandez-Val, and Melly (2013) doi:10.3982/ECTA10582.

• lldistreg – a function to implement a local linear regression (it’s local in just one particular variable – often a ``treatment’’)

In either case, it is often useful to convert these estimates into estimates of conditional distributions themselves. This can be done with the function Fycondx. We give some examples below.

Installation

You can install distreg from github with:

# install.packages("devtools")
devtools::install_github("bcallaway11/distreg")
#> Downloading GitHub repo bcallaway11/distreg@HEAD
#> 
#>      checking for file ‘/tmp/RtmpiH5t3P/remotesd7327af16bb8/bcallaway11-distreg-ff2f263/DESCRIPTION’ ...  ✔  checking for file ‘/tmp/RtmpiH5t3P/remotesd7327af16bb8/bcallaway11-distreg-ff2f263/DESCRIPTION’
#>   ─  preparing ‘distreg’:
#>      checking DESCRIPTION meta-information ...  ✔  checking DESCRIPTION meta-information
#>   ─  checking for LF line-endings in source and make files and shell scripts
#>   ─  checking for empty or unneeded directories
#>   ─  building ‘distreg_1.3.0.tar.gz’
#>      
#> 
#> Installing package into '/tmp/RtmpTFpvLA/temp_libpathc85b78baa01d'
#> (as 'lib' is unspecified)

Example 1

The first example is how to run distribution regression for a single value of (y) of (Y). This example uses the igm dataset which is a collection of 500 parent-child pairs of income along with the parent’s education level which comes from the Panel Study of Income Dynamics (PSID).

library(distreg)
data(igm)
head(igm)
#>      lcfincome lfincome  HEDUC
#> 1943 11.599712 11.46909     HS
#> 823  11.396635 10.71540     HS
#> 597  11.805380 10.87307     HS
#> 1291 11.007568 11.45044     HS
#> 3333 10.915150 11.30180     HS
#> 2717  9.764008 10.80891 LessHS

y0 <- median(igm$lcfincome)
dreg <- distreg(lcfincome ~ lfincome + HEDUC, igm, y0)
dreg
#> $yvals
#> [1] 11.04563
#> 
#> $glmlist
#> $glmlist[[1]]
#> 
#> Call:  glm(formula = formla, family = binomial(link = link), data = dta)
#> 
#> Coefficients:
#> (Intercept)     lfincome      HEDUCHS  HEDUCLessHS  
#>     15.3320      -1.3976       0.1629       0.2256  
#> 
#> Degrees of Freedom: 499 Total (i.e. Null);  496 Residual
#> Null Deviance:       693.1 
#> Residual Deviance: 640.9     AIC: 648.9
#> 
#> 
#> attr(,"class")
#> [1] "DR"

Example 2

In many cases, of primary interest with distribution regression is obtaining (\hat{F}_{Y|X}(y|x)) for some particular values of (y) and (x). That’s what we do in this example.

yvals <- seq(quantile(igm$lcfincome,.05,type=1),
quantile(igm$lcfincome,.95, type=1), length.out=100)
dres <- distreg(lcfincome ~ lfincome + HEDUC, igm, yvals)
xdf <- data.frame(lfincome=10, HEDUC="LessHS")
y0 <- yvals[50]
ecdf(igm$lcfincome)(y0)
#> [1] 0.328
Fycondx(dres, y0, xdf)
#> [[1]]
#> Empirical CDF 
#> Call: NULL
#>  x[1:100] = 9.6856, 9.7073, 9.7291,  ..., 11.814, 11.836

This example says that: (1) the fraction of “children” in the dataset with income below 46628 is 0.33, but (2) we estimate that the fraction of children whose parent’s income is 22026 and have parent’s with less than a HS education with income below 46628 is 0.73.