The TempleMetrics package is a collection of functions implemented by members of the Econometrics Reading Group at Temple University. The main functions (at the moment) are 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, \begin{align*} F_{Y|X}(y|x) = \Lambda(x'\beta) \end{align*}

where $$\Lambda$$ is some known link function, such as logit.

## Installation

You can install TempleMetrics from github with:

# install.packages("devtools")
devtools::install_github("bcallaway11/TempleMetrics")
#> Skipping install of 'TempleMetrics' from a github remote, the SHA1 (b03043d0) has not changed since last install.
#>   Use force = TRUE to force installation

or from CRAN using

install.packages("TempleMetrics")

## 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(TempleMetrics)
data(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
#>  11.04563
#>
#> $glmlist #>$glmlist[]
#>
#> 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")
#>  "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
ecdf(igm\$lcfincome)(y0)
#>  0.328
Fycondx(dres, y0, xdf)
#> []
#> 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.