@author: Miguel Garcia-Duch 18-10-2023
an r test package implementing the oaxaca-blinder decomposition for survey objects, that is, taking sample weights into consideration by means of svyglm superset of standard glm implemented in package Survey.
Install latest version from:
devtools::install_github("iliciuv/OaxacaSurvey)#' @param formula An object of class formula: the model formula. #' @param data A data frame: containing the variables in the formula, group, and weights. #' @param group A character string: the name of the binary group variable in the data. 1 for the first group, and 0 for the second group. #' @param weights A character string: the name of the weights variable in the data. #' @param R An integer: the number of bootstrap replicates. Default is 1000. #' @param conf.level A float less than 1: Confidence level for estimated CI. #' @param method String: one between "normal" (default) or "logit" for logistic models The only implemented method to perform the decomposition is oaxaca_blinder_svy. It performs Oaxaca-Blinder decomposition for 2 groups of controls from a survey with sampling weigths. The function uses the following parameters:
- @param formula An object of class formula: the model formula.
- @param data A data frame: containing the variables in the formula, group, and weights.
- @param group A character string: the name of the binary group variable in the data. 1 for the first group, and 0 for the second group.
- @param weights A character string: the name of the weights variable in the data.
- @param R An integer: the number of bootstrap replicates. Default is 1000.
- @param conf.level A float less than 1: Confidence level for estimated CI.
- @param method String: one between "normal" (default) or "logit" for logistic models.
A working example can be run pointing to the following project path:
source("tests/examples.R")Let's assume we have a linear model of the general form:
Where two distinct groups, let say 1 & 2, sharing certain characteristics, could be subsampled and estimated individually in the form of:
After this first step estimation and assuming the mean difference on the endogenous variable for the groups is by definition:
We then could rearrange both models together to build the so called Oaxaca-Blinder decomposition. The Decomposition computed is the so-called "triple" (even "quadruple" if we also consider the "Unexplained" remainder):
For:
-
$\Delta Y$ is the mean difference in the outcome variable between the two groups. -
$U$ is the unexplained remainder (difference of model intercepts, usually omitted). -
$E$ represents the endowments effect. -
$C$ represents the coefficients effect. -
$I$ represents the interaction effect.
The difference in mean outcomes between the two groups can be expressed as:
Where:
-
$\Delta \bar{Y}$ is the difference in mean outcomes between group 1 and group 2. -
$\hat\beta_{01}$ and$\hat\beta_{02}$ are the estimated intercepts for group 1 and group 2, respectively. -
$\bar{X}_1$ and$\bar{X}_2$ are the mean values of the covariates for group 1 and group 2, respectively. -
$\hat{\beta}_1$ and$\hat{\beta}_2$ are the estimated coefficients for group 1 and group 2, respectively.
The three terms on the right side represent the contributions from differences in unexplained (U), endowments (E), coefficients (C), and interaction effects (I).
last rev: 20/10/2023