causal.decomp (version 0.2.0)

pocr: Product-of-Coefficients-Regression Estimation Method

Description

'pocr' is used to estimate the initial disparity, disparity reduction, and disparity remaining for causal decomposition analysis, using the product-of-coefficients-regression estimation method proposed by Park et al. (2021+).

Usage

pocr(fit.x = NULL, fit.m, fit.y, group, covariates, sims = 100, conf.level = .95,
     cluster = NULL, long = TRUE, mc.cores = 1L, seed = NULL)

Value

result

a matrix containing the point estimates of the initial disparity, disparity remaining, and disparity reduction, and the percentile bootstrap confidence intervals for each estimate.

all.result

a matrix containing the point estimates of the initial disparity, disparity remaining, and disparity reduction for all bootstrap samples. Returned if 'long' is 'TRUE'.

Arguments

fit.x

a fitted model object for intermediate confounder. Can be of class 'lm'. Only necessary if the mediator is categorical. Default is 'NULL'.

fit.m

a fitted model object for mediator. Can be of class 'lm', 'glm', 'multinom', or 'polr'.

fit.y

a fitted model object for outcome. Can be of class 'lm'.

group

a character string indicating the name of the social group indicator such as race or gender (treatment) used in the models. The social group indicator can be categorical with two or more categories (two- or multi-valued factor).

covariates

a vector containing the name of the covariate variable(s) used in the models. Each covariate can be categorical with two or more categories (two- or multi-valued factor) or continuous (numeric).

sims

number of Monte Carlo draws for nonparametric bootstrap.

conf.level

level of the returned two-sided confidence intervals, which are estimated by the nonparametric percentile bootstrap method. Default is to return the 2.5 and 97.5 percentiles of the simulated quantities.

cluster

a vector of cluster indicators for the bootstrap. If provided, the cluster bootstrap is used. Default is 'NULL'.

long

a logical value. If 'TRUE', the output will contain the entire sets of estimates for all bootstrap samples. Default is 'TRUE'.

mc.cores

The number of cores to use. Must be exactly 1 on Windows.

seed

seed number for the reproducibility of results. Default is `NULL'.

Author

Suyeon Kang, University of Central Florida, ; Soojin Park, University of California, Riverside, .

Details

This function returns the point estimates of the initial disparity, disparity reduction, and disparity remaining for a categorical social group indicator (treatment) and a variety of types of outcome and mediator(s) in causal decomposition analysis. It also returns nonparametric percentile bootstrap confidence intervals for each estimate.

The definition of the initial disparity, disparity reduction, and disparity remaining can be found in help('mmi'). As opposed to the 'mmi' and 'smi' function, this function uses the product-of-coefficients-regression method suggested by Park et al. (2021+). It always make the inference conditional on baseline covariates. Therefore, users need to center the data before fitting the models. See the reference for more details.

As of version 0.1.0, the mediator model ('fit.m') can be of class 'lm', 'glm', 'multinom', or 'polr', corresponding respectively to the linear regression models and generalized linear models, multinomial log-linear models, and ordered response models. The outcome model ('fit.y') can be of class 'lm'. The intermediate confounder model ('fit.x') can also be of class 'lm' and only necessary when the mediator is categorical.

References

Park, S., Kang, S., and Lee, C. (2024). "Choosing an optimal method for causal decomposition analysis with continuous outcomes: A review and simulation study", Sociological methodology, 54(1), 92-117.

See Also

mmi, smi

Examples

data(sdata)

# To be conditional on covariates, first create data with centered covariates
# copy data
sdata.c <- sdata
# center quantitative covariate(s)
sdata.c$C.num <- scale(sdata.c$C.num, center = TRUE, scale = FALSE)
# center binary (or categorical) covariates(s)
# only neccessary if the desired baseline level is NOT the default baseline level.
sdata.c$C.bin <- relevel(sdata.c$C.bin, ref = "1")

#---------------------------------------------------------------------------------#
# Example 1: Continuous Mediator
#---------------------------------------------------------------------------------#
fit.m1 <- lm(M.num ~ R + C.num + C.bin, data = sdata.c)
fit.y1 <- lm(Y.num ~ R + M.num + M.num:R + X +
          C.num + C.bin, data = sdata.c)
res1 <- pocr(fit.m = fit.m1, fit.y = fit.y1, sims = 40,
        covariates = c("C.num", "C.bin"), group = "R", seed = 111)
res1

#---------------------------------------------------------------------------------#
# Example 2: Binary Mediator
#---------------------------------------------------------------------------------#
fit.x1 <- lm(X ~ R + C.num + C.bin, data = sdata.c)
fit.m2 <- glm(M.bin ~ R + C.num + C.bin, data = sdata.c,
          family = binomial(link = "logit"))
fit.y2 <- lm(Y.num ~ R + M.bin + M.bin:R + X +
          C.num + C.bin, data = sdata.c)
res2 <- pocr(fit.x = fit.x1, fit.m = fit.m2, fit.y = fit.y2,
        sims = 40, covariates = c("C.num", "C.bin"), group = "R", seed = 111)
res2

#---------------------------------------------------------------------------------#
# Example 3: Ordinal Mediator
#---------------------------------------------------------------------------------#
require(MASS)
fit.m3 <- polr(M.cat ~ R + C.num + C.bin, data = sdata.c)
fit.y3 <- lm(Y.num ~ R + M.cat + M.cat:R + X +
	C.num + C.bin, data = sdata.c)
res3 <- pocr(fit.x = fit.x1, fit.m = fit.m3, fit.y = fit.y3,
       sims = 40, covariates = c("C.num", "C.bin"), group = "R", seed = 111)
res3

#---------------------------------------------------------------------------------#
# Example 4: Nominal Mediator
#---------------------------------------------------------------------------------#
require(nnet)
fit.m4 <- multinom(M.cat ~ R + C.num + C.bin, data = sdata.c)
res4 <- pocr(fit.x = fit.x1, fit.m = fit.m4, fit.y = fit.y3,
        sims = 40, covariates = c("C.num", "C.bin"), group = "R", seed = 111)
res4