CA conducts CA estimation and inference on user-specified objects of interest: first (weighted)
moment or (weighted) distribution. Users can use t to specify variables in interest. When object
of interest is moment, use cl to specify linear combinations for hypothesis testing. All estimates
are bias-corrected and all confidence bands are monotonized. The bootstrap procedures follow algorithm 2.2
as in Chernozhukov, Fernandez-Val and Luo (2018).
CA(fm, data, method = "ols", var.type = "binary", var.T, compare,
subgroup = NULL, samp_weight = NULL, taus = c(1:9)/10, u = 0.1,
cl = matrix(c(1, 0), nrow = 2), t = c(1, 1, rep(0, dim(data)[2] -
2)), interest = "moment", cat = NULL, alpha = 0.1, B = 10,
ncores = 1, seed = 1, bc = TRUE, range.cb = c(0.5:99.5)/100,
boot.type = "nonpar")Regression formula
The data in use (full sample or subpopulation in interset)
Models to be used for estimating partial effects. Four options: "logit" (binary response),
"probit" (binary response), "ols" (interactive linear with additive errors), "QR" (linear model
with non-additive errors). Default is "ols".
The type of parameter in interest. Three options: "binary", "categorical", "continuous". Default
is "binary".
Variable T in interset. Should be a character.
If parameter in interest is categorical, then user needs to specify which two category to
compare with. Should be a 1 by 2 character vector. For example, if the two levels to compare
with is 1 and 3, then c=("1", "3"), which will calculate partial effect from 1 to 3. To use
this option, users first need to specify var.T as a factor variable.
Subgroup in interest. Default is NULL. Specifcation should be a logical variable. For example, suppose data contains
indicator variable for women (female if 1, male if 0). If users are interested in women SPE, then users
should specify subgroup = data[, "female"] == 1.
Sampling weight of data. If null then function implements empirical bootstrap.
If data specifies sampling weight, put that in and the function implements
weighted (i.i.d exponential weights) bootstrap. Default is NULL.
Indexes for quantile regression. Default is c(1:9)/10.
Percentile of most and least affected. Default is set to be 0.1.
A pre-specified linear combination. Should be a 2 by L matrix. Default is matrix(c(1,0), nrow=2). L-th column denotes L-th hypothesis
For "moment" interest L means the number of hypotheses. cl must be specified as a matrix
An index for CA object. Should be a 1 by ncol(data) indicator vector. Users can either
(1) specify names of variables of interest directly, or
(2) use 1 to indicate the variable of interest. For example, total number of variables is 5 and interested in the 1st and 3rd vars, then specify
t = c(1, 0, 1, 0, 0).
Generic objects in the least and most affected subpopulations. Two options:
(1) "moment": weighted mean of Z in the u-least/most affected subpopulation.
(2) "dist": distribution of Z in the u-least/most affected subpopulation.
Default is interest = "moment".
P-values in classification analysis are adjusted for multiplicity to account for joint testing of
zero coefficients on for all variables within a category. Specify all variables in interest in a list using numbers
to denote relative positions. For example, if variables in interest are "educ", "male", "female", "low income", "middle income",
and "high income", cat should be specified as cat = list(a=1, b=c(2,3), c=c(4,5,6)). Default of cat is NULL.
Size for confidence interval. Shoule be between 0 and 1. Default is 0.1
Number of bootstrap draws. Default is 10. For more accurate results, we recommend 500.
Number of cores for computation. Default is set to be 1. For large dataset, parallel computing is highly recommended since bootstrap is time-consuming.
Pseudo-number generation for reproduction. Default is 1.
Whether want the estimate to be bias-corrected. Default is TRUE. If FALSE uncorrected
estimate and corresponding confidence bands will be reported.
When interest = "dist", we sort and unique variables in interest to estimate weighted CDF. For large dataset there can be
memory problem storing very many of observations, and thus users can provide a Sort value and the package will sort and unique
based on the weighted quantile of Sort. If users don't want this feature, set range.cb = NULL. Default is c(0.5:99.5)/100.
To see how range.cb makes a difference in the plot, refer to the examples in the companion vignette.
Type of bootstrap. Default is boot.type = "nonpar", and the package implements nonparametric
bootstrap. An alternative is boot.type = "weighted", and the package implements weighted
bootstrap.
If subgroup = NULL, all outputs are whole sample. Otherwise output are subgroup results. When
interest = "moment", the output is a list showing
est Estimates of variables in interest.
bse Bootstrap standard errors.
joint_p P-values that are adjusted for multiplicity to account for joint testing for all variables.
If users have further specified cat (e.g., !is.null(cat)), the output has a fourth component
p_cat P-values that are adjusted for multiplicity to account for joint testing for all variables within a category.
When interest = "dist", the output is a list of two components:
infresults A list that stores estimates, upper and lower confidence bounds for all variables
in interest for least and most affected groups.
sortvar A list that stores sorted and unique variables in interest.
We recommend using CAplot command for result visualization.
# NOT RUN {
data("mortgage")
fm <- deny ~ black + p_irat
t <- c(rep(1, 2), rep(0, 14)) # Specify variables in interest
cl <- matrix(c(1,0,0,1), nrow=2) # Meaning: show variables in interest for both groups
CA <- CA(fm = fm, data = mortgage, var.T = "black", method = "logit", cl = cl, t = t)
# Tabulate the results
est <- matrix(CA$est, ncol=2)
se <- matrix(CA$bse, ncol=2)
Table <- matrix(0, ncol=4, nrow=2)
Table[, 1] <- est[, 1] # Least Affected Bias-corrected estimate
Table[, 2] <- se[, 1] # Corresponding SE
Table[, 3] <- est[, 2] # Most affected
Table[, 4] <- se[, 2] # Corresponding SE
rownames(Table) <- colnames(CA$est)[1:2] # assign names to each row
colnames(Table) <- rep(c("Estimate", "SE"), 2)
# }
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