cfd.semipar.mean {cfdecomp}

Mean Decomposition: semiparametric version

Description

Decompose the mean difference in outcome Y between groups. In this semiparametric version, we do not assume a parametric model for the mediator: instead, we sample from the distribution of the mediator in the reference group; this can be done within strata of one or more third variables.

Usage

cfd.semipar.mean(
  formula,
  mediator,
  group,
  strata = NA,
  nbin = 5,
  data,
  family = "binomial",
  bs.size = 1000,
  mc.size = 50,
  alpha = 0.05,
  print.iteration = FALSE
)

Arguments

formula

the formula for the multivariable model (see glm) for the outcome Y.

mediator

the column name of the mediator M.

group

column name of the variable containing the group identifier.

strata

the name of a variable containing the strata of a third variable (or set of variables) within which we equalize mediator values. Ideally this is a factor variable.

nbin

if a numeric (i.e. non-factor or character) strata variable is defined, how many bins should be made from it within which we equalize the mediator distribution?

data

a data frame containing the variables in the model.

family

a description of the error distribution to be used in the model, see family for details. For the outcome variable any member of the glm family can be used.

bs.size

the number of bootstrap iterations to be performed.

mc.size

the number of Monte Carlo iterations to be performed (more = more MC error reduction).

alpha

the alpha level used to construct confidence intervals (0.05 = 95 percent confidence interval).

print.iteration

print the bootstrap iteration

Value

out_nc returns the mean level of the outcome under the natural course, which is a value that should be close to the empirically observed value of the outcome for each group. out_nc_quantile provides the alpha/2 and 1-alpha/2 bootstrap quantiles for this mean (AKA bootstrap percentile confidence intervals).Similarly, out_cf, out_cf_quantile,provide the corresponding values for the counterfactual scenario where the mediators of the groups are equalized. mediation returns the proportion mediated by setting the intervened on mediator to be equal in level to the reference group and mediation_quantile returns the 1-alpha confidence interval.

Examples

set.seed(100)
# the decomposition functions in our package are computationally intensive
# to make the example run quick, I perform it on a subsample (n=250) of the data:
cfd.example.sample <- cfd.example.data[sample(250),]
mean.semipar.results.1 <- cfd.semipar.mean(formula='out.gauss ~ SES + med.gauss + med.binom + age',
                                          mediator='med.gauss',
                                          group='SES',
                                          strata='age',
                                          nbin=5,
                                          data=cfd.example.sample,
                                          family='gaussian',
                                          bs.size=50,
                                          mc.size=10,
                                          alpha=0.05)
# also note that normally we would recommend an bs.size of 250+
# and an mc.size of 50+
# see README.md for a more detailed description of the functions in this package.