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How to choose code for Bootstrap R prob models

In this question, we consider a way to select a code variable in a probit model with limit effects (either directly or by calling some previously existing package).

I conduct a small probit regression of the effects of free and commercial availability of films at the level of piracy of these films in the form of a blog related to the TLAPD post .

A simple way to start broken through in R usually goes through glm, that is:

probit <- glm(y ~ x1 + x2, data=data, family =binomial(link = "probit"))

but this is problematic for interpretation, since it does not produce marginal effects.

As a rule, if I want to use the marginal effects of a regression probit, I define this function (I do not remember the original source, but this is a popular function that is repeatedly republished):

mfxboot <- function(modform,dist,data,boot=500,digits=3){
  x <- glm(modform, family=binomial(link=dist),data)
  # get marginal effects
  pdf <- ifelse(dist=="probit",
                mean(dnorm(predict(x, type = "link"))),
                mean(dlogis(predict(x, type = "link"))))
  marginal.effects <- pdf*coef(x)
  # start bootstrap
  bootvals <- matrix(rep(NA,boot*length(coef(x))), nrow=boot)
  set.seed(1111)
  for(i in 1:boot){
    samp1 <- data[sample(1:dim(data)[1],replace=T,dim(data)[1]),]
    x1 <- glm(modform, family=binomial(link=dist),samp1)
    pdf1 <- ifelse(dist=="probit",
                   mean(dnorm(predict(x, type = "link"))),
                   mean(dlogis(predict(x, type = "link"))))
    bootvals[i,] <- pdf1*coef(x1)
  }
  res <- cbind(marginal.effects,apply(bootvals,2,sd),marginal.effects/apply(bootvals,2,sd))
  if(names(x$coefficients[1])=="(Intercept)"){
    res1 <- res[2:nrow(res),]
    res2 <- matrix(as.numeric(sprintf(paste("%.",paste(digits,"f",sep=""),sep=""),res1)),nrow=dim(res1)[1])
    rownames(res2) <- rownames(res1)
  } else {
    res2 <- matrix(as.numeric(sprintf(paste("%.",paste(digits,"f",sep=""),sep="")),nrow=dim(res)[1]))
    rownames(res2) <- rownames(res)
  }
  colnames(res2) <- c("marginal.effect","standard.error","z.ratio")
  return(res2)
}

:

mfxboot(modform = "y ~ x1 + x2",
        dist = "probit",
        data = piracy)

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#================================================
# read in data, and perform variable selection for
#   a probit model
#================================================
dfE = read.csv("ENAE_Probit.csv")
formE = emploi ~ genre + 
  filiere + satisfaction + competence + anglais
glmE = glm(formula = formE, 
           family = binomial(link = "probit"),
           data = dfE)

# perform model (variable) selection
glmStepE = step(object = glmE)
  1. , .
#================================================
# function: compute marginal effects for logit and probit models
# NOTE: this assumes that an intercept has been included by default
#================================================
fnMargEffBin = function(objBinGLM) {
  stopifnot(objBinGLM$family$family == "binomial")
  vMargEff = switch(objBinGLM$family$link, 
                    probit = colMeans(outer(dnorm(predict(objBinGLM, 
                                                         type = "link")),
                                           coef(objBinGLM))[, -1]),
                    logit = colMeans(outer(dlogis(predict(objBinGLM, 
                                                        type = "link")),
                                          coef(objBinGLM))[, -1])
  )
  return(vMargEff)
}

# test the function
fnMargEffBin(glmStepE)

:

> fnMargEffBin(glmStepE)
     genre    filiere 
0.06951617 0.04571239
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#================================================
# compute bootstrap std. err. for the marginal effects
#================================================
margEffBootE = Boot(object = glmStepE, f = fnMargEffBin, 
     labels = names(coef(glmE))[-1], R = 100)
summary(margEffBootE)

:

> summary(margEffBootE)
          R original  bootBias   bootSE  bootMed
genre   100 0.069516 0.0049706 0.045032 0.065125
filiere 100 0.045712 0.0013197 0.011714 0.048900

:

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