How can I generate marginal effects for a logit model when using survey weights?

Question

I normally generate logit model marginal effects using the mfx package and the logitmfx function. However, the current survey I am using has weights (which have a large effect on the proportion of the DV in the sample because of oversampling in some populations) and logitmfx doesn't appear to have any way to include weights.

I have fitted the model with svyglm as follows:

library(survey)

survey.design <- svydesign(ids = combined.survey$id,
                                        weights = combined.survey$weight,
                                            data = combined.survey)

vote.pred.1 <- svyglm(formula = turnout ~ gender + age.group + 
                                    education + income, 
                                 design = survey.design)
summary(vote.pred.1)

How can I generate marginal effects from these results?

Answer 1

I had the same question. Below I modified a function from the mfx package to calculate marginal effects using data organized as a survey object. I didn't do much, mostly replacing 'mean()' and similar commands that are designed to run on non-survey data with the survey-package equivalents. After the modified mfx code, there is code that runs an example.

Background

Details on the mfx package by Alan Fernihough: https://cran.r-project.org/web/packages/mfx/mfx.pdf

Code for the mfx package on github (the files that I modified are probitmfxest.r and probitmfx.r): https://github.com/cran/mfx/tree/master/R

In the mfx calculator, I commented out a lot of the flexibility built into the original functions that handled different assumptions about clusters and robust SEs. I could be wrong but I think those issues are already accounted for by using the regression estimation command from the survey package, svyglm().

Marginal effects calculator

 library(survey)

 probitMfxEstSurv <-
    function(formula, 
             design, 
             atmean = TRUE, 
             robust = FALSE, 
             clustervar1 = NULL, 
             clustervar2 = NULL, 
             start = NULL
             #           control = list() # this option is found in the original mfx package
    ){

      if(is.null(formula)){
        stop("model formula is missing")
      }

      for( i in 1:length(class(design))){
        if(!((class(design)[i] %in% "survey.design2") | (class(design)[i] %in% "survey.design"))){
          stop("design arguement must contain survey object")
        }
      }

      # from Fernihough's original mfx function
      # I dont think this is needed because the  
      # regression computed by the survey package should
      # take care of stratification and robust SEs
      # from the survey info
      # 
      #     # cluster sort part
      #     if(is.null(clustervar1) & !is.null(clustervar2)){
      #       stop("use clustervar1 arguement before clustervar2 arguement")
      #     }    
      #     if(!is.null(clustervar1)){
      #       if(is.null(clustervar2)){
      #         if(!(clustervar1 %in% names(data))){
      #           stop("clustervar1 not in data.frame object")
      #         }    
      #         data = data.frame(model.frame(formula, data, na.action=NULL),data[,clustervar1])
      #         names(data)[dim(data)[2]] = clustervar1
      #         data=na.omit(data)
      #       }
      #       if(!is.null(clustervar2)){
      #         if(!(clustervar1 %in% names(data))){
      #           stop("clustervar1 not in data.frame object")
      #         }    
      #         if(!(clustervar2 %in% names(data))){
      #           stop("clustervar2 not in data.frame object")
      #         }    
      #         data = data.frame(model.frame(formula, data, na.action=NULL),
      #                           data[,c(clustervar1,clustervar2)])
      #         names(data)[c(dim(data)[2]-1):dim(data)[2]] = c(clustervar1,clustervar2)
      #         data=na.omit(data)
      #       }
      #     }

      # fit the probit regression
      fit = svyglm(formula, 
                   design=design, 
                   family = quasibinomial(link = "probit"), 
                   x=T
      )
      # TS: summary(fit)

      # terms needed
      x1 = model.matrix(fit)
      if (any(alias <- is.na(coef(fit)))) {   # this conditional removes any vars with a NA coefficient
        x1 <- x1[, !alias, drop = FALSE]
      }

      xm = as.matrix(svymean(x1,design)) # calculate means of x variables
      be = as.matrix(na.omit(coef(fit))) # collect coefficients: be as in beta
      k1 = length(na.omit(coef(fit))) # collect number of coefficients or x variables
      xb = t(xm) %*% be # get the matrix product of xMean and beta, which is the model prediction at the mean
      fxb = ifelse(atmean==TRUE, dnorm(xb), mean(dnorm(x1 %*% be))) # collect either the overall predicted mean, or the average of every observation's predictions

      # get variances
      vcv = vcov(fit)

      # from Fernihough's original mfx function
      # I dont think this is needed because the  
      # regression computed by the survey package should
      # take care of stratification and robust SEs
      # from the survey info
      # 
      #     if(robust){
      #       if(is.null(clustervar1)){
      #         # white correction
      #         vcv = vcovHC(fit, type = "HC0")
      #       } else {
      #         if(is.null(clustervar2)){
      #           vcv = clusterVCV(data=data, fm=fit, cluster1=clustervar1,cluster2=NULL)
      #         } else {
      #           vcv = clusterVCV(data=data, fm=fit, cluster1=clustervar1,cluster2=clustervar2)
      #         }
      #       }
      #     }
      #     
      #     if(robust==FALSE & is.null(clustervar1)==FALSE){
      #       if(is.null(clustervar2)){
      #         vcv = clusterVCV(data=data, fm=fit, cluster1=clustervar1,cluster2=NULL)
      #       } else {
      #         vcv = clusterVCV(data=data, fm=fit, cluster1=clustervar1,cluster2=clustervar2)
      #       }
      #     }

      # set mfx equal to predicted mean (or other value) multiplied by beta
      mfx = data.frame(mfx=fxb*be, se=NA)

      # get standard errors
      if(atmean){#    fxb *  id matrix - avg model prediction * (beta X xmean)
        gr = as.numeric(fxb)*(diag(k1) - as.numeric(xb) *(be %*% t(xm)))
        mfx$se = sqrt(diag(gr %*% vcv %*% t(gr)))            
      } else {
        gr = apply(x1, 1, function(x){
          as.numeric(as.numeric(dnorm(x %*% be))*(diag(k1) - as.numeric(x %*% be)*(be %*% t(x))))
        })
        gr = matrix(apply(gr,1,mean),nrow=k1)
        mfx$se = sqrt(diag(gr %*% vcv %*% t(gr)))                
      }

      # pick out constant and remove from mfx table
      temp1 = apply(x1,2,function(x)length(table(x))==1)
      const = names(temp1[temp1==TRUE])
      mfx = mfx[row.names(mfx)!=const,]

      # pick out discrete change variables
      temp1 = apply(x1,2,function(x)length(table(x))==2)
      disch = names(temp1[temp1==TRUE])

      # calculate the disctrete change marginal effects and standard errors
      if(length(disch)!=0){
        for(i in 1:length(disch)){
          if(atmean){
            disx0 = disx1 = xm
            disx1[disch[i],] = max(x1[,disch[i]])
            disx0[disch[i],] = min(x1[,disch[i]])
            # mfx equal to    prediction @ x=1     minus prediction @ x=0
            mfx[disch[i],1] = pnorm(t(be) %*% disx1) - pnorm(t(be) %*% disx0)
            # standard errors
            gr = dnorm(t(be) %*% disx1) %*% t(disx1) - dnorm(t(be) %*% disx0) %*% t(disx0)
            mfx[disch[i],2] = sqrt(gr %*% vcv %*% t(gr))
          } else {
            disx0 = disx1 = x1
            disx1[,disch[i]] = max(x1[,disch[i]])
            disx0[,disch[i]] = min(x1[,disch[i]])  
            mfx[disch[i],1] = mean(pnorm(disx1 %*% be) - pnorm(disx0 %*% be))
            # standard errors
            gr = as.numeric(dnorm(disx1 %*% be)) * disx1 - as.numeric(dnorm(disx0 %*% be)) * disx0
            avegr = as.matrix(colMeans(gr))
            mfx[disch[i],2] = sqrt(t(avegr) %*% vcv %*% avegr)
          }
        }
      } 
      mfx$discretechgvar = ifelse(rownames(mfx) %in% disch, 1, 0)
      output = list(fit=fit, mfx=mfx)
      return(output)
    }



  probitMfxSurv <-
    function(formula, 
             design, 
             atmean = TRUE, 
             robust = FALSE, 
             clustervar1 = NULL, 
             clustervar2 = NULL, 
             start = NULL 
             #           control = list() # this option is found in original mfx package
    )
    {
      #    res = probitMfxEstSurv(formula, design, atmean, robust, clustervar1, clustervar2, start, control)
      res = probitMfxEstSurv(formula, design, atmean, robust, clustervar1, clustervar2, start)

      est = NULL
      est$mfxest = cbind(dFdx = res$mfx$mfx,
                         StdErr = res$mfx$se,
                         z.value = res$mfx$mfx/res$mfx$se,
                         p.value = 2*pt(-abs(res$mfx$mfx/res$mfx$se), df = Inf))
      colnames(est$mfxest) = c("dF/dx","Std. Err.","z","P>|z|")
      rownames(est$mfxest) =  rownames(res$mfx)

      est$fit = res$fit
      est$dcvar = rownames(res$mfx[res$mfx$discretechgvar==1,])  
      est$call = match.call() 
      class(est) = "probitmfx"
      est
    }

Example

  # initialize sample data
  nObs = 100
  x1 = rbinom(nObs,1,.5)
  x2 = rbinom(nObs,1,.3)
  #x3 = rbinom(100,1,.9)
  x3 = runif(nObs,0,.9)

  id = 1:nObs
  w1 = sample(c(10,50,100),nObs,replace=TRUE)
  #   dependnt variables
  ystar = x1 + x2 - x3 + rnorm(nObs)
  y = ifelse(ystar>0,1,0)
  #   set up data frame
  data = data.frame(id, w1, x1, x2, x3, ystar, y)

  # initialize survey
  survey.design <- svydesign(ids = data$id,
                             weights = data$w1,
                             data = data)

  mean(data$x2)
  sd(data$x2)/(length(data$x2))^0.5
  svymean(x=x2,design=survey.design)

  probit = svyglm(y~x1 + x2 + x3, design=survey.design, family=quasibinomial(link='probit'))
  summary(probit)

  probitMfxSurv(formula = y~x1 + x2 + x3, design = survey.design)