First Differences of a Bayesian Logit or Probit model

R function to calculate first differences after a Bayesian logit or probit model. First differences are a method to summarize effects across covariates. This quantity represents the difference in predicted probabilities for each covariate for cases with low and high values of the respective covariate. For each of these differences, all other variables are held constant at their median. For more, see Long (1997, Sage Publications) and King, Tomz, and Wittenberg (2000, American Journal of Political Science 44(2): 347-361).

mcmcFD(
  modelmatrix,
  mcmcout,
  link = "logit",
  ci = c(0.025, 0.975),
  percentiles = c(0.25, 0.75),
  fullsims = FALSE
)

Arguments

modelmatrix: model matrix, including intercept (if the intercept is among the parameters estimated in the model). Create with model.matrix(formula, data). Note: the order of columns in the model matrix must correspond to the order of columns in the matrix of posterior draws in the mcmcout argument. See the mcmcout argument for more.
mcmcout: posterior distributions of all logit coefficients, in matrix form. This can be created from rstan, MCMCpack, R2jags, etc. and transformed into a matrix using the function as.mcmc() from the coda package for jags class objects, as.matrix() from base R for mcmc, mcmc.list, stanreg, and stanfit class objects, and object$sims.matrix for bugs class objects. Note: the order of columns in this matrix must correspond to the order of columns in the model matrix. One can do this by examining the posterior distribution matrix and sorting the variables in the order of this matrix when creating the model matrix. A useful function for sorting column names containing both characters and numbers as you create the matrix of posterior distributions is mixedsort() from the gtools package.
link: type of generalized linear model; a character vector set to "logit" (default) or "probit".
ci: the bounds of the credible interval. Default is c(0.025, 0.975) for the 95% credible interval.
percentiles: values of each predictor for which the difference in Pr(y = 1) is to be calculated. Default is c(0.25, 0.75), which will calculate the difference between Pr(y = 1) for the 25th percentile and 75th percentile of the predictor. For binary predictors, the function automatically calculates the difference between Pr(y = 1) for x = 0 and x = 1.
fullsims: logical indicator of whether full object (based on all MCMC draws rather than their average) will be returned. Default is FALSE.

Value

An object of class mcmcFD. If fullsims = FALSE (default), a data frame with five columns:

median_fd: median first difference
lower_fd: lower bound of credible interval of the first difference
upper_fd: upper bound of credible interval of the first difference
VarName: name of the variable as found in modelmatrix
VarID: identifier of the variable, based on the order of columns in modelmatrix and mcmcout. Can be adjusted for plotting

If fullsims = TRUE, a matrix with as many columns as predictors in the model. Each row is the first difference for that variable based on one set of posterior draws. Column names are taken from the column names of modelmatrix.

References

King, Gary, Michael Tomz, and Jason Wittenberg. 2000. “Making the Most of Statistical Analyses: Improving Interpretation and Presentation.” American Journal of Political Science 44 (2): 347–61. http://www.jstor.org/stable/2669316
Long, J. Scott. 1997. Regression Models for Categorical and Limited Dependent Variables. Thousand Oaks: Sage Publications

Examples

# \donttest{
if (interactive()) {
## simulating data
set.seed(1234)
b0 <- 0.2 # true value for the intercept
b1 <- 0.5 # true value for first beta
b2 <- 0.7 # true value for second beta
n <- 500 # sample size
X1 <- runif(n, -1, 1)
X2 <- runif(n, -1, 1)
Z <- b0 + b1 * X1 + b2 * X2
pr <- 1 / (1 + exp(-Z)) # inv logit function
Y <- rbinom(n, 1, pr) 
df <- data.frame(cbind(X1, X2, Y))

## formatting the data for jags
datjags <- as.list(df)
datjags$N <- length(datjags$Y)

## creating jags model
model <- function()  {
  
  for(i in 1:N){
    Y[i] ~ dbern(p[i])  ## Bernoulli distribution of y_i
    logit(p[i]) <- mu[i]    ## Logit link function
    mu[i] <- b[1] + 
      b[2] * X1[i] + 
      b[3] * X2[i]
  }
  
  for(j in 1:3){
    b[j] ~ dnorm(0, 0.001) ## Use a coefficient vector for simplicity
  }
  
}

params <- c("b")
inits1 <- list("b" = rep(0, 3))
inits2 <- list("b" = rep(0, 3))
inits <- list(inits1, inits2)

## fitting the model with R2jags
set.seed(123)
fit <- R2jags::jags(data = datjags, inits = inits, 
                    parameters.to.save = params, n.chains = 2, n.iter = 2000, 
                    n.burnin = 1000, model.file = model)

## running function with logit
xmat <- model.matrix(Y ~ X1 + X2, data = df)
mcmc <- coda::as.mcmc(fit)
mcmc_mat <- as.matrix(mcmc)[, 1:ncol(xmat)]
object <- mcmcFD(modelmatrix = xmat,
                 mcmcout = mcmc_mat)
object
}
# }