R/pulkrob.chisq.R

In generalhoslem: Goodness of Fit Tests for Logistic Regression Models

pulkrob.chisq <- function(model, catvars) {
  epi.cp.pulkrob <- function(dat){
    # adapted from epiR::epi.cp() by Mark Stevenson et al
    ndat <- data.frame(id = 1:nrow(dat), dat)
    if (!is.null(dim(ndat[, ncol(ndat):2]))) {
      ndat$indi <- apply(X = ndat[, ncol(ndat):2], MARGIN = 1, FUN = function(x) as.factor(paste(x, collapse = "")))
      cp.id <- tapply(ndat$id, ndat$indi, function(x) paste(x, collapse = ","))
      cp <- unique(ndat[, 2:ncol(ndat)])
      n <- as.numeric(unlist(lapply(strsplit(cp.id, ","), length)))
      id <- tapply(ndat$id, ndat$indi, function(x) (x)[1])
      lookup <- data.frame(id = 1:length(n), indi = row.names(id))
      cov.pattern <- data.frame(id = 1:length(n), n, cp[,-ncol(cp)])
      rownames(cov.pattern) <- rownames(cp)
      id <- lookup$id[match(ndat$indi, lookup$indi)]
    } else {
      cp.id <- tapply(ndat$id, ndat[2], function(x) paste(x, collapse = ","))
      cp <- unique(ndat[, 2:ncol(ndat)])
      n <- as.numeric(unlist(lapply(strsplit(cp.id, ","), length)))
      cov.pattern <- data.frame(id = 1:length(n), n, cp)
      id <- cov.pattern$id[match(as.vector(as.matrix(ndat[2])), cov.pattern$cp)]
    }
    list(cov.pattern = cov.pattern, id = id)
  }
  if (class(model) == "polr") {
    yhat <- as.data.frame(fitted(model))
  } else if (class(model) == "clm") {
    predprob <- model$model[, 2:ncol(model$model), drop = F]
    yhat <- as.data.frame(predict(model, newdata = predprob, type = "prob")$fit)
  } else warning("Model is not of class polr or clm. Test may fail.")
  formula <- formula(model$terms)
  DNAME <- paste("formula: ", deparse(formula))
  METHOD <- "Pulkstenis-Robinson chi-squared test"
  covars <- model$model[-1]
  covars <- covars[names(covars) %in% catvars]
  covpat <- epi.cp.pulkrob(covars)
  yhat$score <- apply(sapply(1:ncol(yhat), function(i) { yhat[, i] * i }), 1, sum)
  yhat <- cbind(id=1:nrow(yhat), yhat, covpat=covpat$id)
  medians <- cbind(covpat=covpat$cov.pattern$id,
                   med=sapply(covpat$cov.pattern$id, function(x) median(yhat[yhat$covpat==x, ]$score)))
  yhat <- merge(x = yhat, y = medians, by = "covpat", all.x = TRUE)
  yhat$covpatsplit <- sapply(1:nrow(yhat), function(i) ifelse(yhat[i, ]$score <= yhat[i, ]$med,
                                                              paste0(yhat[i, ]$covpat, "a"),
                                                              paste0(yhat[i, ]$covpat, "b")))
  dfobs <- cbind(id=1:nrow(model$model), model$model[1])
  dfobs <- merge(x = dfobs, y = yhat[, c("id", "covpatsplit")], by = "id", all.x = TRUE)
  dfobsmelt <- melt(dfobs[, -1], id.vars = "covpatsplit")
  observed <- cast(dfobsmelt, covpatsplit ~ value, length)                           
  observed.cols <- observed[, names(observed[, 2:ncol(observed)])]
  observed.cols <- observed.cols[order(names(observed[, 2:ncol(observed)]))]
  observed <- cbind(covatsplit = observed[, 1], observed.cols)
  dfexp <- yhat[, !colnames(yhat) %in% c("id", "covpat", "med", "score")]
  dfexpmelt <- melt(dfexp, id.vars = ncol(dfexp))
  expected <- cast(dfexpmelt, covpatsplit ~ variable, sum)
  expected.cols <- expected[, names(expected[, 2:ncol(expected)])]
  expected.cols <- expected.cols[order(names(expected[, 2:ncol(expected)]))]
  expected <- cbind(covatsplit = expected[, 1], expected.cols)
  stddiffs <- abs(observed[, 2:ncol(observed)] - expected[, 2:ncol(expected)]) / sqrt(expected[, 2:ncol(expected)])
  if (any(expected[, 2:ncol(expected)] < 1))
    warning("At least one cell in the expected frequencies table is < 1. Chi-square approximation may be incorrect.")
  chisq <- sum((observed[, 2:ncol(observed)] - expected[, 2:ncol(expected)])^2 / expected[, 2:ncol(expected)])
  I2 <- nrow(observed)
  J <- length(levels(as.factor(model$model[, 1])))
  k <- length(catvars)
  PARAMETER <- ((I2 - 1) * (J - 1)) - k - 1
  PVAL <- 1 - pchisq(chisq, PARAMETER)
  names(chisq) <- "X-squared"
  names(PARAMETER) <- "df"
  structure(list(statistic = chisq, parameter = PARAMETER, 
                 p.value = PVAL, method = METHOD, data.name = DNAME, observed = observed, 
                 expected = expected, stddiffs = stddiffs), class = "htest")
}