Example 8.8: more Hosmer and Lemeshow

This is a special R-only entry.

In Example 8.7, we showed the Hosmer and Lemeshow goodness-of-fit test. Today we demonstrate more advanced computational approaches for the test.

If you write a function for your own use, it hardly matters what it looks like, as long as it works. But if you want to share it, you might build in some warnings or error-checking, since the user won't know its limitations the way you do. (This is likely good advice even if you are the only one to use your code!)

In R, you can add another layer of detail so that your function conforms to standards for built-in functions. This is a level of detail we don't pursue in our book, but is worth doing in many settings. Here we provided a modified version of a Hosmer-Lemeshow test sent to us by Stephen Taylor of the Auckland University of Technology. We've added a few annotations.

Note that the function accepts a glm object, rather than the two vectors our function used.

hosmerlem2 = function(obj, g=10) {
# first, check to see if we fed in the right kind of object
   stopifnot(family(obj)$family=="binomial" && family(obj)$link=="logit")
   y = obj$model[[1]]
   # the double bracket (above) gets the index of items within an object
   if (is.factor(y)) 
      y = as.numeric(y)==2
   yhat = obj$fitted.values
   cutyhat = cut(yhat, quantile(yhat, 0:g/g), include.lowest=TRUE)
   obs = xtabs(cbind(1 - y, y) ~ cutyhat)
   expect = xtabs(cbind(1 - yhat, yhat) ~ cutyhat)
   if (any(expect < 5))
      warning("Some expected counts are less than 5. Use smaller number of groups")
   chisq = sum((obs - expect)^2/expect)
   P = 1 - pchisq(chisq, g - 2)
   # by returning an object of class "htest", the function will perform like the 
   # built-in hypothesis tests
   return(structure(list(
      method = c(paste("Hosmer and Lemeshow goodness-of-fit test with", g, "bins", sep=" ")),
      data.name = deparse(substitute(obj)),
      statistic = c(X2=chisq),
      parameter = c(df=g-2),
      p.value = P
   ), class='htest'))
}

We can run this using last entry's data from the HELP study.

ds = read.csv("http://www.math.smith.edu/r/data/help.csv")
attach(ds)
logreg = glm(homeless ~ female + i1 + cesd + age + substance,
  family=binomial)

The results are the same as before:

> hosmerlem2(logreg)
 Hosmer and Lemeshow goodness-of-fit test with 10 bins

data:  logreg 
X2 = 8.4954, df = 8, p-value = 0.3866