# [R] Hosmer- Lemeshow test

Frank E Harrell Jr f.harrell at vanderbilt.edu
Tue Sep 16 13:08:02 CEST 2008

```saggak wrote:
> Dear R - help,
>
> I am working on the Credit scorecard model. I am using the Logistic regression to arrive at the regression coefficients model.
>
> I want to use the Hosmer - Lemeshow test .
>
> In order to understand the use of R - language, I had referred the following URL
>
> Â Â Â Â Â  http://www.stat.sc.edu/~hitchcock/diseaseoutbreakRexample704.txt
>
> The related data 'diseaseoutbreak' is available at the following URL
>
> Â Â Â Â Â Â  http://www.stat.sc.edu/~hitchcock/diseaseoutbreakdata.txt
>
> The R code as mentioned therein is
>
> ####
> # A function to do the Hosmer-Lemeshow test in R.
> # R Function is due to Peter D. M. Macdonald, McMaster University.
> #
> hosmerlem <-
> function (y, yhat, g = 10)
> {
>     cutyhat <- cut(yhat, breaks = quantile(yhat, probs = seq(0,
>         1, 1/g)), include.lowest = T)
>     obs <- xtabs(cbind(1 - y, y) ~ cutyhat)
>     expect <- xtabs(cbind(1 - yhat, yhat) ~ cutyhat)
>     chisq <- sum((obs - expect)^2/expect)
>     P <- 1 - pchisq(chisq, g - 2)
>     c("X^2" = chisq, Df = g - 2, "P(>Chi)" = P)
> }
> #
> ######
>
> # Doing the Hosmer-Lemeshow test
> # (after copying the above function into R):
>
> hosmerlem(disease, fitted(disease.logit))
> However when I ran these commands / functions in R, I got following errors
>
> Error in model.frame.default(formula = cbind(1 - y, y) ~ cutyhat) :
> Â  invalid type (list) for variable 'cbind(1 - y, y)'
>
> Can anyone please guide me as to how to run Hosmer- Lemeshow test, as also how to find out the other usual logistic regression related "Log - likelihood, AIC, Pseudo R etc"?
>
> Thanking you all in advance
>
> Saggak

That test is too dependent on cutpoints and does not have adequate power
.  I recommend replacing it with

@ARTICLE{hos97com,
author = {Hosmer, D. W. and Hosmer, T. and {le Cessie}, S. and
Lemeshow, S.},
year = 1997,
title = {A comparison of goodness-of-fit tests for the logistic
regression
model},
journal = Statistics in Medicine,
volume = 16,
pages = {965-980},
annote = {goodness-of-fit for binary logistic model;difficulty with
Hosmer-Lemeshow statistic being dependent on how groups are
defined;sum of squares test;cumulative sum test;invalidity
of naive