HLtest: Hosmer-Lemeshow Goodness of Fit Test

Description

The HLtest function computes the classical Hosmer-Lemeshow (1980) goodness of fit test for a binomial glm object in logistic regression

The general idea is to assesses whether or not the observed event rates match expected event rates in subgroups of the model population. The Hosmer-Lemeshow test specifically identifies subgroups as the deciles of fitted event values, or other quantiles as determined by the g argument. Given these subgroups, a simple chisquare test on g-2 df is used.

In addition to print and summary methods, a plot method is supplied to visualize the discrepancies between observed and fitted frequencies.

Usage

HosmerLemeshow(model, g = 10)
HLtest(model, g = 10)
# S3 method for HLtest
print(x, ...)
# S3 method for HLtest
summary(object, ...)
# S3 method for HLtest
plot(x, ...)
# S3 method for HLtest
rootogram(x, ...)

Arguments

model

A glm model object in the binomial family

Number of groups used to partition the fitted values for the GOF test.

x, object

A HLtest object

…

Other arguments passed down to methods

Value

A class HLtest object with the following components:

table

A data.frame describing the results of partitioning the data into g groups with the following columns: cut, total, obs, exp, chi

chisq

The chisquared statistics

Degrees of freedom

p.value

p value

groups

Number of groups

call

model call

%% ...

References

Hosmer, David W., Lemeshow, Stanley (1980). A goodness-of-fit test for multiple logistic regression model. Communications in Statistics, Series A, 9, 1043-1069.

Hosmer, David W., Lemeshow, Stanley (2000). Applied Logistic Regression, New York: Wiley, ISBN 0-471-61553-6

Lemeshow, S. and Hosmer, D.W. (1982). A review of goodness of fit statistics for use in the development of logistic regression models. American Journal of Epidemiology, 115(1), 92-106.

Examples

Run this code

# NOT RUN {
data(birthwt, package="MASS")
# how to do this without attach?
attach(birthwt)
	race = factor(race, labels = c("white", "black", "other"))
	ptd = factor(ptl > 0)
	ftv = factor(ftv)
	levels(ftv)[-(1:2)] = "2+"
	bwt <- data.frame(low = factor(low), age, lwt, race,
    	smoke = (smoke > 0), ptd, ht = (ht > 0), ui = (ui > 0), ftv)
detach(birthwt)
options(contrasts = c("contr.treatment", "contr.poly"))
BWmod <- glm(low ~ ., family=binomial, data=bwt)

(hlt <- HLtest(BWmod))
str(hlt)
summary(hlt)
plot(hlt)

# basic model
BWmod0 <- glm(low ~ age, family=binomial, data=bwt)
(hlt0 <- HLtest(BWmod0))
str(hlt0)
summary(hlt0)
plot(hlt0)


# }