# HLtest: Hosmer-Lemeshow Goodness of Fit Test In vcdExtra: 'vcd' Extensions and Additions

 HLtest R Documentation

## 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 class 'HLtest'
print(x, ...)
## S3 method for class 'HLtest'
summary(object, ...)
## S3 method for class 'HLtest'
plot(x, ...)
## S3 method for class 'HLtest'
rootogram(x, ...)

```

### Arguments

 `model` A `glm` model object in the `binomial` family `g` 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 chisquare statistics `df` Degrees of freedom `p.value` p value `groups` Number of groups `call` `model` call

Michael Friendly

### 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.

`rootogram`, ~~~

### Examples

```
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)

```

vcdExtra documentation built on April 21, 2022, 5:10 p.m.