binomTools (version 1.0-1)

HLtest.Rsq: Goodness-of-fit tests for GLMs for binary data

Description

Goodness-of-fit tests for GLMs for binary data including the Hosmer-Lemeshow decile test and X-squared test with normal approximation.

Usage

## S3 method for class 'Rsq':
HLtest(object, method = c("deciles", "fixed"),
         decile.type = 8, ...)

## S3 method for class 'HLtest.Rsq':
print(x, digits = getOption("digits"), ...)

## S3 method for class 'Rsq':
X2GOFtest(x, ...)

## S3 method for class 'X2GOFtest.Rsq':
print(x, ...)

Arguments

object

An Rsq object

x

An HLtest.Rsq or an X2GOFtest.Rsq object

method

The type of Hosmer-Lemeshow test to be performed. The "deciles" method should be more accurate (Hosmer et al, 1997)

decile.type

The quantile computation method; see quantile for details

digits

the desired number of printed digits

...

currently not used

Value

• For HLtest.Rsq an object of class HLtest.Rsq with components
• expected
  the expected frequencies in the 2 x 10 entries
• observed
  the observed frequencies in the 2 x 10 entries
• resid
  Pearson residuals
• X2
  the Pearson X-squared statistic
• p.value
  the p-value for the goodness-of-fit test
• method
  the method used for the test
• For X2GOFtest an object of class X2GOFtest with components
• p.value
  the p-value for the goodness-of-fit test
• z.score
  the standardized z-score for the goodness-of-fit test
• RSS
  the residual sums of squares term
• X2
  the pearson chi-squared statistic

Details

These tests are known to have very low power. They are only appropriate when the fitted frequencies are very low and when the covariate pattern dictates strictly binary observations.

References

Hosmer, D.W. and Lemeshow, S. (1980). Goodness of fit tests for the multiple logistic regression model. Communications in Statistics - Theory and Methods, A9(10), p. 1043-1069.

Examples

## Lifted from example(predict.glm):
ldose <- rep(0:5, 2)
numdead <- c(1, 4, 9, 13, 18, 20, 0, 2, 6, 10, 12, 16)
sex <- factor(rep(c("M", "F"), c(6, 6)))
SF <- cbind(numdead, numalive=20-numdead)
budworm.lg <- glm(SF ~ sex*ldose, family=binomial)
## summary(budworm.lg)

(Rsq.budworm <- Rsq(budworm.lg))

HLtest(Rsq.budworm)
HLtest(Rsq.budworm, method="fixed")
X2GOFtest(Rsq.budworm)