glmtoolbox (version 0.1.12)

anova2: Comparison of nested Generalized Linear Models

Description

Allows to compare nested generalized linear models using Wald, score, gradient, and likelihood ratio tests.

Usage

anova2(
  object,
  ...,
  test = c("wald", "lr", "score", "gradient"),
  verbose = TRUE
)

Value

A matrix with three columns which contains the following:

Chi

The value of the statistic of the test.

Df

The number of degrees of freedom.

Pr(>Chi)

The p-value of the test computed using the Chi-square distribution.

Arguments

object

an object of the class glm which is obtained from the fit of a generalized linear model.

...

another objects of the class glm which are obtained from the fit of generalized linear models.

test

an (optional) character string indicating the required type of test. The available options are: Wald ("wald"), Rao's score ("score"), Terrell's gradient ("gradient"), and likelihood ratio ("lr") tests. As default, test is set to "wald".

verbose

an (optional) logical indicating if should the report of results be printed. As default, verbose is set to TRUE.

Details

The Wald, Rao's score and Terrell's gradient tests are performed using the expected Fisher information matrix.

References

Buse A. (1982) The Likelihood Ratio, Wald, and Lagrange Multiplier Tests: An Expository Note. The American Statistician 36, 153-157.

Terrell G.R. (2002) The gradient statistic. Computing Science and Statistics 34, 206 – 215.

Examples

## Example 1
Auto <- ISLR::Auto
fit1 <- glm(mpg ~ weight, family=inverse.gaussian("log"), data=Auto)
fit2 <- update(fit1, . ~ . + horsepower)
fit3 <- update(fit2, . ~ . + horsepower:weight)
anova2(fit1, fit2, fit3, test="lr")
anova2(fit1, fit2, fit3, test="score")
anova2(fit1, fit2, fit3, test="wald")
anova2(fit1, fit2, fit3, test="gradient")

## Example 2
burn1000 <- aplore3::burn1000
mod <- death ~ age + tbsa + inh_inj
fit1 <- glm(mod, family=binomial("logit"), data=burn1000)
fit2 <- update(fit1, . ~ . + inh_inj + age*inh_inj + tbsa*inh_inj)
anova2(fit1, fit2, test="lr")
anova2(fit1, fit2, test="score")
anova2(fit1, fit2, test="wald")
anova2(fit1, fit2, test="gradient")

## Example 3
data(aucuba)
fit <- glm(lesions ~ 1 + time, family=poisson("log"), data=aucuba)
anova2(fit, test="lr")
anova2(fit, test="score")
anova2(fit, test="wald")
anova2(fit, test="gradient")