vdtest.lm {glmtoolbox}

Test for Varying Dispersion Parameter in Normal Linear Models

Description

Performs Rao's score test for varying dispersion parameter in weighted and unweighted normal linear models.

Usage

## S3 method for class 'lm'
vdtest(model, varformula, verbose = TRUE, ...)

Arguments

model

an object of the class lm.

varformula

an (optional) formula expression of the form ~ z1 + z2 + ... + zq indicating the potential explanatory variables for the dispersion parameter. As default, the same explanatory variables are taken as in the model for the mean.

verbose

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

...

further arguments passed to or from other methods.

Details

From the heteroskedastic normal linear model in which \log(\sigma^2)=\gamma_0 + \gamma_1z_1 + \gamma_2z_2 + ...+ \gamma_qz_q, where \sigma^2 is the dispersion parameter of the distribution of the random errors, the Rao's score test (denoted here as S) to assess the hypothesis H_0: \gamma=0 versus H_1: \gamma\neq 0 is computed, where \gamma=(\gamma_1,\ldots,\gamma_q). The corresponding p-value is computed from the chi-squared distribution with q degrees of freedom, that is, p-value = Prob[\chi^2_{q} > S]. If the object model corresponds to an unweighted normal linear model, then the test assess the assumption of constant variance, which coincides with the non-studentized Breusch-Pagan test against heteroskedasticity.

Value

a list list with components including

statistic	value of the Rao's score test (S),
df	number of degrees of freedom (q),
p.value	p-value of the test,
vars	names of explanatory variables for the dispersion parameter,

References

Breusch T.S., Pagan A.R. (1979) A simple test for heteroscedasticity and random coefficient variation. Econometrica 47, 1287–1294.

Cook R.D., Weisberg S. (1983) Diagnostics for heteroscedasticity in regression. Biometrika 70, 1–10.

See Also

vdtest.glm

Examples

###### Example 1: Fuel consumption of automobiles
fit1 <- lm(mpg ~ log(hp) + log(wt), data=mtcars)
vdtest(fit1)
vdtest(fit1,varformula = ~ hp + wt)
vdtest(fit1,varformula = ~ hp + wt + hp*wt)

###### Example 2: Species richness in plots
data(richness)
fit2 <- lm(Species ~ Biomass + pH, data=richness)
vdtest(fit2)

### The test conclusions change when the outlying observations are excluded
fit2a <- lm(Species ~ Biomass + pH, data=richness, subset=-c(1,3,18,20))
vdtest(fit2a)

###### Example 3: Gas consumption in a home before and after insulation
whiteside <- MASS::whiteside
fit3 <- lm(Gas ~ Temp + Insul + Temp*Insul, data=whiteside)
vdtest(fit3)

### The test conclusions change when the outlying observations are excluded
fit3a <- lm(Gas ~ Temp + Insul + Temp*Insul, data=whiteside, subset=-c(8,9,36,46,55))
vdtest(fit3a)