R: Wald test for a term in a regression model

regTermTest {survey} | R Documentation

## Wald test for a term in a regression model

### Description

Provides Wald test and working likelihood ratio (Rao-Scott) test of the hypothesis that all coefficients associated with a particular regression term are zero (or have some other specified values). Particularly useful as a substitute for `anova` when not fitting by maximum likelihood. The Wald tests use a chisquared or F distribution, the LRT uses a linear combination of chisquared or F distributions as in `pchisqsum`.

### Usage

    regTermTest(model, test.terms, null=NULL,df=NULL,
    method=c("Wald","LRT"), lrt.approximation="saddlepoint")

### Arguments

`model` | A model object with `coef` and `vcov` methods
`test.terms` | Character string or one-sided formula giving name of term or terms to test
`null` | Null hypothesis values for parameters. Default is zeros
`df` | Denominator degrees of freedom for an F test. If `NULL` these are estimated from the model. Use `Inf` for a chi-squared test.
`method` | If `"Wald"`, the Wald-type test; if `"LRT"` the Rao-Scott test based on the estimated log likelihood ratio
`lrt.approximation` | method for approximating the distribution of the LRT statistic; see `pchisqsum`

### Value

An object of class `regTermTest` or `regTermTestLRT`.

### Note

The `"LRT"` method will not work if the model had starting values supplied for the regression coefficients. Instead, fit the two models separately and use `anova(model1, model2, force=TRUE)`

### References

Rao, JNK, Scott, AJ (1984) "On Chi-squared Tests For Multiway Contingency Tables with Proportions Estimated From Survey Data" Annals of Statistics 12:46-60.

Lumley T, Scott A (2012) "Partial likelihood ratio tests for the Cox model under complex sampling" Statistics in Medicine 17 JUL 2012. DOI: 10.1002/sim.5492

Lumley T, Scott A (2014) "Tests for Regression Models Fitted to Survey Data" Australian and New Zealand Journal of Statistics 56:1-14 DOI: 10.1111/anzs.12065

### See Also

`anova`, `vcov`, `contrasts`,`pchisqsum`

### Examples

     data(esoph)
     model1 <- glm(cbind(ncases, ncontrols) ~ agegp + tobgp *
         alcgp, data = esoph, family = binomial())
     anova(model1)

     regTermTest(model1,"tobgp")
     regTermTest(model1,"tobgp:alcgp")
     regTermTest(model1, ~alcgp+tobgp:alcgp)

     data(api)
     dclus2<-svydesign(id=~dnum+snum, weights=~pw, data=apiclus2)
     model2<-svyglm(I(sch.wide=="Yes")~ell+meals+mobility, design=dclus2, family=quasibinomial())
     regTermTest(model2, ~ell)
     regTermTest(model2, ~ell,df=NULL)
     regTermTest(model2, ~ell, method="LRT", df=Inf)
     regTermTest(model2, ~ell+meals, method="LRT", df=NULL)

[Package survey version 3.32-1 Index]