survey (version 4.1-1)

# regTermTest: Wald test for a term in a regression model

## Description

Provides Wald test and working Wald 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.

## Usage

```regTermTest(model, test.terms, null=NULL,df=NULL,

## 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; If `"WorkingWald"` the Wald-type test using the variance matrix under simple random sampling

lrt.approximation

method for approximating the distribution of the LRT and Working Wald statistic; see `pchisqsum`.

## Value

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

## Details

The Wald test uses a chisquared or F distribution. The two working-model tests come from the (misspecified) working model where the observations are independent and the weights are frequency weights. For categorical data, this is just the model fitted to the estimated population crosstabulation. The Rao-Scott LRT statistic is the likelihood ratio statistic in this model. The working Wald test statistic is the Wald statistic in this model. The working-model tests do not have a chi-squared sampling distribution: we use a linear combination of chi-squared or F distributions as in `pchisqsum`. I believe the working Wald test is what SUDAAN refers to as a "Satterthwaite adjusted Wald test".

To match other software you will typically need to use `lrt.approximation="satterthwaite"`

## 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

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

## Examples

Run this code
```# NOT RUN {
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)

regTermTest(model2, ~ell+meals, method="WorkingWald", df=NULL)

# }
```

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