Wald test for a term in a regression model

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.

regTermTest(model, test.terms, null=NULL,df=NULL,
method=c("Wald","WorkingWald","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; 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

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)

Examples

 data(esoph)
 model1 <- glm(cbind(ncases, ncontrols) ~ agegp + tobgp * 
     alcgp, data = esoph, family = binomial())
 anova(model1)
#> Analysis of Deviance Table
#> 
#> Model: binomial, link: logit
#> 
#> Response: cbind(ncases, ncontrols)
#> 
#> Terms added sequentially (first to last)
#> 
#> 
#>             Df Deviance Resid. Df Resid. Dev
#> NULL                           87     367.95
#> agegp        5  121.045        82     246.91
#> tobgp        3   36.639        79     210.27
#> alcgp        3  127.933        76      82.34
#> tobgp:alcgp  9    5.451        67      76.89

 regTermTest(model1,"tobgp")
#> Wald test for tobgp
#>  in glm(formula = cbind(ncases, ncontrols) ~ agegp + tobgp * alcgp, 
#>     family = binomial(), data = esoph)
#> F =  6.080611  on  3  and  67  df: p= 0.0010073 
 regTermTest(model1,"tobgp:alcgp")
#> Wald test for tobgp:alcgp
#>  in glm(formula = cbind(ncases, ncontrols) ~ agegp + tobgp * alcgp, 
#>     family = binomial(), data = esoph)
#> F =  0.5880663  on  9  and  67  df: p= 0.80234 
 regTermTest(model1, ~alcgp+tobgp:alcgp)
#> Wald test for alcgp alcgp:tobgp
#>  in glm(formula = cbind(ncases, ncontrols) ~ agegp + tobgp * alcgp, 
#>     family = binomial(), data = esoph)
#> F =  8.358247  on  12  and  67  df: p= 2.2352e-09 


 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)
#> Wald test for ell
#>  in svyglm(formula = I(sch.wide == "Yes") ~ ell + meals + mobility, 
#>     design = dclus2, family = quasibinomial())
#> F =  6.055448  on  1  and  36  df: p= 0.018792 
 regTermTest(model2, ~ell,df=NULL)
#> Wald test for ell
#>  in svyglm(formula = I(sch.wide == "Yes") ~ ell + meals + mobility, 
#>     design = dclus2, family = quasibinomial())
#> F =  6.055448  on  1  and  36  df: p= 0.018792 
 regTermTest(model2, ~ell, method="LRT", df=Inf)
#> Working (Rao-Scott) LRT for ell
#>  in svyglm(formula = I(sch.wide == "Yes") ~ ell + meals + mobility, 
#>     design = dclus2, family = quasibinomial())
#> Working 2logLR =  6.781297 p= 0.0096772 
#> df=1
 regTermTest(model2, ~ell+meals, method="LRT", df=NULL)
#> Working (Rao-Scott+F) LRT for ell meals
#>  in svyglm(formula = I(sch.wide == "Yes") ~ ell + meals + mobility, 
#>     design = dclus2, family = quasibinomial())
#> Working 2logLR =  4.692659 p= 0.11957 
#> (scale factors:  1.6 0.37 );  denominator df= 36

 regTermTest(model2, ~ell+meals, method="WorkingWald", df=NULL)
#> Working (Rao-Scott+F)  for ell meals
#>  in svyglm(formula = I(sch.wide == "Yes") ~ ell + meals + mobility, 
#>     design = dclus2, family = quasibinomial())
#> Working Wald statistic =  4.196737 p= 0.14263 
#> (scale factors:  1.6 0.37 );  denominator df= 36