anova.svyglm {survey}

Model comparison for glms.

Description

A method for the anova function, for use on svyglm and svycoxph objects. With a single model argument it produces a sequential anova table, with two arguments it compares the two models.

Usage

## S3 method for class 'svyglm'
anova(object, object2 = NULL, test = c("F", "Chisq"), 
 method = c("LRT", "Wald"), tolerance = 1e-05, ..., force = FALSE)
## S3 method for class 'svycoxph'
anova(object, object2=NULL,test=c("F","Chisq"),
 method=c("LRT","Wald"),tolerance=1e-5,...,force=FALSE)
## S3 method for class 'svyglm'
AIC(object,...,k=2, null_has_intercept=TRUE)
## S3 method for class 'svyglm'
BIC(object,...,maximal)
## S3 method for class 'svyglm'
extractAIC(fit,scale,k=2,..., null_has_intercept=TRUE)
## S3 method for class 'svrepglm'
extractAIC(fit,scale,k=2,..., null_has_intercept=TRUE)

Arguments

object, fit

A svyglm orsvycoxph object.

object2

Optionally, another svyglm or svycoxph object.

test

Use (linear combination of) F or chi-squared distributions for p-values. F is usually preferable.

method

Use weighted deviance difference (LRT) or Wald tests to compare models

tolerance

For models that are not symbolically nested, the tolerance for deciding that a term is common to the models.

...

For AIC and BIC, optionally more svyglm objects

scale

not used

null_has_intercept

Does the null model for AIC have an intercept or not? Must be FALSE if any of the models are intercept-only.

force

Force the tests to be done by explicit projection even if the models are symbolically nested (eg, for debugging)

maximal

A svyglm model that object (and ... if supplied) are nested in.

k

Multiplier for effective df in AIC. Usually 2. There is no choice of k that will give BIC

Details

The reference distribution for the LRT depends on the misspecification effects for the parameters being tested (Rao and Scott, 1984). If the models are symbolically nested, so that the relevant parameters can be identified just by manipulating the model formulas, anova is equivalent to regTermTest.If the models are nested but not symbolically nested, more computation using the design matrices is needed to determine the projection matrix on to the parameters being tested. In the examples below, model1 and model2 are symbolically nested in model0 because model0 can be obtained just by deleting terms from the formulas. On the other hand, model2 is nested in model1 but not symbolically nested: knowing that the model is nested requires knowing what design matrix columns are produced by stype and as.numeric(stype). Other typical examples of models that are nested but not symbolically nested are linear and spline models for a continuous covariate, or models with categorical versions of a variable at different resolutions (eg, smoking yes/no or smoking never/former/current).

A saddlepoint approximation is used for the LRT with numerator df greater than 1.

AIC is defined using the Rao-Scott approximation to the weighted loglikelihood (Lumley and Scott, 2015). It replaces the usual penalty term p, which is the null expectation of the log likelihood ratio, by the trace of the generalised design effect matrix, which is the expectation under complex sampling. For computational reasons everything is scaled so the weights sum to the sample size.

BIC is a BIC for the (approximate) multivariate Gaussian models on regression coefficients from the maximal model implied by each submodel (ie, the models that say some coefficients in the maximal model are zero) (Lumley and Scott, 2015). It corresponds to comparing the models with a Wald test and replacing the sample size in the penalty by an effective sample size. For computational reasons, the models must not only be nested, the names of the coefficients must match.

extractAIC for a model with a Gaussian link uses the actual AIC based on maximum likelihood estimation of the variance parameter as well as the regression parameters.

Value

Object of class seqanova.svyglm if one model is given, otherwise of class regTermTest or regTermTestLRT

Note

At the moment, AIC works only for models including an intercept.

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. (2014). "Tests for Regression Models Fitted to Survey Data". Australian and New Zealand Journal of Statistics, 56 (1), 1-14.

Lumley T, Scott AJ (2015) "AIC and BIC for modelling with complex survey data" J Surv Stat Methodol 3 (1): 1-18.

See Also

regTermTest, pchisqsum

Examples

data(api)
dclus2<-svydesign(id=~dnum+snum, weights=~pw, data=apiclus2)

model0<-svyglm(I(sch.wide=="Yes")~ell+meals+mobility, design=dclus2, family=quasibinomial())
model1<-svyglm(I(sch.wide=="Yes")~ell+meals+mobility+as.numeric(stype), 
     design=dclus2, family=quasibinomial())
model2<-svyglm(I(sch.wide=="Yes")~ell+meals+mobility+stype, design=dclus2, family=quasibinomial())

anova(model2)	
anova(model0,model2)					     		    
anova(model1, model2)

anova(model1, model2, method="Wald")

AIC(model0,model1, model2)
BIC(model0, model2,maximal=model2)

## AIC for linear model is different because it considers the variance
## parameter

model0<-svyglm(api00~ell+meals+mobility, design=dclus2)
model1<-svyglm(api00~ell+meals+mobility+as.numeric(stype), 
     design=dclus2)
model2<-svyglm(api00~ell+meals+mobility+stype, design=dclus2)
modelnull<-svyglm(api00~1, design=dclus2)

AIC(model0, model1, model2)

AIC(model0, model1, model2,modelnull, null_has_intercept=FALSE)

## from ?twophase
data(nwtco)
dcchs<-twophase(id=list(~seqno,~seqno), strata=list(NULL,~rel),
        subset=~I(in.subcohort | rel), data=nwtco)
a<-svycoxph(Surv(edrel,rel)~factor(stage)+factor(histol)+I(age/12), design=dcchs)
b<-update(a, .~.-I(age/12)+poly(age,3))
## not symbolically nested models
anova(a,b)