Loglinear models

Description

Fit and compare hierarchical loglinear models for complex survey data.

Usage

svyloglin(formula, design, ...)
## S3 method for class 'svyloglin':
update(object,formula,...)
## S3 method for class 'svyloglin':
anova(object,object1,...,integrate=FALSE)
## S3 method for class 'anova.svyloglin':
print(x,pval=c("F","saddlepoint","lincom","chisq"),...)
## S3 method for class 'svyloglin':
coef(object,...,intercept=FALSE)

Arguments

Details

The loglinear model is fitted to a multiway table with probabilities estimated by svymean and with the sample size equal to the observed sample size, treating the resulting table as if it came from iid multinomial sampling, as described by Rao and Scott. The variance-covariance matrix does not include the intercept term, and so by default neither does the coef method. A Newton-Raphson algorithm is used, rather than iterative proportional fitting, so starting values are not needed.

The anova method computes the quantities that would be the score (Pearson) and likelihood ratio chi-squared statistics if the data were an iid sample. It computes four p-values for each of these, based on the exact asymptotic distribution (see pchisqsum), a saddlepoint approximateion to this distribution, a scaled chi-squared distribution, and a scaled F-distribution. When testing the two-way interaction model against the main-effects model in a two-way table the score statistic and p-values match the Rao-Scott tests computed by svychisq.

The anova method can only compare two models if they are for exactly the same multiway table (same variables and same order). The update method will help with this. It is also much faster to use update than svyloglin for a large data set: its time complexity depends only on the size of the model, not on the size of the data set.

It is not possible to fit a model using a variable created inline, eg I(x<10), since the multiway table is based on all variables used in the formula.

Value

Object of class "svyloglin"

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.

See Also

svychisq, svyglm,pchisqsum

Examples

 data(api)
 dclus1<-svydesign(id=~dnum, weights=~pw, data=apiclus1, fpc=~fpc)
 a<-svyloglin(~stype+comp.imp,dclus1)
 b<-update(a,~.^2)
 an<-anova(a,b)
 an
 print(an, pval="saddlepoint")

 ## Wald test
 regTermTest(b, ~stype:comp.imp)

 ## linear-by-linear association
 d<-update(a,~.+as.numeric(stype):as.numeric(comp.imp))
 an1<-anova(a,d)
 an1