survey (version 3.9-1)

svyglm: Survey-weighted generalised linear models.

Description

Fit a generalised linear model to data from a complex survey design, with inverse-probability weighting and design-based standard errors.

Usage

## S3 method for class 'survey.design':
svyglm(formula, design, subset=NULL, ...)
## S3 method for class 'svyrep.design':
svyglm(formula, design, subset=NULL, ..., rho=NULL,
return.replicates=FALSE, na.action)
## S3 method for class 'svyglm':
summary(object, correlation = FALSE, df.resid=NULL,
...)
## S3 method for class 'svyglm':
predict(object,newdata,total=NULL,
                         type=c("link","response"),se=TRUE,vcov=TRUE,...)

Arguments

formula

Model formula

design

Survey design from svydesign or svrepdesign. Must contain all variables in the formula

subset

Expression to select a subpopulation

...

Other arguments passed to glm or summary.glm

rho

For replicate BRR designs, to specify the parameter for Fay's variance method, giving weights of rho and 2-rho

return.replicates

Return the replicates as a component of the result?

object

A svyglm object

correlation

Include the correlation matrix of parameters?

na.action

Handling of NAs

df.resid

Optional denominator degrees of freedom for Wald tests

newdata

new data frame for prediction

total

population size when predicting population total

type

linear predictor (link) or response

se

if TRUE, return variances of predictions

vcov

if TRUE and se=TRUE return variance-covariance matrix of predictions

Value

• svyglm returns an object of class svyglm. The predict method returns an object of class svystat

Details

There is no anova method for svyglm as the models are not fitted by maximum likelihood. The function regTermTest may be useful for testing sets of regression terms.

If df.resid is not specified the df for the null model is computed by degf and the residual df computed by subtraction. It's not that these are particularly good approximations in a regression model but they are relatively standard. To get tests based on a Normal distribution use df.resid=Inf.

predict gives fitted values and sampling variability for specific new values of covariates. When newdata are the population mean it gives the regression estimator of the mean, and when newdata are the population totals and total is specified it gives the regression estimator of the population total. Regression estimators of mean and total can also be obtained with calibrate.

By default the variance-covariance matrix of the predictions is returned. If newdata has many rows this may be very large.

See Also

svydesign, glm, regTermTest,

calibrate

Examples

data(api)

  glm(api00~ell+meals+mobility, data=apipop)

  dstrat<-svydesign(id=~1,strata=~stype, weights=~pw, data=apistrat, fpc=~fpc)
  dclus2<-svydesign(id=~dnum+snum, weights=~pw, data=apiclus2)
  rstrat<-as.svrepdesign(dstrat)
  rclus2<-as.svrepdesign(dclus2)

  summary(svyglm(api00~ell+meals+mobility, design=dstrat))
  summary(svyglm(api00~ell+meals+mobility, design=dclus2))
  summary(svyglm(api00~ell+meals+mobility, design=rstrat))
  summary(svyglm(api00~ell+meals+mobility, design=rclus2))

  ## use quasibinomial, quasipoisson to avoid warning messages
  summary(svyglm(sch.wide~ell+meals+mobility, design=dstrat,
        family=quasibinomial()))


  ## Compare regression and ratio estimation of totals
  api.ratio <- svyratio(~api.stu,~enroll, design=dstrat)
  pop<-data.frame(enroll=sum(apipop$enroll, na.rm=TRUE))
  npop <- nrow(apipop)
  predict(api.ratio, pop$enroll)

  ## regression estimator is less efficient
  api.reg <- svyglm(api.stu~enroll, design=dstrat)
  predict(api.reg, newdata=pop, total=npop)
  ## same as calibration estimator
  svytotal(~api.stu, calibrate(dstrat, ~enroll, pop=c(npop, pop$enroll)))

  ## svyglm can also reproduce the ratio estimator
  api.reg2 <- svyglm(api.stu~enroll-1, design=dstrat,
                    family=quasi(link="identity",var="mu"))
  predict(api.reg2, newdata=pop, total=npop)

  ## higher efficiency by modelling variance better
  api.reg3 <- svyglm(api.stu~enroll-1, design=dstrat,
                    family=quasi(link="identity",var="mu^3"))
  predict(api.reg3, newdata=pop, total=npop)
  ## true value
  sum(apipop$api.stu)