svyglm

From survey v3.9-1 by Thomas Lumley

Survey-weighted generalised linear models.

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

Keywords: regression, survey

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

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.

Value

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

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)

Documentation reproduced from package survey, version 3.9-1, License: GPL-2 | GPL-3

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