survey (version 2.8-1)

svyCprod: Computations for survey variances

Description

Computes the sum of products needed for the variance of survey sample estimators.

Usage

svyCprod(x, strata, psu, fpc, nPSU,certainty=NULL, postStrata=NULL
      lonely.psu=getOption("survey.lonely.psu"))

Arguments

x

A vector or matrix

strata

A vector of stratum indicators, or NULL

psu

A vector of cluster indicators or NULL

fpc

A data frame of population stratum sizes or NULL

nPSU

Table of original sample stratum sizes (or NULL)

certainty

logical vector with stratum names as names. If TRUE and that stratum has a single PSU it is a certainty PSU

postStrata

Post-stratification variables

lonely.psu

One of "remove", "adjust", "fail", "certainty", "average". See Details below

Value

• A covariance matrix

Details

The observations for each cluster are added, then centered within each stratum and the outer product is taken of the row vector resulting for each cluster. This is added within strata, multiplied by a degrees-of-freedom correction and by a finite population correction (if supplied) and added across strata.

If there are fewer clusters (PSUs) in a stratum than in the original design extra rows of zeroes are added to x to allow the correct subpopulation variance to be computed.

The variance formula gives 0/0 if a stratum contains only one sampling unit. If the certainty argument specifies that this is a PSU sampled with probability 1 (a "certainty" PSU) then it does not contribute to the variance. If certainty is FALSE for this stratum or is not supplied the result depends on lonely.psu.

The options are "fail" to give an error, "remove" or "certainty" to give a variance contribution of 0 for the stratum, "adjust" to center the stratum at the grand mean rather than the stratum mean, and "average" to assign strata with one PSU the average variance contribution from strata with more than one PSU. The choice is controlled by setting options(survey.lonely.psu). If this is not done the factory default is "fail". Using "adjust" is conservative, and it would often be better to combine strata in some intelligent way. The properties of "average" have not been investigated thoroughly, but it may be useful when the lonely PSUs are due to a few strata having PSUs missing completely at random.

The "remove"and "certainty" options give the same result, but "certainty" is intended for situations where there is only one PSU in the population stratum, which is sampled with certainty (also called `self-representing' PSUs or strata). With "certainty" no warning is generated for strata with only one PSU. Ordinarily, svydesign will detect certainty PSUs, making this option unnecessary.

When a subset of a survey design has only one PSU in a stratum the standard formulas give zero for the contribution of that stratum to the variance. svyCprod will warn that this has happened, and if lonely.psu="adjust" or lonely.psu="average" will use the same adjustment as if the whole survey had only one PSU in that stratum by design.

See Also

svydesign, svy.varcoef