##### https://github.com/cran/lavaan.survey

Tip revision:

**86e6cf8abb72a283862946ed4a502d4c84506729**authored by**Daniel Oberski**on**25 October 2012, 00:00 UTC****version 0.5** Tip revision:

**86e6cf8** lavaan.survey.Rd

```
\name{lavaan.survey}
\alias{lavaan.survey}
\title{
Complex survey analysis of structural equation models (SEM)
}
\description{
Takes a lavaan fit object and a complex survey design object as input
and returns a structural equation modeling analysis based on the fit
object, where the complex sampling design is taken into account.
The structural equation model parameter estimates and standard errors
are design-based. See Satorra and Muthen (1995) for details on the
procedure.
}
\usage{
lavaan.survey(lavaan.fit, survey.design)
}
%- maybe also 'usage' for other objects documented here.
\arguments{
\item{lavaan.fit}{
A \code{\linkS4class{lavaan}} object resulting from a lavaan call.
It probably makes most sense to use estimator="MLM" in the call
since this is the estimator that will be used in the complex sample
estimates, but it is not strictly necessary.
}
\item{survey.design}{
An \code{\link{svydesign}} object resulting from a call to
svydesign in the survey package. This allows for incorporation of
clustering, stratification, unequal probability weights, and finite
population correction. See the survey documentation for more
information.
}
}
\details{
The user specifies a complex sampling design with the survey package's
\code{\link{svydesign}} function, and a structural equation model with
\code{\link{lavaan}}.
When calling lavaan.survey, the following steps are then completed:
\enumerate{
\item The covariance matrix of the observed variables
(or matrices in the case of multiple
group analysis) is estimated using the svyvar command from the
survey package.
\item The asymptotic covariance matrix of the variances and
covariances is obtained from the svyvar output (the "Gamma"
matrix)
\item The lavaan model is re-fit using Maximum Likelihood
with the covariance matrix as data. After normal-theory ML
estimation, the standard errors (vcov matrix), likelihood ratio
("chi-square") statistic, and all derived fit indices and
statistics are adjusted for the complex sampling design using
the Gamma matrix. I.e. the Satorra-Bentler (SB) corrections are
obtained ("MLM" estimation in lavaan terminology).
}
The Satorra-Bentler ("aggregrated modeling") approach to complex
survey analysis of SEM was discussed by Satorra and Muthen (1995).
An alternative method to take clustering into account is multilevel
SEM ("disaggregated modeling").
}
\value{
An object of class \code{\linkS4class{lavaan}}, where the estimates,
standard errors, vcov matrix, chi-square statistic, and fit measures
based on the chi-square take into account the complex survey
design. Several methods are available for \code{\linkS4class{lavaan}}
objects, including a \code{summary} method.}
\references{
Oberski, D. and Saris, W. (2012). A model-based procedure to evaluate
the relative effects of different TSE components on structural equation
model parameter estimates. Presentation given at the International
Total Survey Error Workshop in Santpoort, the Netherlands.
\url{http://daob.org/}
Satorra, A., & Bentler, P. M. (1994). Corrections to test statistics
and standard errors in covariance structure analysis.
Satorra, A., and Muthen, B. (1995). Complex sample data in structural
equation modeling. Sociological methodology, 25, 267-316.
}
\author{
Daniel Oberski - \url{http://daob.org} - \email{daniel.oberski@gmail.com}
}
\note{
The function has been testing using simulation.
Currently only continuous observed variables are implemented.
}
%% ~Make other sections like Warning with \section{Warning }{....} ~
\seealso{
\code{\link{svydesign}}
\code{\link{svyvar}}
\code{\link{lavaan}}
}
\examples{
###### A single group example #######
data(ess.dk)
dk.model <- "
socialTrust ~ 1 + systemTrust + fearCrime
systemTrust ~ 1 + socialTrust + efficacy
socialTrust ~~ systemTrust
"
lavaan.fit <- lavaan(dk.model, data=ess.dk, auto.var=TRUE, estimator="MLM")
summary(lavaan.fit)
survey.design <- svydesign(ids=~intnum, data=ess.dk)
survey.fit <- lavaan.survey(lavaan.fit=lavaan.fit, survey.design=survey.design)
summary(survey.fit)
attr(survey.fit,"creff.svy")
# A test for R CMD CHECK
stopifnot(abs(attr(survey.fit,"creff.svy")[2] - 1.2713339) < 1e-6)
###### A multiple group example #######
data(HolzingerSwineford1939)
# The Holzinger and Swineford (1939) example - some model with complex restrictions
HS.model <- ' visual =~ x1 + x2 + c(lam31, lam31)*x3
textual =~ x4 + x5 + c(lam62, lam62)*x6
speed =~ x7 + x8 + c(lam93, lam93)*x9
speed ~ textual
textual ~ visual'
# Fit multiple group per school
fit <- lavaan(HS.model, data=HolzingerSwineford1939,
auto.var=TRUE, auto.fix.first=TRUE, group="school",
auto.cov.lv.x=TRUE, estimator="MLM")
summary(fit, fit.measures=TRUE)
# Create fictional clusters in the HS data
set.seed(20121025)
HolzingerSwineford1939$clus <- sample(1:100, size=nrow(HolzingerSwineford1939), replace=TRUE)
survey.design <- svydesign(ids=~clus, data=HolzingerSwineford1939)
summary(fit.survey <- lavaan.survey(fit, survey.design))
# Obtain a "relative efficiency" measure:
attr(fit.survey, "creff.svy")
#TODO: stopifnot
}
% Add one or more standard keywords, see file 'KEYWORDS' in the
% R documentation directory.
\keyword{survey}
\keyword{models}
\keyword{regression}
\keyword{robust}
\keyword{multivariate}
```