**Marianne (Marnie) Bertolet**

Linear mixed-effects (LME) models analyze data that contain
complex patterns of variability, specifically involving different
nested layers. While LME models can match well the stratification and
clustering of survey data, it is not clear how sampling weights should
be incorporated into LME estimates. This report uses twelve
simulation studies to compare two published methods of inserting
sampling weights into LME estimates, Pfeffermann, et al. (1998),
denoted PSHGR, and Rabe-Hesketh and Skrondal (2006), denoted RHS.
There are five main conclusions based on these simulations. 1) The
PSHGR and RHS point estimates are very similar, with differences due
to numerical instabilities in the estimation procedures. 2)
Confidence intervals based on the sandwich estimator and the design
based estimator of the variances provide similar coverage when there
is no model misspecification. However, when there is model
misspecification, the design-based variance estimator has unexpectedly
large coverage, implying that the variance estimates are too large.
3) When there is model misspecification that does not induce
informative sampling, weighted estimates do not reduce bias of the
estimators. 4) When there is informative sampling, the weighted
estimators do reduce the bias of the point estimates, though they do
not eliminate it. 5) The unweighted estimate has the smallest
variance. When there is informative sampling, the unweighted
estimates are biased. The weighted unscaled estimate corrects the
bias in the fixed effects, but produces more bias in the random
effects. The scaled 1 weightings remove the bias in the fixed
effects, and overcorrect for the weighted unscaled bias in the random
effects. The scaled 2 weightings remove the bias in the fixed effects
and are in between the weighted unscaled and weighted scaled 1 bias in
the random effects.

*Keywords:* Linear mixed-effects models, survey sampling, weighting
bias, sampling bias, sandwich estimator, design-based estimators.

Heidi Sestrich 2009-01-29 Here is the full PDF text for this technical report. It is 1352833 bytes long.