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Date:    Tue, 23 Aug 2005 14:11:03 -0400
From:    "M.V. (Trey) Hood III" <[log in to unmask]>
Subject: Weighting in Multi-Level Modeling

I am using some survey data from New Orleans where I have individuals
(level-1) nested within zip codes (level-2).  Our sample needs to be
adjusted after the fact to match certain population parameters so we have
created some post-stratification weights.  Question: If a level-1
probability weight is being used in a model, does one need to also apply a
level-2 weight and, if so, what would this look like?  We've been using
Gllamm to estimate these models.

Thanks,
Trey Hood
UGA



Trey,

No, level-2 weights are not required. However, you can use them if you
wish. As an example, my co-authors and I use level-1 weights in a
forthcoming paper on the AJPS website that employs multilevel models
with two levels. In general, it depends on whether you wish to make
generalizations at level-1 or level-2 and your sampling methods. As
Raudenbush et al. (2001) write in their HLM5 software manual, "The
appropriate weighting scheme will depend not only on the sampling plan
but also on the conceptual orientation of the study. In some cases
researchers will aim to supply generalizations that apply to a
population of level-1 units, e.g., students. In other cases, the goal
may be to make statements about the population of level-2 units, e.g.,
schools." Goldstein (2003) provides a more comprehensive discussion of
weighting at various levels on pages 77-79 of his Multilevel Statistical
Models book.

In practice, weighting in multilevel models depends on the software you
are using and the structure of your data (e.g., how many units you have
at each level, how heterogeneous they are, and whether you have a
continuous or categorical dependent variable). For example, in HLM5, the
manual states that "design weights may not be used when specifying
nonlinear models." In MLwiN 2.0, level-1 weights work well for
continuous or dichotomous dependent variables, but the program often
crashes if you try to weight with an ordinal or multinomial dependent
variable. There are weighting options in the lme and nlme packages for
R. The gllamm routine in Stata weights through the pweight subcommand,
but the help file includes the warning that it "...should be used with
caution if the sampling weights apply to units at a lower level than the
highest level in the multilevel model. The weights are not rescaled;
scaling is the responsibility of the user."

Jason Barabas
The Institute for Quantitative Social Science
Harvard University

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