[Rasch] Hierarchical Rasch Modeling

Stuart Luppescu slu at ccsr.uchicago.edu
Sat Jun 8 08:08:55 EST 2013

Hello Raschies, In work we do here, we make measures from survey data
using Bigsteps/Winsteps, and put the measures into HLM to get
school-level estimates. The HLM is a 3-level model with a measurement
model at level 1, individuals at level 2, and schools at level 3. The
level 1 equation (as described in Raudenbush and Bryk 2002, p. 354ff.)
adjusts for different amounts of measurement error in the measures, so
the level-2 outcome becomes the latent person measure adjusted for
measurement error. We may have occasion to include multiple measures as
outcomes at level 1 in order to estimate school-level covariances among
the measures.

A reviewer has criticized this technique, saying it would be more
efficient to do the entire analysis using multilevel Rasch analysis
(instead of taking the two-step approach). My question is, is this even
possible? My concerns are: 
1) Is it possible to do multilevel Rasch analysis when the items are of
multiple response formats? E.g., in one measure, some items could be
strongly disagree, ..., strongly agree format, and others, say, none,
some, most, all. (This is handled in Winsteps using GROUPS=.) I don't
think the software that comes to mind first (HLM, lme4) can handle
multiple formats. 
2) Is it possible to adjust for measurement error in the analysis as we
do in the two-step process? I don't think HLM or lme4 can.
3) Can we analyze multiple measures simultaneously in order to get
school-level measure covariances?

I can't think of any software that will enable such analysis, but if you
know of any, please let me know.


Stuart Luppescu <slu at ccsr.uchicago.edu>
University of Chicago
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