Preprint #96-31
On Linear Latent Variable Analysis of Multiple
Populations
by
Savas Papadopoulos and Yasuo Amemiya
Abstract
Latent variable or structural equation modeling is used heavily in
applications, especially in social and behavioral sciences. Since the
normality based model fitting procedures are simple and widely available,
and since such procedures are often applied to non-normal or non-random
sample data, it is important to investigate the appropriateness of
such practice and to suggest simple remedies. This paper addresses these
issues for the analysis of multiple populations. For a very general class
of latent variable models, a particular parameterization is proposed for
meaningful and interpretable analysis of several populations. It is shown
that under this parameterization the large-sample statistical inferences
based on the assumption of normal and independent populations are valid for
virtually any non-normal and dependent populations. This result is also
shown to be valid when some latent variables are treated as fixed instead
of random, or when multi-populations in fact correspond to a group of
individuals measured over several time points longitudinally. Simulation
studies are conducted to verify the theoretical results and assess the
use of asymptotic results in finite samples.
Copies of preprints are available from the author upon request. Use
the preprint number (located at the top of the page) and
make the request directly to the author, Iowa State
University,
Department of Statistics, Snedecor Hall, Ames, IA 50011-1210.