Evaluation of single- and multilevel factor mixture model estimation
Abstract
Confirmatory factor analysis (CFA) models test the plausibility of latent
constructs hypothesized to account for relations among observed variables. CFA models
can be used to model both hierarchical data structures as a result of cluster sampling
designs and investigate the plausibility of latent classes or unobserved classes of
individuals. Recent research has suggested preliminary evidence on the accuracy of
typical fit indices (AIC, BIC, aBIC, LMR aLRT) among various single-level latent class
models, multilevel latent class models that correct for biased standard error estimates as a
result of nested data, and growth mixture models (Clark & Muthén, 2007; Nylund et al.,
vii
2006, Tofighi & Enders, 2006). But few, if any, researchers have studied the accuracy of
the fit indices in multilevel factor mixture models. The purpose of this study was to
extend the literature in this less researched area and assess the performance of typical fit
indices used to compare factor mixture models. Class separation, intraclass correlation,
and between-cluster sample size were manipulated to emulate realistic typical research
conditions.
The proportion of times out of a possible 100 replications in which each of the
AIC, BIC, aBIC, and LMR aLRT led to selection of the correctly specified model among
other mis-specified models was recorded. Results for data generated to fit one-class
models indicated that the BIC and aBIC outperformed the AIC and the LMR aLRT was
nonsignificant nearly 100% of the time, supporting the correct one-class model.
Performance of all fit indices was, however, poor when data were generated to originate
from two-class models. The AIC and LMR aLRT tended to perform better than the BIC
and aBIC, although accuracy of all fit indices increased as a function of increasing class
separation and between-cluster sample size. Implications and recommendations regarding
optimal fit indices under various conditions are reported. It is hoped that the current
research has provided initial evidence of conditions in which the various fit indices are
more likely to model the correct number of latent classes in multilevel data.
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