Bayesian lasso for random intercept factor model
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Structural Equation Models (SEM) are often used in psychological research. In many studies, determining the number of variables is di fficult because maximum likelihood estimates are empirically under-identi fied when more factors are estimated in the model than are present in the data. In this study, the Random Intercept factor model is considered as a psychometric measurement model which, although useful in many research contexts, does not assume simple structure. We compare the RIF model to other factor models using Bayesian estimation to determine the dimensionality of the data as well as to investigate other psychometric measurement models for the data. The Bayesian Lasso method is explored as an efficient approach which estimates the parameters of the model and adjudicates model selection simultaneously. In an examination of both simulated and empirical data ML SEM's were empirically underidenti fied for overcomplex measurement models. Both conjugate Bayesian approaches and the Bayesian Lasso (BLasso) were found to yield superior estimates of parameters and consistently agreed upon the same measurement model for the data. Taken together, the results suggest that Bayesian approaches are preferable to ML for selection of an appropriate psychometric measurement model for the data. Of the two Bayesian approaches, the BLasso may be preferred given that it does not require specifi cation and model comparison of the several types of measurement models considered.