Non-Linear Latent Variable Models: A Study of Factor Score Approaches

Abstract: Non-linear latent variable models are associated with problems which are difficult to handle in applied sciences. Four methods for estimating factor scores, with the purpose of estimating latent variable models with an interaction term, were investigated. The LISREL procedure provided inconsistent estimates of the interaction term for all sample sizes and distributions of the latent exogenous variables. The Bartlett-Thompson approach yielded consistent estimates only when the distribution of the latent exogenous variables was normal, whereas the Hoshino-Bentler and adjusted LISREL approaches yielded consistency for all distributions of the latent exogenous variables. In the Bartlett-Thompson and LISREL approaches the interaction term is formed from multiplying latent variable scores, whereas in the Hoshino-Bentler and adjusted LISREL approaches the interaction term is treated as yet another factor which is freely estimated. It was, hence, concluded that the methods treating the interaction term as a factor were more appropriate (in terms of consistency and robustness) than those using products of factor scores for estimating the latent variable model.