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Abstract:
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Structural equation models have been used extensively in social and behavioral sciences where relationships between latent variables are of interest. Although most established procedures assume linear relationships between the latent variables it is necessary to resort to nonlinear relationships motivated by psychological theories. As a result a vast variety of procedures have evolved in the last decades to estimate and test interaction and quadratic effects. However, most procedures and models assume continuous indicators. This study proposes a frequentist method to estimate model parameters by marginal maximum likelihood, in the presence of ordinal indicator variables. Inference on factor scores is also discussed. A simulation study is conducted in order to investigate the performance of the proposed method.
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