Modeling structure in ordinal data

Abstract

Structural equation modeling (SEM) is a technique that allows a set of relationships between one or more independent observed or unobserved variables and one or more dependent observed or unobserved variables, to be examined. A SEM is made up of two models: the measurement model and the latent variable model. The measurement model specifies the relationships between the observed and the latent variables, whilst the latent variable model involves the structural equations that summarize the relationships between latent variables. The structural equation modeling process thus, involves validation of the measurement model and hence fitting of the structural model. The former is accomplished primarily through confirmatory factor analysis, while the latter is accomplished through path analysis with latent variables. Five steps characterize most applications of SEMs: model specification, identification, estimation, testing fit and respecification. Once in the estimation phase, fitting a SEM to a dataset involves a choice of a correlation matrix estimator and an estimation technique for the model parameters, depending upon the type of variables present in the dataset. In accordance to this choice, adequacy of fit of the resulting model possibly followed by model respecification is carried out.