2.4 CFA Model with Categorical Indicators
Mplus is developed on the basis of the LISCOMP,13 a SEM program that was well- suited for SEM with categorical outcomes. It is convenient to implement SEM with categorical outcome in Mplus. In this section, we extend the conventional CFA model to a CFA model with categorical indicators (binary or ordered categorical). Assuming an ordered categorical variable has M categories (m = 1, 2, . . . , M) with observed values of (U = 1), (U = 2), . . . , (U = M), and (U = 1) < (U = 2) < . . . (U = M), then there would be (M − 1) unknown thresholds that separate the adjacent categories; that is:
where y* is an unobserved normally distributed continuous latent variable underlying the observed categorical variable U; the , , . . . , and are (M − 1) thresholds and , that link the underlying latent y* variable to the values of the observed categorical variable U.
Traditionally, the ADF estimator (Browne, 1984) is used for SEM with categorical outcomes ...