Dynamic structural equation models with binary and ordinal outcomes in M plus

Intensive longitudinal designs are increasingly popular, as are dynamic structural equation models (DSEM) to accommodate unique features of these designs. Many helpful resources on DSEM exist, though they focus on continuous outcomes while categorical outcomes are omitted, briefly mentioned, or considered as a straightforward extension. This viewpoint regarding categorical outcomes is not unwarranted for technical audiences, but there are non-trivial nuances in model building and interpretation with categorical outcomes that are not necessarily straightforward for empirical researchers. Furthermore, categorical outcomes are common given that binary behavioral indicators or Likert responses are frequently solicited as low-burden variables to discourage participant non-response. This tutorial paper is therefore dedicated to providing an accessible treatment of DSEM in M plus exclusively for categorical outcomes. We cover the general probit model whereby the raw categorical responses are assumed to come from an underlying normal process. We cover probit DSEM and expound why existing treatments have considered categorical outcomes as a straightforward extension of the continuous case. Data from a motivating ecological momentary assessment study with a binary outcome are used to demonstrate an unconditional model, a model with disaggregated covariates, and a model for data with a time trend. We provide annotated M plus code for these models and discuss interpretation of the results. We then discuss model specification and interpretation in the case of an ordinal outcome and provide an example to highlight differences between ordinal and binary outcomes. We conclude with a discussion of caveats and extensions.