Exploring how many categories are needed to model ordinal intensive longitudinal data as continuous with dynamic structural equation models.

Technological innovations facilitate collecting intensive longitudinal data (ILD), which is characterized by many repeated measures over a short timeframe. Dynamic structural equation models (DSEMs) have been proposed to accommodate unique features of ILD. Ordinal responses are common in ILD to reduce participant burden and mitigate nonresponse, but treating outcomes as continuous in DSEM is most common in empirical studies. However, it is currently unclear whether or when it is defensible to model ordinal ILD as continuous. Similar questions have been addressed in factor analysis, but these findings may not generalize because DSEM (a) is a multilevel model that decomposes variance into within-person and between-person sources, (b) does not emphasize global fit, (c) relies on Bayesian estimation, and (d) tends to have lower sample sizes than factor analysis. The two goals of this article are therefore to (a) determine if the recently proposed probit DSEM for ordinal data has desirable statistical properties at realistic ILD sample sizes and (b) assess under which conditions ordinal ILD may be defensibly modeled as continuous. Whereas five-category data can be defensibly modeled as continuous in factor analysis, results suggest that ILD typically need at least seven categories to accurately estimate within-person effects. However, between-person effects could be estimated reasonably accurately with as few as five-or sometimes even three-categories. Broadly, results suggested that the factor analysis literature on modeling ordinal data as continuous is not necessarily applicable to ILD, which warrants more targeted examination to refine best practice recommendations in DSEM and ILD more broadly. (PsycInfo Database Record (c) 2025 APA, all rights reserved).