In this seventh post of the causal inference series, we apply our approach to ordinal models. Ordinal models make causal inference tricky, and it’s not entirely clear what the causal estimand should even be. We explore two of the estimands that have been proposed in the literature, and I offer a third estimand of my own.
This is a follow-up to my earlier post, Notes on the Bayesian cumulative probit. This time, the topic we’re addressing is: After you fit a full multilevel Bayesian cumulative probit model of several Likert-type items from a multi-item questionnaire, how can you use the model to compute an effect size in the sum-score metric?
In this post, I have reformatted my personal notes into something of a tutorial on the Bayesian cumulative probit model. Using a single psychometric data set, we explore a variety of models, starting with the simplest single-level thresholds-only model and ending with a conditional multilevel distributional model.