I am working with some ordinal response data (5-point Likert scale) for several different questions.
The raw data show a fairly obvious trend of higher ratings in the “Post” condition:
Often, I will create central tendency summaries using
posterior_epred() and weighting the probabilities by the numeric response positions. But, in cases where the data are far removed from any sort of interval scale, my understanding is that it’s better to work on the latent scale. I think we get the latent scale using
But, when I use
posterior_linpred() to get latent predictions, I see almost no difference in the distributions:
Am I misunderstanding what
posterior_linpred() provides or is there just no difference on the latent scale?
Given that it’s an ordinal model, I would guess that it’s the thresholds that are differing between the conditions. So while the two conditions may have the same latent distributions one condition may require a lower level of latent severity to rate in a higher category. This would give them comparatively higher ratings than the other condition for the same latent score
Is there a way to incorporate threshold information into the linear predictions?
Not really, since they’re two separate sources of information - they’re essentially the link function translating the latent responses to the observed. What you could do is overlay the estimated thresholds on the plot, so that it’s visually clear how latent severity might be differently related to the observed responses.
Although I should clarify that means you would need to update your model to have the thresholds estimated separately for each condition, since they’re constrained equal by default
I’ll give that a try. The model allows thresholds to wary by condition, so it’s just a matter of wrangling things into a plot.