I have found the technical appendices quite helpful in understanding how various estimators and procedures are implemented in Mplus. I am wondering if there are technical appendices/references related to the estimation of CFA models with count indicators (or even path analysis models with multiple count outcomes), as implemented in Mplus. I am only writing this post after thoroughly, seemingly exhaustively, searching for such documentation and materials, both on the Mplus/statmodel site and via Google Scholar (etc).
My primary interests at this point lie in finding the appropriate technical references to better understand how multivariate expectations are generated for models with count outcomes (in lieu of traditional continuous variance/covariance expectations or ordinal polychoric/polyserial expectations, since these do not apply to count data) and how model identification might differ in models with count outcomes. I would also be interested in more info about how the estimation algorithm handles count variables, but this is secondary. (MLR with numerical integration is the standard estimator for counts, but are there others?).
Many thanks in advance for your help directing me toward technical documentation re: how count models are estimated in Mplus!
With count outcomes we use the methods described in the book by Hilbe (2011) referenced in the User's Guide. It all draws on regression with a single DV because their is no multivariate DV version in the literature. That then covers not only observed covariates but also latent ones such as factors with count indicators. If you have 2 count DVs you can create a residual covariance between them by creating a factor that influences (is measured by) both. There is no underlying y* formulation for counts which makes it hard with path models where a count variable is a mediator - you have to treat is as continuous in the part where it is a predictor which isn't very satisfactory.
We use ML and MLR - with numerical integration when needed
We discuss count modeling in our Short courses with videos and handouts on our website, both in Topic 2 and in the mixture topics.
Thank you very much for your prompt reply, Dr. Muthén! This is *extremely* helpful. I have actually looked at (and even downloaded) some of the Topic 2 videos and slides, which were certainly illuminating. Are there any specific videos/handouts you would recommend for this, in particular (there maybe something particularly relevant that I overlooked)?
Thank you so, so much, again!
PS: It was an absolute pleasure meeting you, Tihomir Asparouhov, and Ellen Hamaker at the IMPS Dynamic SEM workshop in Zurich this past summer. (Albeit briefly/passingly – so I wouldn't expect you to remember me from the crowd. But the workshop was thoroughly helpful and enjoyable, so thank you very much for that as well!)
Thank you very much! Good point ... the mediation book is on my shelf and I hadn't thought to look there for this topic, although as you say it I remember now that it does cover counts (and, as you point out, the DV -> IV switch of a count mediator from regression 1 to regression 2 is a particularly tricky issue) ....