Mingnan Liu posted on Thursday, January 30, 2014 - 7:05 am
When doing LCA, I noticed that Mplus produces the estimated probability of being on each response category given the level of the LC factor means that you calculate for any given value of the latent value the probability of having given a certain answer (called "latent profile" in Latent Gold).
I wonder if Mplus can calculate something slightly reversed. That is the latent means scores which is a mean value on the LC factor for each given response category (called “latent means” in Latent Gold). The paper I read reports this since the LC D-Factor model they apply defines levels of the LC factor as equidistant (hence: scores 0 .5 and 1 in the case of a three class level latent variable.
I guess the differences between the two is similar to estimating row versus column percentages in cross-tabulations.
Not sure what model you are considering here. You mention LCA but then you also talk about a factor and factor means, so it sounds like you include a continuous latent variable, that is, a factor mixture model like in the Mplus UG ex 7.26 and ex 7.27.
I don't know what an "LC D-Factor model" is. Looking at the LG documentation it seems like it has several categorical latent variables that are either binary or ordinal. Mplus can handle several latent class variables but does not have an option for ordinal variables. UG ex 7.26 might be of interest.
Mingnan Liu posted on Thursday, January 30, 2014 - 11:47 pm
Thank you Bengt!
The paper I'm reading is Moors, Guy 2008. "Exploring the effect of a middle response category on response style in attitude measurement." Quality and Quantity 42:779-794.
Specifically, I am trying to get the result they have on Figure 1, which they call it "mean probability scores". On p.786 first paragraph they say "A probability mean is the mean latent-class factor score for each response category and ranges from 0 to 1."
My understanding is they treat the items as nominal and latent variable as ordinal or interval. Given each response option, they calculated something called "mean probability score".
I don't know how Figure 1 of the Moors article is computed, but Mplus can do this type of modeling where you do "confirmatory LCA" and have (1) several latent class variables, each influencing different observed variables, and (2) have fixed ordinal values for the latent classes of each latent class variable. As for (2), you do this by taking a "non-parametric" approach where you fix the means at the ordinal values for a zero-variance factor. See UG ex 7.26. I have a similar approach in
Muthén, B. (2006). Should substance use disorders be considered as categorical or dimensional? Addiction, 101 (Suppl. 1), 6-16.
- see Figure 3.
For an overview of related models, see
Muthén, B. (2008). Latent variable hybrids: Overview of old and new models. In Hancock, G. R., & Samuelsen, K. M. (Eds.), Advances in latent variable mixture models, pp. 1-24. Charlotte, NC: Information Age Publishing, Inc. Click here for information about the book.