latent class analysis which modifies "given a certain class, probability for a respondent to show observed response"

Question

Context

I am trying to model a latent class model, which i give a priori restriction for the class-specific probabilities I'm using an SP data, for which respondents chose an alternative in 3 different choice situation In the data, the respondents can be divided into 2 groups: Say, Group 1 and Group 2 with some indicator I assume 2 classes(say, class A and B), and i want to give prior restriction that

"given class B, probability of respondent in Group 1 to show observed response to be 0"

"given class B, probability of respondent in Group 2 to show observed response to be 1"

In other words:

Suppose there are total N respondents and that the type indicator = 0 for M respondents, = 1 for N-M respondents.

My intention is to assume that:

(i) M respondents will always belong to Class A

(ii) the remaining N-M respondents probabilistically belong to either Class A or Class B

I'm trying to apply some random effect in the model for some of the N-M respondents to be in Class B (or A)

Problem

I have been looking for ways to give this restriction for class allocation, however i couldn't find an appropriate one. (I looked especially on R packages)

I mean, i couldn't find way to modify class-specific probability for each respondent(given a certain class, probability for a respondent to show observed response)

I've seen some people saying R package flexmix and mixtools are powerful, will those packages capable of what I'm trying to do now?

Any other suggestions on other packages or statistical software are welcomed

Any hints? Thank you in advance!

Answer 1

Latent class models have a nearly 70 year provenance. The original work is due to Paul Lazarsfeld, the late Columbia sociologist, and dates back to the post-WWII era. His approach amounts to an unsupervised clustering based on nominal or categorical data inputs in which the unique, cross-classified groupings of responses to the attributes form the "replications" and the derived, "latent" classifications proceed from those aggregated units of analysis. More recent approaches include the supervised models developed in marketing such as Bill Dillon's LADI (latent discriminant interactions model), Wagner Kamakura's model, both based on Jour Mktg Res papers published in the 80s, as well as the "degree-of-membership" models that have been used in sociology and education.

The key thing with this type of supervised latent class model is that the replications are within an observation unit (e.g., in marketing, consumers) and the classes are formed based on minimizing the heterogeneity of the residuals or error term output from the model. These models can be very flexible in terms of how they are specified and it is possible to "fix" certain parameters to be zero as you propose. However, this does not guarantee that the posterior classifications and latent class membership probabilities will also be zero if the outcomes are strongly associated. If that proves to be the case, you might want to adjust your ingoing assumptions and/or theory.

I do not know how this is done in R. My preference is to use the software package Latent Gold which is available from Statistical Innovations for the relatively nominal price of $1k. LG has all of the functionality required to specify the model you're requesting as well as, being a maximum-likelihood, finite mixture model algorithm, is invariant to differences in data scale types.

* additional thoughts * On second thoughts, I realized that my answer could amount to a sales pitch for LG. The big stats packages also have latent class routines, e.g., SAS has a third party macro (the last I knew, LC models were available in a proc in SAS) that, having tried it, really sucked. I'm pretty sure SPSS has one too. As for the other packages, Stata is likely to have one given its strong econometric focus, but I can't say for sure. There are other free, downloadable routines out there other than R modules. For instance, the late Clifford Clogg's old, highly serviceable MLLSA package (for unsupervised, categorically scaled data only) was being maintained by a guy at the U of Iowa. Some guys in New Zealand used to offer something called Multimix. And there's another product called PolCA which is a stand-alone routine, again for unsupervised, categorical data only.