I'm running a model with 2 separate latent class variables, a 3-class and a 4-class variable, along with a covariate. The 3-class variable is regressed on the covariate, and the 4-class variable is regressed on both the covariate and 3-class variable. I'm also introducing an interaction b/w the covariate and 3-class model by allowing the value of the covariate on 4-class to vary across the 3-class levels. In some ways, this seems conceptually akin to an LTA-type model (even though the variables for the 2 LCAs are not the same. Is example 8.14 an appropriate model for this approach (minus the cross-time constraints)?
Also, can you clarify how to interpret the "interaction effect"? I'm a bit confused by the headings "Latent Class Pattern 1 1" and "2 1" that precede the tests of the covariate on the 4-class model within specified 3-class patterns. Why isn't there a heading for "1 2" and "1 3" etc.? I've got 1 significant effect (the covariate negatively predicts 4-class#2 for Latent Class Pattern 2 1).
Any relevant articles that might serve as examples?
you would have Latent Class Pattern 1 1 and 2 1 as the relevant patterns for which c2 on x differs. The first number refers to c1 and the second to c2 so you see that for these patterns only c1 classes change. Patterns 1 2 and 1 3 refer to the same c1 class so c2 on x would not differ across these patterns. If you look at the ex 81.3 output (on the web site or on your Mplus CD) you find that you also have c2 on x in the "overall" part which then refers to the last c1 class.
Oops -- yes, I did mean 8.13 (not 8.14) that seemed conceptually similar. Appreciate the clarification.
Just to follow-up. If my covariate (gender) is significantly & positively associated with c2#2 in the overall model and then negatively associated with c2#2 for Pattern 2 1, would that indicate that males have a higher conditional probability of c2#2 than females, except when c1#2 -- i.e., females have a higher risk of c2#2 when classified as c1#2?
Also, if we wanted to examine 3-way interactions (e.g., race & gender differences) how would we specify the interactions in the %c#1% and %c#2% models?
One last clarification re: interpretation. Is it more accurate to describe the finding with respect to gender and c2#2 in the overall model as describing the general pattern (i.e., a main effect of gender on c2#2 membership relative to my reference class for c2) with the c1 subclass analyses indicating an additional interaction for gender specific to those c1 classes -- or is it more accurate to describe the overall model as indicating the pattern for my last c1 class, with the subclass analyses indicating the patterns specific to the other c1 classes? Or, is this really the same thing? In re-reading your email response, I believe you initially suggested the later, but my interpretation was of the former.
and then say c2#1-c2#3 on x@0; in all of the three c1 class-specific statements. Then the parameterization is perhaps clearer because you can focus on the c2 on x relationship in each c1 class without having to refer to the overall.
I was hoping you could further clarify the interpretation of an interaction term in LTA. Assuming a model:
classes = c1(3) c2(3) c3(3);
and a single covariate. There are presumably 3x2 = 6 odds ratios describing the relation between the covariate and transitions from time 1 to time 2, and similarly 6 odds ratios describing the relation from time 2 to time 3. I have specified the model as described in Example 8.13, but I am only left with odds ratios for patterns: 1 1 1, 1 2 1, and 2 1 1. What do the odds ratios for c2 on x and c3 on x for these different patterns represent?
Consider c2 regressed on the covariate. You have the 6 slopes (giving the 6 odds ratios) as:
2 slopes for Latent class pattern 1 1 1
2 slopes for Latent class pattern 2 1 1
2 slopes from the section above this, called "Categorical Latent Variables" - this comes from your "c2 on x" statement in %Overall%, referring to the third category of c1 (the %c1#3% section does not have c2 on x so it is taken from Overall).
Another follow-up to our exchange back in November re: interpretation of interaction effects when regressing one LCA on another (and then testing for relation of a given dichotomous covariate to the DV LCA within levels of the IV LCA).
Essentially, we have two LCAs (drug use and sex behavior)and gender (coded f:0, m:1). We regressed drug use and sex beh on gender, and then regressed sex beh on drug use). Finally, within 3 of the 4 levels of drug use, we tested the relation of gender to sex beh.
We have a strong positive effect of being male on higher risk sex behavior, and a strong positive effect of increased drug use on higher risk sex behavior. However, within drug use groups (with non-users set to reference), we have significant negative beta weights for gender on sex behavior (with abstainers set to reference). My initial interpretation was that this suggested males were at lower proportional risk for engaging in high risk sex behavior when substances were involved. However, plotting out the proportions of male/female across different groups (using saved cprobs) does not appear to support this interpretation.
Can you please clarify the reference for these interactions (i.e., what is the negative beta actually referring to)?
A related follow-up: In additional analyses of a multi-process LCA (with a 3-class model regressed on a 4-class model and a gender interaction) I received an indication that the model was not converging due to spareness). Further investigation of a cross-tab of the two LCA models split by gender (using the c-probs generated from a previous run without the interaction effects) indicated that one cell is empty for females and two cells for males.
Is it possible to constrain the model to reflect the absense of certain relationships while still allowing the model to converge? How would that be indicated in the model statment?
You can restrict class probabilities, but in my experience zero classes is not a cause of non-convergence. With a knownclass variable "cg" in addition to a substantive class "c", I assume you allow "cg with c". If you like you can send your non-converging run's input, output, and data plus your license number to firstname.lastname@example.org.
I can send the output along (my colleague and I are re-running the model currently following a brief modification).
To clarify -- there is not a particular zero class; all classes are represented in each gender. The zero-cells emerge in the crossing of two classes (i.e., no boys in a given mental health class are identified with a given substance use class).
This question pertains to the model described by Christian Connell in the previous messages in this thread. We have received feedback about some of the parameter estimates of the model being too close to the boundary space. This is due to sparseness within cells of the model (zero cells in crossing of two classes) and is not due to sample size (N is over 12,000). The use of priors was identified as one of the better ways to handle this issue. Is it possible to add priors to LCA in Mplus? And are there options for use of different priors?
The model estimates printed produce the zero cell. This may happen with some parameter estimates close to the boundary space but I don't see that as a problem. For instance, if a binary latent class indicator has threshold +15 this logit value indicates that the probability is 0. I don't see why priors would be needed here. Mplus currently does not handle priors for this.
Thank you for your response to Tamika's questions (above). One issue with estimation of conditional probabilities on the boundary of parameter space appears to be in correct estimation of standard errors (e.g., they may be estimated as too narrow). How is this issue best handled in Mplus without the use of priors?
What about the SE's of the logistic estimates regarding influence of membership in one latent class on another? For example, in our model of sexual risk behavior and substance use, the odds of a frequent polysubstance user being classified as a member of the high frequency sex class was 7918.84 with a 95% CI 1062.10-59041.74.
Can we trust these estimates in such close proximity to the boundary space (infinity)? Are there suggested techniques to account for this in Mplus?
You can trust the estimates. It is indeed the boundary case of infinity. We don't really view this as a problem. The interpretation of this model is that there is a deterministic relationship between the variables. In the above example substance use implies (with 100% certainty) high frequency sex class. SE are not really a meaningful quantity in this case for the logit scale regression parameter, however, in probability scale the parameter has a standard error of 0, that is the conditional probability parameter P(high frequency sex class|substance use)is 1 with a SE of 0.