I have conducted latent class analysis on 8 continuous variables (4 conflict behaviors of adolescents and 4 conflict behaviors of mothers) to identify profiles of mother-adolescent conflict behaviors. I used the 3 step method (BCH command) to validate my 4-class solution to several distal outcomes (some reported by adolescents and some reported by mothers).
One of the reviewers states that my data structure is hierarchical (mother-adolescent dyads) and that my observations are not independent. He suggests that I should do some kind of multilevel analyses to take this dependency into account. He doesn't question the dependency issue for the LCA but only for the comparison of the means of the outcome variables.
My question is: Is it possible to conduct the 3-step method in a multilevel manner?
And if not, is there an elegant way to account for this dependency of the observations? I used MLR as estimator.
I assume that the latent class variable influences both the mother and child outcomes. If so, the correlation between mother and child is accounted for. Because of your "wide" analysis format, yous observational unit is the dyad, not its members and the non-independence is modeled (by the latent class variable).
I would like to ask for somewhat more clarification just to be sure I understand you correctly.
Do you mean that the BCH command in the 3 step method controls for the correlations between the distal outcomes? I thought that the BCH command only generates individual tests of equality of means for each outcome variable separately (like in an ANOVA). Could you help me understand this?
I am also not quite sure that i understand what you mean exactly with the last sentence "Because of your "wide" analysis format, your observational unit is the dyad, not its members and the non-independence is modeled (by the latent class variable)". How does putting information from perceptions of both children’s and their mothers' conflict resolution styles in one LCA take into account the non-independence between these measures (as children and mothers are part of the same dyad)?
The correlations between the distal outcomes is accounted for by them all being influenced by the latent class variable.
Wide format analysis means that if mothers have 5 variables and children have 5 variables, you are analyzing 10 variables, that is, there are 10 columns in your data (so wide). Because the latent class variable influences all 10 variables, the mother and child correlation is accounted for by the latent class variable (because it influences both types of variables).
Just wanting to follow-up on the 2nd part of your above post. Is it the case (am I understanding correctly) that in an x-sectional LCA/LPA of, say, 5 parent and 5 child interactive behavioral indicators, that the latent class variable in a way accounts for the clustered nature of the data at the dyad level? Would this change if one wanted to do a FMM and model a latent cont. variable within each class?
I ask as I have been unable to find any applications of LCA to dyadic analyses almost all of which is done in the context of lead-lag multi-level type models.
Many thanks, Bengt. To clarify one further point: in the case of the x-sectional dyadic data example I provided above--parent and child behaviors in a standardized paradigm (5 indicators parent, 5 indicators child) would I need to also used TYPE=COMPLEX etc. (cf. UG chap 9) and create a 'dyad' grouping variable to account for this clustering or will the analyses itself (LPA) be enough assuming the LI assumption is met?
It's not really complex survey data but it would seem relevant.
The clustering can be handled in the modeling or correcting SEs and chi-2 by Type=Complex. If you analyze the 5+5 variables in one model and the model uses latent variables(factors or classes) that influence both sets of 5 variables, then you have accounted for the clustering in the model and don't need complex. You are essentially doing a twolevel analysis but in wide format.