Ben Chapman posted on Tuesday, April 24, 2007 - 11:12 am
A colleague brought up the interesting question of whether LPA is appropriate if one's indicators are completely orthogonal. If the comparisons of LCA to factor analysis with a categorical latent variable is apt, it seems like an excellent point.
Yet it seems from a mixture perspective like the mixing of different distributions need not ALWAYS yield correlations of observed variables in the overall data. In fact, I wonder if one relaxes local independence within classes, and indicators are positively correlated in some classes but negatively or not correlated in others, a situation of "global independence" but not local independence could arise.
Would the application of LPA necessarily entail observed correlations among indicators? Or does it simply entail the presumption of unobserved heterogeneity which may or may not give rise to observed indicator correlations?
I think LPA is appropriate with indicators that are uncorrelated. Imagine a 2-class situation, where in each class you have uncorrelated variables. Imagine a scatter plot in 2 dimensions (2 variables: y, x). If the class-specific scatters showing uncorrelated y and x for the 2 classes are positioned side by side on the x axis at the same y axis value, then y and x would be uncorrelated in the mixture (the full sample).
LPA generalized to allowing within-class correlation could also be relevant for variables that are uncorrelated in the mixture. For example, one class can have a negative correlation and the other class a positive one, canceling out in the mixture.
I am receiving a warning message when I run my LPA about my variables being constrained to be correlated @ 0 within class. I'd like to relax this constraint. What should I add to my syntax to do so? Thanks.
Thanks so much. Now that I've tried this new syntax, the indicator means within latent class are outside the range of my items. This was not the case with my original syntax (which contained the inter-correlation constraint). Any idea why and also how I can fix this to use the means in a meaningful way?