Jon Heron posted on Monday, October 19, 2015 - 7:04 am
i'm investigating the non-normal nature of a trait through the use of a semi-parametric FA.
I have eight 3-category items and am estimating a 2-class model.
My first attempt yielded 25 parameters (7 invariant loadings, 16 invariant thresholds, a single non-zero factor mean in class 1 and a mean for my latent-class split). However, plot3 gave me precious little other than a scatterplot or two.
I then added "algorithm = integration". This gives me many more plots (ICC/TIF etc) and an additional parameter - a within-class factor variance. However my model is now struggling. My likelihood has changed markedly and I am unable to replicate it.
I have tried to impose a constraint to regain my 25-parameter model e.g. fix my within-class variance to one, or my within-class means to zero and one, but no success. I've also boosted the random starts and also the integration points.
Any thoughts? has something rather fundamental change now I've applied integration?
It may be a function of the data - perhaps that within-class variance isn't needed. The UG examples 7.17 and 7.27 are close to what you are doing, so in principle this can work fine.
Jon Heron posted on Tuesday, October 20, 2015 - 4:05 am
ace, thanks Bengt
Jon Heron posted on Tuesday, October 20, 2015 - 10:32 am
Ahh, I have achieved enlightenment. I'm sharing, with no additional questions:-
My first model (without integration) is actually NP-FA. This explains the lack of a quoted factor variance and also the lack of ICC/TIF.
Constraining the within-class variance to zero in the second model (the one with integration) does indeed yield the first model.
So with categorical data and no integration only means are estimated whereas with continuous indicators (as in 7.17) one also obtains a within-class factor variance. To model factor variances with categorical indicators one needs integration.
This sounds just the same as the situation for LCGA and GMM.