Jon Heron posted on Thursday, July 29, 2010 - 2:54 am
I'm working on teaching material in which I derive latent classes from six repeated binary outcomes and then demonstrate the different ways one might relate these classes to a distal outcome (cts) and a covariate (categorical)
This is motivated by Clark, S. & Muthén, B. (2009). Relating latent class analysis Petras, H & Masyn, K. (2009). General growth mixture analysis
I compare modal class (entropy ~0.9), pseudo-class (Mplus + also Stata), prob-weighting in Stata and finally a 1 stage approach (although I don't fit covariate AND outcome at the same time).
Outcome: Good agreement in estimates across the board, including the 1-stage where the measurement model is pretty unaffected by the inclusion of the cts measure. Prob-weighting much lower SE's but the rest do OK.
Exposure: 2-stage results all in good agreement. Prob-weighting slightly lower SE's. 1-stage model only leads to minor tweaks in terms of class profiles and class distribution. However, regression estimates much higher than all the 2-stage results.
I am a little stuck now. I usually teach prob-weighting but I want to show the options and that conclusions could depend on one's choice. Do I conclude that (in this ex) all 2-stage models underestimate parameters or perhaps my model may be mis-specified?
It would be misspecified if the class formation changes much when adding the covariates and doing a 1-step run.
Jon Heron posted on Monday, August 02, 2010 - 1:25 am
that begs the question which I expect is v hard to answer - what is an important change in class formation?
From examining class profiles alone it appears (at least to me) that very little has changed - distribution and interpretation of classes is maintained. Had I not compared my results with pseudo-class I would not have suspected a problem. :-S
I would include direct effects from the covariates to the latent class indicators (in addition to c ON x). So u1 on x1-xq, then u2 on x1-xq, etc to search for significant direct effects. And including such effects, then again see if the class formation is similar.
Jon Heron posted on Wednesday, August 04, 2010 - 12:36 am
that sounds like a test for measurement invariance / uniform DIF within a MIMIC model.
Is that essentially what we have here, albeit with a categorical latent var?
Jon Heron posted on Wednesday, August 04, 2010 - 9:46 am
That's good to know.
A stepwise approach has shown bias i.e. a main effect for two of my six items.
Class distribution has changed slightly and covariate effects on C have changed considerably, in the direction of those obtained from pseudo-class but agreement between 1-stage and 2-stage is still poor.
I feel these new bias-adjusted estimates are more valid than the original 1-stage estimates and if anything I am surprised that they moved *towards* the 2-stage results since they too are not adjusted for bias.