Inconsistencies when freeing residual... PreviousNext
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 Ann-Renee Blais posted on Thursday, December 31, 2015 - 11:48 am
Hello,

I am attempting to identify profiles based on 10 variables (personal value ratings). In order to control for style biases (as routinely done by other researchers in that area), I ran latent profile analyses as well as factor mixture models that include a continuous style factor (its loadings are fixed to equality across classes). The fit indices are best for the FMMs (vs. the LPAs), and point to a 2-profile + 1 style factor solution. So far so good.

When I try to relax the assumption of equal variances by freeing the residual variances across classes, things get messy, however. Only the 2-profile/1-factor solution converges (the models with more classes don't), and even then, the 2-profile/1-factor solution with unequal variances results in a model that is very different from the one with equal variances (i.e., the factor loadings are different, the profiles don't look the same at all, some items now have very small error variances in one class vs. the other, etc.).

I'm confused as to which final model to choose, the one with equal variances or the one with unequal variances? All of the indices of fit suggest the model with unequal variances is superior, but I'm puzzled by the inconsistent and vastly different results between the two models.

Thank you for any advice you may have!

ARB
 Bengt O. Muthen posted on Thursday, December 31, 2015 - 5:45 pm
Relaxing residual variances in an already quite flexible model can cause these problems. Small variances can cause spikes in the likelihood without providing a useful solution. You may want to let only the factor variance differ across classes. Or, if you want to vary the residual variances, you may want the classes to differ with respect to only a scale difference in residual variances - so only 1 parameter different per class(may not be very useful, however).
 Jithin SV posted on Friday, July 03, 2020 - 6:11 am
Hi Drs Muthen,
I am trying to fit a Latent Variable Mixture Model with an intercept, slope and quadratic slope (latter two determined by a covariate - m), and predicting class membership using another covariate (x).

! s1-s4 are incomes from early life, early adulthood, mid adulthood and late adulthood
! x is maternal schooling
! m is attained schooling of the participant
VARIABLE:
NAMES = id x s1 s2 s3 s4;
MISSING=.;
IDVARIABLE = id;
USEVAR = x m s1 s2 s3 s4;
CLASSES = c(3);
ANALYSIS:
TYPE = MIXTURE;
ALGORITHM = INTEGRATION;
STARTS = 500 20;
STITERATIONS = 20;
MODEL:
%OVERALL%
i s q| s1@0 s2@1 s3@2 s4@3;
i-q@0;
s q ON m;
c ON x;
%c#1%
s1-s4;
%c#2%
s1-s4;
%c#3%
s1-s4;

My questions related to the above model are as follows:

1. How do we decide free-ing up residual variance in all classes? The model converges and the entropy is 0.56. The observed residual variances seem to be different between classes but is there a way to evaluate the differences apart from improvement in fit?

I will post the residual variances and two other questions on the same model below (size constraints)
 Jithin SV posted on Friday, July 03, 2020 - 6:12 am
Result for observed residual variances for each of 3 classes:
s1 0.073 0.030 0.188
s2 0.282 0.353 0.348
s3 0.303 0.109 0.199
s4 0.327 0.233 0.099

2. How do we decide if we are to adjust for covariates that differ between classes at baseline?

3. Different articles mention that we should report all the attempted model formulations for a comprehensive picture. Is there an example of how to present the different combinations for number of classes, adjusting/not adjusting for covariates and constraints on residual variances?

Thanks a lot!

Jithin
 Bengt O. Muthen posted on Saturday, July 04, 2020 - 6:01 am
1. Use BIC. Typically, it is better to let the i variance to be different across groups.

2. Ask on SEMNET.

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