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Mplus Discussion > Growth Modeling of Longitudinal Data >
 Cathy Nylin posted on Saturday, January 04, 2014 - 1:25 am
Using the sample syntax from the User Guide (two-part semicontinuous growth model for a continuous outcome), I built a model to look at alcohol use measured at years 2, 3, and 4 of a study. The model had excellent fit and terminated normally without any warnings. I then added a time invariant covariate of school involvement measured at year 1 of the study (variable name intW1) using the commands su ON intW1; sy ON intW1; iy ON intW1; .

Running this model resulted in the message WARNING: THE LATENT VARIABLE COVARIANCE MATRIX (PSI) IS NOT POSITIVE DEFINITE, etc., and looking at the TECH4 output showed that sy and iy had a correlation of 1.158. In looking at others' posts about latent variables with correlations higher than one, I have seen that the advice is usually to build a new model.

Will you please tell me if there is another solution here? And will you please explain what can cause the latent variables to correlate higher than one, or in other words, what could be wrong with this model that I need to avoid in testing another model?

Thank you.
 Bengt O. Muthen posted on Saturday, January 04, 2014 - 7:00 pm
There isn't enough to go on here, for instance why you don't have iu ON intW1, what residual correlation structure you have among your growth factors, and what the iy-sy correlation is without adding the covariate (perhaps it is also high).

Generally speaking, if two factors have a correlation close to 1 you need only one of them. So one investigation would be to see if you really need sy - checking if its mean is significant, if its variance is significant.
 Cathy Nylin posted on Friday, January 10, 2014 - 7:49 pm
In the model without the covariate, there was an error warning.

Using the syntax for DATA and the MODEL below to model drinking behavior, I get the warning "WARNING: THE LATENT VARIABLE COVARIANCE MATRIX (PSI) IS NOT POSITIVE DEFINITE...." and TECH4 shows a correlation greater than 1 between iu and iy. As per my understanding, the syntax splits the one variable into a set of dichotomous yes/no variables and then a continuous variable for those in the yes category. Wouldn't the iu and iy latent variables be expected to be highly correlated as they are two parts of the same data? What would it mean to say only one of them is needed? Since the variance of sy is small and nonsignificant, I understand that the frequency of drinking didn't change significantly over time among those who did get drunk - does that mean that it should be left out of further tests with a covariate (only model the dichotomous variable)?

NAMES = RCmbdk4-RCmbdk6;
BINARY = bin4-bin6;
CONTINUOUS = cont4-cont6;
iu su | bin4@0 bin5@1 bin6@2;
iy sy | cont4@0 cont5@1 cont6@2;
iu WITH sy@0;
 Bengt O. Muthen posted on Friday, January 10, 2014 - 10:16 pm
That correlation is usually high, but it isn't acceptable when it goes over 1.

Perhaps you want to free the su variance and covary all 4 growth factors to see if the intercept correlation goes below 1.

Even when the variance of sy is small, its mean can be significantly different from zero so it needs to be in the model. And even when its variance is zero you can regress it on covariates - whereupon its residual variance may be positive.
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