Latent growth modeling with three tim... PreviousNext
Mplus Discussion > Growth Modeling of Longitudinal Data >
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 Ben Luo posted on Wednesday, September 07, 2011 - 7:49 pm
Hi, I am a beginner of MPlus. I am grateful if you could help me with the following question.

I tested a latent growth model with 102 subjects and three points in time. The code was as follows.

Variable: NAMES ARE C_1 C_2 C_3;
MISSING = ALL (-99);
ANALYSIS: ESTIMATOR = ML;
MODEL: I S | C_1@0 C_2@1 C_3@2;
OUTPUT: TECH1;
TECH4;

Here, C_1, C_2, and C_3 are all continuous.

However, the output showed a warning message, that 'THE LATENT VARIABLE COVARIANCE MATRIX (PSI) IS NOT POSITIVE DEFINITE. THIS COULD INDICATE A NEGATIVE VARIANCE/RESIDUAL VARIANCE FOR A LATENT VARIABLE, A CORRELATION GREATER OR EQUAL TO ONE BETWEEN TWO LATENT VARIABLES, OR A LINEAR DEPENDENCY AMONG MORE THAN TWO LATENT VARIABLES. CHECK THE TECH4 OUTPUT FOR MORE INFORMATION. PROBLEM INVOLVING VARIABLE I.'

I noticed that the variances of I and S are both negative (while the residual variances are both positive). In addition, in TECH4 output, the correlation between I and S is 999.000.

These are consistent with what the warning says.

What might the underlying probelm be? How can I fix it? Many thanks!
 Bengt O. Muthen posted on Wednesday, September 07, 2011 - 8:55 pm
A growth model is not suitable for any data set. You should first do a Type=Basic analysis and look at the means and variances for the 3 outcomes as well as plot the observed individual curves for each subject. This will tell you if a linear model seems appropriate for the data. For instance, if the means increase over time and the variances decrease over time, a growth model might be hard to fit. Or, perhaps there is no trend so that you don't need a slope growth factor.
 Ben Luo posted on Wednesday, October 12, 2011 - 12:26 am
Thank you, Dr. Muthen! Your instructions are very helpful to me.

Following your suggestions, I have calculated the means and variances of three variables, and found that the means have a U shape while the variances have an inverted-U shape across three time points.

In addition, I have also checked the individual curves for each case, and found that about half of the cases presented a U shape, one fifth linearly increase, and one fifth linearly decrease.

Based on these results, can I say that there is little likelihood that a linear growth model fits well with the data?

Can I model a U-shaped growth model instead with my three time-point dataset?

Is it possible that including another variable (time-invariant or time-variant) will improve the goodness of fit for the growth model?

Thank you for considering my na´ve questions! Many thanks!

Ben
 Linda K. Muthen posted on Wednesday, October 12, 2011 - 12:21 pm
The problem with having only three time points is that you cannot fit a quadratic model. The linear model has only one degree of freedom. For further details, see Slide 52 of the Topic 3 course handout.
 Ben Luo posted on Sunday, October 16, 2011 - 10:49 pm
Thanks Dr. Muthen! Now I know my dataset can only possibly fit a linear model.

There is one follow-up question that I hope you can help with.

As so far the univariate linear growth model does not work for my dataset, is it possible that a more complicated, multivariate LGM still can instead fit better with the data? In other words, is univariate LGM a basis of multivariate LGM?

Thanks a lot!

Ben
 Linda K. Muthen posted on Monday, October 17, 2011 - 1:05 pm
A univariate linear growth model is the same as a multivariate linear growth model with the exception that the residual variances are held equal across time for the univariate model. The model I refer to with one degree of freedom is a multivariate linear growth model where residual variances are estimated at each time point.
 Rimantas Vosylis posted on Sunday, December 11, 2016 - 5:00 am
Hi,
I have a three wave longitudinal data and I want to run LGM analysis with one linear slope factor and one intercept. My time intervals are equally spaced.
My main question is this:
it ok to add equality constraints for first and third time point residual variances?

I have been doing some simple regressions using timepoints as predictors, for each individual separately and I noticed that residuals are always equal for first and third timepoints. So it does seem that variances of the residuals in LGM model of first and third time point should also be equal. However I have never seen this done before, so I thought i might ask

thank You
 Bengt O. Muthen posted on Monday, December 12, 2016 - 10:36 am
Sounds a bit like data fishing. Typically you either hold all residual variances equal or none. Unless you have a theoretical reason for just doing it for some time points.
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