Longitudinal CFA
Message/Author
 Ryan Krone posted on Tuesday, June 02, 2015 - 7:56 pm
I have a CFA model using 5 indicators with multiple time points (29 time points). Is it possible to see how each of the indicators contribute to the latent factor over time? Is this something that the latent growth curve model can accomplish?
 Bengt O. Muthen posted on Wednesday, June 03, 2015 - 10:39 am
Although heavy computationally, you can do longitudinal factor analysis where you consider data in the wide format with 5*29 variables and 29 factors.

An alternative is UG ex9.27 using random parameters and able to handle many time points. See also the paper on our website:

Asparouhov, T. & Muthén, B. (2014). General random effect latent variable modeling: Random subjects, items, contexts, and parameters. Version 2. Forthcoming in the edited book "Advances in Multilevel Modeling for Educational Research: Addressing Practical Issues Found in Real-World Applications”.
 Ryan Krone posted on Saturday, June 06, 2015 - 12:53 pm
Thank you for your response, Dr. Muthen. Sorry for the delay in mine.
I have a couple of questions having reviewed the model you suggested (9.27). I should mention that my data is 190 observations over 29 time points. Is this still a valid model?
If so, would the data be arranged in long format with both a subject id and a time id?

Regards.
 Bengt O. Muthen posted on Saturday, June 06, 2015 - 3:20 pm
UG ex 9.27 has 75 subjects over 100 time points. See the User's Guide examples on our web site for the data layout. It is in long form with subject and time id.
 Ryan Krone posted on Thursday, December 03, 2015 - 6:30 pm
Dr. Muthen,

I’ve run the model in 9.27 and I have results. I’ve read the paper you suggested above (Asparouhov, T. & Muthén, B. 2014). However, I think I still need help understanding how to interpret these results. Given the discussion in the paper, in 9.27, observations are cross-nested within individual and time, correct? I think I’m confused because there are three levels in 9.27., so there must be an individual level, a time level, and a cross-nested level. Is WITHIN the cross-nested level?

Regards,
 Bengt O. Muthen posted on Friday, December 04, 2015 - 6:24 am
Within is nested within the cross-classification of individual and time. See multilevel books such as the one by Joop Hox.
 Ryan Krone posted on Saturday, December 05, 2015 - 2:41 pm
Thanks Dr. Muthen. I'm reviewing his book.
I have two other questions.

1) Is there a way to determine model fit with these types of models? I noticed there wasn't the typical model fit indices.

2) Just so I understand how to name this particular model for publication purposes would it be appropriate to call it a "Cross-classifed Random Effects CFA"?

 Bengt O. Muthen posted on Sunday, December 06, 2015 - 10:49 am
1) Not that I know. But you can always compare neighboring models using DIC.

2) Yes.
 Ryan Krone posted on Saturday, January 30, 2016 - 12:13 pm
Dear Drs. Muthen:

Full disclosure, I come from a frequentist background and my experience with Bayesian techniques is limited. What is the reason for not producing goodness of fit stats?

Also, does the Bayesian estimator handle missing data in any particular way using the model for example 9.27?

Regards,
 Bengt O. Muthen posted on Monday, February 01, 2016 - 10:06 am
Fit is given by the PPC for models where chi-square is given with ML.

Bayes handles missing data just like
"FIML".
 Ryan Krone posted on Sunday, March 20, 2016 - 12:19 pm
Dr. Muthen,

I've run a model similar to the one in example 9.27 and I have results. I’ve read your paper (Asparouhov and Muthen 2014) but I think I need help linking the results in Mplus to the structure of the paper.

Using the TOCA example from your paper for the cross-classified intensive longitudinal growth model and comparing it to the results of the model in 9.27:

In the Within Level, the intercepts are fixed at zero. Residual variances of the factor loadings are produced on this level in the results. What column of Table 6 (TOCA example) do these residual variances at the individual level refer to?

In the between time level, the means of the random loading factors and the variances of the loading factors are produced in the results. I understand that this level tests for measurement non-invariance. However, what columns of Table 6 (TOCA example) do these means and variances in the results refer to?

In the between subjects level, I'm assuming the results of this model produces the mean of the slope growth factor (S in results = Bi in your paper), the variance of the intercept growth factor (F in results = ai in your paper) and the variance of the slope growth factor (S in results = Bi in your paper).

Is this framework on this level analogous to an interpretation of a basic growth model?

Am I on the right track here? Your help is greatly appreciated.
 Tihomir Asparouhov posted on Tuesday, March 22, 2016 - 11:15 am
> What column of Table 6 (TOCA example) do these residual variances at the individual level refer to?

None. The TOCA example is for categorical variables (residual variances are fixed to 1) while example 9.27 is for continuous variables.

> However, what columns of Table 6 (TOCA example) do these means and variances in the results refer to?

The last two (but note that the model is not the same as in 9.27, the extra term lambda_p sigma_t term in equation (56) models the common variation in the random loading / time specific factor variance)

> Is this framework on this level analogous to an interpretation of a basic growth model?

Yes
 Ryan Krone posted on Sunday, March 27, 2016 - 2:22 pm
Thank you for your help on this and this will be my last set of questions. Because 9.27 is different from the TOCA example in the paper because they have categorical DVs, help me understand the continuous version.

On the within subject level, are the residual variances the within-subjects variance across time points? Does this represent the presence of measurement error or just unexplained variance in general?

On the between time level, are the means of the random factor loadings (s1,s2,s3) the intra-individual mean change in factor loadings over time?

On the between time level, what is the difference between the random intercept (y1,y2,y3) and the random factor loading (s1,s2,s3) variances? Are the variances of the random intercept the intra-individual differences in initial values of the factor loadings? If so, what do the random factor loading variances represent (s1,s2,s3), intra-individual changes?

Best Regards,
 Tihomir Asparouhov posted on Monday, March 28, 2016 - 9:05 am
> On the within subject level, are the residual variances the within-subjects variance across time points?

Yes

> Does this represent the presence of measurement error or just unexplained variance in general?

measurement error

> On the between time level, are the means of the random factor loadings (s1,s2,s3) the intra-individual mean change in factor loadings over time?

The random loadings in this example do not vary across individual due to this command

%BETWEEN subject%
s1-s3@0;

The means of the random factor loadings on the between time level represent the average loadings across time. The residuals of (s1,s2,s3) represent the time specific deviations from the means (measurement non-invariance).

> On the between time level, what is the difference between the random intercept (y1,y2,y3) and the random factor loading (s1,s2,s3) variances?

> Are the variances of the random intercept the intra-individual differences in initial values of the factor loadings?

The variance of the random intercept only applies to the intercpets. For example, if a particular measurement Y1 has a time specific deviation from the average explained by the growth model it is represented by that random intercept - "weather" specific effects on depression for example (on average worse depression beyond systematic model).

> If so, what do the random factor loading variances represent (s1,s2,s3), intra-individual changes?

It represents changes in the quality of an measurement item. For example if you are measuring aggressive behavior in students, "fighting with other students" measurement item may decrease in quality for later grades as the behavior is not as prevalent in later grades.
 Ryan Krone posted on Monday, March 28, 2016 - 2:56 pm
Thanks Tihomir. This makes sense now. Much appreciated.