Latent Growth Curve modeling - some Q... PreviousNext
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 Lee_50 posted on Friday, December 30, 2005 - 12:46 pm
I use the Mplus User's Guide and then have some questions.

1. Some papers write down the status facotr, it is the same the intercept growth factor, isn't it? ( I think it is same but I want to make sure.)

2. Fix the model, consist of two basic random-effects growth factors: an overall status factor and a linear growth facotr...so overall status factor is also the same in (1).

3. Want to use: Full-information maximum-likelihood estimation under missingness, so I search it but the option='estimator', it is not find...could you tell me? just default or ML( is the FIML)

4. Want to use: satorra-bentler corrections to chi-square tests of model fit and parameter standard errors, but if I just use the Multilevel model, I got chi-square test value. is this same??

5. Use the other kind of modelin, I got the P-value from output, but the mulitlevel model result didn't give this part(p-value) how to calcuate p-value? or it is possible in Mplus?

Some questions is not difficult. But I really want to make sure. Cuz, each book and paper..they use the different word even if the same meanning..this kinds of thing it is not good me..confuse.
Thank you so much for helping. It is too help to me.
 Linda K. Muthen posted on Saturday, December 31, 2005 - 9:37 am
1-2. When the slope growth factor has the zero time score at the first timepoint, the intercept growth factor describes initial status. If the zero time score is at the last timepoint, the intercept growth factor describes final status. Perhaps this is what you mean.

3. Any maximum likelihood estimator will give you full-information maximum likelihood.

4. MLM gives the Satorra-Bentler chi-square.

5. I think you mean you are not getting chi-square and the p-value for chi-square. When means, variances, and covariances are not sufficient statistics for model estimation, chi-square is not available.
 Geertje Leflot posted on Tuesday, February 24, 2009 - 4:53 am
I have run a latent growth curve model to analyze the development of ADH problems. I have analyzed whether the development of these problems is different in the control and intervention condition, by regressing the intercept and the slope of the growth curve model on the intervention status (cond). There is a significant effect of the intervention status on the slope (not on the intercept).
QUESTION: I would like to visualize the growth of ADH problems in the control and intervention condition. Can this be done in Mplus?

I have already tried this, but I cannot find a way to visualize the growth in the two groups:
Iadh Sadh | ADHD1@0 ADHD2@.5 ADHD3@1 ADHD4@1.5;

Iadh Sadh;
Iadh with Sadh;

Iadh on male cond;
Sadh on male cond;


output: sampstat modindices(3) stand cinterval
TECH4 TECH1;

PLOT: TYPE IS PLOT3;
SERIES is adhd1 - adhd4 (Sadh);
 Linda K. Muthen posted on Tuesday, February 24, 2009 - 9:22 am
Look at the adjusted means plot. I think that will give you what you want.
 Lisa M. Yarnell posted on Thursday, September 29, 2011 - 4:47 pm
Hi Linda, I am running a latent growth model with 4 time points, and received this message: THE MODEL ESTIMATION TERMINATED NORMALLY WARNING: 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 SLOPE.

Do you see anything wrong with my code below? I tried loosening starting values for loadings to slope, and tried providing a positive starting value for the variance of SLOPE, since the message suggested that there may be a negative variance for this factor--I did indeed see this in the TECH4. Can you give me suggestions, or may I send you my data? Thank you!

USEVARIABLES ARE ALDH2DI YEAR1 YEAR2 YEAR3 YEAR4;

MISSING IS .;
ANALYSIS: TYPE = MEANSTRUCTURE;

MODEL:

INTERCEPT BY YEAR1@1 YEAR2@1 YEAR3@1 YEAR4@1;

SLOPE BY YEAR1@0 YEAR2*.33 YEAR3*.67 YEAR4@1;

INTERCEPT ON ALDH2DI;

SLOPE ON ALDH2DI;

INTERCEPT WITH SLOPE;

OUTPUT: SAMP STAND RES MODINDICES(0) tech1 tech4;
 Linda K. Muthen posted on Thursday, September 29, 2011 - 5:38 pm
Part of the problem may be that you are not specifying the growth model correctly. If you use BY, you must fix the intercepts to zero and free the growth factor means. It would be easier if you use the growth language:

intercept slope | YEAR1@0 YEAR2*.33 YEAR3*.67 YEAR4@1;

Then everything is done correctly as the default and the default starting values are better than those for the BY statements.

I would also fit the growth model before adding ON statements.
 Lisa M. Yarnell posted on Monday, October 03, 2011 - 2:02 pm
Thanks, Linda! It worked! I have one more question: I saw both variance of latent intercept and slope, and RESIDUAL variance for latent intercept and slope reported in Bengt Muthen's writeup of a similar analysis, where he modeled the effect of predictors on latent intercept and latent slope: http://gseis.ucla.edu/faculty/muthen/Papers/Article_080.pdf

In my output, I do see the residual variances, including for latent intercept and latent slope, but not the variances of latent intercept and slope themselves.

Where do I find variance of latent intercept and latent slope in the Mplus output (not residual variances)?

Thank you so much!
 Linda K. Muthen posted on Monday, October 03, 2011 - 2:56 pm
You can find these in TECH4.
 Lisa M. Yarnell posted on Monday, October 03, 2011 - 4:13 pm
Thanks, Linda. I see this in the TECH4:

ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES

INTERCEP SLOPE ETHNIC
INTERCEP 1.677
SLOPE -0.318 1.117
ETHNIC 0.033 -0.082 0.250

But, what are the standard errors and significance levels? I saw that Bengt provided these along with the latent intercept and slope variances in his aforementioned writeup.

Thanks again.
 Lisa M. Yarnell posted on Monday, October 03, 2011 - 7:02 pm
Linda, can you tell me whether standard errors and significance levels are available for these variances?
 Bengt O. Muthen posted on Monday, October 03, 2011 - 8:25 pm
To get the SEs of thes TECH4 quantities, you would have to express the quantities in Model Constraint as new parameters. Then the SEs are obtained automcatically using the delta method.
 Lisa M. Yarnell posted on Tuesday, October 04, 2011 - 4:30 pm
Thanks, Bengt. Can you tell me what I am doing wrong here (see code below)?

Is it possible to estimate both the variance and residual variance of a latent variable using the delta method? I get the message: THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES COULD NOT BE COMPUTED. THE MODEL MAY NOT BE IDENTIFIED. CHECK YOUR MODEL. PROBLEM INVOLVING PARAMETER 14. THE CONDITION NUMBER IS 0.000D+00.


USEVARIABLES ARE ETHNIC YEAR1 YEAR2 YEAR3 YEAR4;

MISSING IS .;

DEFINE: ETHNIC = ETHNIC-1;

ANALYSIS: TYPE = MEANSTRUCTURE;

MODEL:

INTERCEPT SLOPE | YEAR1@0 YEAR2* YEAR3* YEAR4@1;

INTERCEPT ON ETHNIC;

SLOPE ON ETHNIC;

INTERCEPT WITH SLOPE;

MODEL CONSTRAINT:
NEW(INTERCEPT SLOPE);

OUTPUT: SAMP STAND RES MODINDICES(0) tech1 tech4;
 Bengt O. Muthen posted on Tuesday, October 04, 2011 - 9:18 pm
You have to define New parameters in Model Constraint - you haven't done that. For an example, see UG ex 5.20.
 Lisa M. Yarnell posted on Wednesday, October 05, 2011 - 9:30 pm
Bengt, I apologize for any oversight I am making, but I can't think of how to define the variances of latent intercept and latent slope using other terms in the model, except R2 + residual variance (i.e., variance explained plus variance unexplained). However, R2 and residual variance are not have explicitly named terms in the model; these are just statistics produced automatically by Mplus.

What I am looking for are the standard errors of the variances for latent intercept and latent slope in my latent growth model, as you reported in your writeup here: http://gseis.ucla.edu/faculty/muthen/Papers/Article_080.pdf

I see the variances in the TECH4 output, but not the standard errors of the variances.

Can you tell me how you would write these model constraints?
 Lisa M. Yarnell posted on Thursday, October 06, 2011 - 12:25 am
I apologize: In my previous post, I meant to write, "However, R2 and residual variance are not explicitly named terms in the model; these are just statistics produced automatically by Mplus." So, I am just not sure how to write the model constraints.
 Linda K. Muthen posted on Thursday, October 06, 2011 - 8:31 am
TECH4 does not have standard errors. For a well-fitting model, you can obtain standard errors for the variances by running the unconditional model where variances are estimated. This is probably the best solution in your case where residual variances at not model parameters.
 Lisa M. Yarnell posted on Monday, November 21, 2011 - 5:10 pm
Hello again Linda.

If a predictor GENDER with females coded as 1 affects a latent growth factor negatively, is it more appropriate to say that females showed LESS growth from the starting point (reflected by score on Initial Status) or showed SLOWER growth from the starting point?

I have heard velocity of latent growth. How does one measure velocity of latent growth? Is this something different than what is reflected by the loadings onto the latent growth factor, or the effect of a predictor such as gender on the latent growth factor?

Thank you for your knowledge,
Lisa
 Lisa M. Yarnell posted on Monday, November 21, 2011 - 9:46 pm
Linda, my quesrtion is:
How does one measure velocity of latent growth? Is this something different than what is reflected by the loadings onto the latent growth factor, or the effect of a predictor such as gender on the
latent growth factor? Is it reflected in how much freely estimated loadings onto the latent growth factor jump from one time point to another? For example, if you have several loadings: .00, *, *, *, *, 1.00 (with * meaning it is freely estimated), and the jump between loadings between time 1 and time 2 is a bigger jump than the loadings between time 4 and time 5, could you say that the first part of the trajectory has greater VELOCITY of growth? Is this velocity quantifiable?
 Bengt O. Muthen posted on Tuesday, November 22, 2011 - 5:54 pm
I am not familiar with the concept of velocity of growth - perhaps you can google for references that describe it.
 Mary Ann Simpson posted on Wednesday, November 30, 2011 - 4:24 pm
Hi, Dr. Muthen! I think Lisa M. Yarnell may be referring to the linear term in a growth model. I've heard the linear term referred to as velocity and the quadratic term as acceleration. I think the mean of the linear term in the LGM is what she's looking for.
 Lisa M. Yarnell posted on Thursday, December 15, 2011 - 11:31 am
Drs. Muthen: If in a 4 time point LGM, I set error variance to be the same across time points (which I see demonstrated in the Mplus manual), is it also possible to correlate errors for subsequent time points? Given that it is the same scale administered at multiple time points, it makes sense that scores would be correlated. However, does this introduce some sort of dependency issue in the model--either due to the errors being set to be equal across the time points, or otherwise? The model below runs well without the correlated errors, but crashes when I correlate them in either of the patterns shown below (in the correlations between YEAR1-YEAR4).

MODEL:

INTERCEPT SLOPE | YEAR1@0 YEAR2@0.385 YEAR3@0.692 YEAR4@1;

INTERCEPT ON GENDER ETHNIC;
SLOPE ON ALLELE;
INTERCEPT WITH SLOPE;

YEAR1-YEAR4 (1);

YEAR1 WITH YEAR2;
YEAR2 WITH YEAR3;
YEAR3 WITH YEAR4;

!YEAR1 WITH YEAR2 YEAR3 YEAR4;
!YEAR2 WITH YEAR3 YEAR4;
!YEAR3 WITH YEAR4;
 Linda K. Muthen posted on Thursday, December 15, 2011 - 12:55 pm
The fact that the same item is repeatedly measured is what the growth models takes into account. There may also be a need for residual covariances across time. You can look at modification indices to check this. You can hold the residual variances equal across time or not. There are generally held equal in multilevel modeling programs but that is not necessary in Mplus. If you want me to look at your output, please send it and your license number to support@statmodel.com.
 Gabriella Melis posted on Thursday, August 01, 2013 - 8:15 am
I am running a conditional LGCM with multiple indicators at each time point; each indicator is an ordered categorical. In my model I have time-varying (TVC) and time-invariant covariates (TIC). TVC and TIC are included as sets of dummies, as they are all categorical too.
The model runs well, however I loose 50% of the cases compared with the unconditional LGCM.

Then I tried to run the same conditional model after restating the names of the TIC and TVC, as we do for other models when we want Mplus to use all the available cases (full-information ML), for example:
construct1991 0n educ1 educ2;
educ1 educ2;
...

In this second case I only loose around 15% of cases, but unfortunately the model does not converge (message: number of iterations exceeded).

Please, can I do anything to avoid dropping all those cases and get my model to run?

If not, would it be correct to compare results, e.g. growth factors' estimates, between the unconditional and conditional models if the number of cases varies so much between the two?

Thank you.
 Bengt O. Muthen posted on Thursday, August 01, 2013 - 2:03 pm
Here's a trick that we suggest when you have missing on tics and the missingness for the tic at time t implies that the outcomes y at time t are missing. Score the tics at values not designated as missing data symbols. Then subjects with missing on tics will be included but not affect the likelihood due to missing on outcomes.
 ywang posted on Wednesday, March 26, 2014 - 12:56 pm
Dear Drs. Muthen,

We worked on a latent class growth model. The outcome variable is clearly very skewed. One reviewer mentioned that it has implications for erroneously identifying latent classes in a population when we treated it as a continuous variable. What can we do for the skewed outcome variable in latent class growth modeling (and the parallel latent growth modeling linked to another outcome)?
Thanks a lot!
 Linda K. Muthen posted on Thursday, March 27, 2014 - 2:02 pm
Two issues are relevant in this situation. One is whether the classes make substantive sense based on theory. The other is whether external validity can be demonstrated using a distal outcome. See the following paper which is available on the website:

Muthén, B. (2003). Statistical and substantive checking in growth mixture modeling. Psychological Methods, 8, 369-377.
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