Multilevel latent growth curve model
Message/Author
 Sophie posted on Tuesday, March 22, 2016 - 3:57 am
I specified a latent growth curve model to test the effectiveness of an intervention. As the intervention was provided to mothers, and I am analyzing data at the child level (91 mothers with 133 children; ICC ranged between 37-88%), I need to control for the multilevel structure (I am not interested in the difference between/within change). What variable do I need for this and how can I specify this in my lgcm? Thanks in advance!
 Bengt O. Muthen posted on Tuesday, March 22, 2016 - 1:31 pm
Your cluster variable is mother id. Using that, you can either do a Type=Complex analysis which keeps your model the same as what you have or you can do a Type=Twolevel analysis in line with UG ex 9.12.
 Frank Egloff posted on Monday, February 06, 2017 - 6:35 am
Dear Drs. Muthen,

I ran a two-level (classes, students) latent growth curve model(free slope). My goal is to look at cross-level and between-level-interaction effects of the variable “cos”.

Input:

VARIABLE:
………
between = cos;
cluster = class;
ANALYSIS:
type = TWOLEVEL Random;
ALGORITHM=INTEGRATION
MODEL:
%within%
iw sw | t1@0 t2 t3 t4 t5 t6 t7 t8@1;
t1 - t8 (1);
sw@0 ! because of negative (non-significant) residual variances of the within slope
b | sw ON iw
%between%
ib sb | t1@0 t2 t3 t4 t5 t6 t7 t8@1;
t1_tv - t8_tv@0;
ibxcos | IB XWITH cos;
b sb ON cos;
sb ON ibxcos;

Questions:

Does it make sense in this model that I…
1. …constrained residual variances to be equal over time on the within level?
2. …fixed the residual variances @0 on the between level?

3. How are the slope between (sb) and the intercept between (ib) to be interpreted? Are their factor scores affected by all points of measurement (as in linear growth modeling)? Or are they affected by the first (and the last) point(s) of measurement only?

Thank you so much!
 Bengt O. Muthen posted on Monday, February 06, 2017 - 3:38 pm
1-2. Yes

3. ib and sb are the between-level parts of the growth factors. Factor scores are affected by all points.
 Frank Egloff posted on Tuesday, February 07, 2017 - 3:19 am
Dear Dr. Muthen,

thank you so much for your quick answer.

My goal is to use the between level slope growth factor (sb) as a dependent variable. It is supposed to represent reading skill competence growth of school classes. Do you think that the freely estimated slope model (as I used it) is an appropriate way to represent skill growth? Or would it make more sense to use a linear or quadratic model for my purpose? If so, could you name some reasons for this?

Model fit (when I modeled the data in a non-hierarchical way/type=complex) was best for the freely estimated slope model, it was not as good for the linear slope model and even worse for the linear slope model.

Thank you so much again!

Frank
 Bengt O. Muthen posted on Wednesday, February 08, 2017 - 2:22 pm
First, note that you should hold free time scores equal across the two levels; otherwise the mean structure and the covariance structure are different and not in line with growth modeling.

I would try to use linear or quadratic growth because of easier interpretations.
 Frank Egloff posted on Tuesday, February 14, 2017 - 10:09 am
Dear Dr. Muthen,

thank you so much!

Now the question is between linear and quadratic modeling, but I have difficulties with testing multilevel quadratic lgms (yet without covariates):

Ignoring the multilevel structure of my data to model in a single level way is no problem: The quadratic factor mean is sign. and fit compared to a linear model is improved.

Still: Accounting for the multilevel structure I get error messages (each concerning different kinds of measures to be modeled):

1. NON-ZERO DERIVATIVE OF THE OBSERVED-DATA LOGLIKELIHOOD

2. NON-POSITIVE DEFINITE FISHER INFORMATION MATRIX

%within%
iw sw qw| t1@0 t2@1 t3@2 t4@3 t5@4
t6@5 t7@6 t8@7;
t1 - t8 (1);
%between%
ib sb qb| t1@0 t2@1 t3@2 t4@3 t5@4
t6@5 t7@6 t8@7;
t1 - t8@0;

1. Is sth. wrong with my input?
2. What may have caused the errors?
3. Do I have to model in the same way on both levels (quadratic on both levels)?
 Bengt O. Muthen posted on Tuesday, February 14, 2017 - 6:35 pm
Send your output to Support along with your license number.
 Alexander O'Donnell posted on Sunday, September 10, 2017 - 6:35 pm
Dear Dr. Muthen,

If I have independent observations across three years in 30-40 different countries, and I wished to examine change over time on a macro-level. Could it be appropriate to nest individual cases within years, nest years within countries, and then run a latent growth curve on the higher-level country between-level, by using cluster-means for each year of observations? Or does the independent observations on the within-level make this type of modelling impossible or invalid? Additionally, would I have to specify to Mplus I am interested in cluster-means, or will that be run automatically.

Warm regards,
Alex
 Bengt O. Muthen posted on Monday, September 11, 2017 - 5:40 pm
If the same subjects are measured at the 3 time points, you can let the outcome for the 3 years be 3 columns in your data so that you do growth modeling in wide form. If you want country to be treated as a random mode of variation rather than a fixed mode - where fixed leads to multiple-group modeling - then country would represent level 2 in a two-level analysis. See UG ex 9.14.

But if you have different subjects at the different time points, growth modeling is not possible.
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