Interpretation of multilevel LGM
Message/Author
 lotti posted on Thursday, November 22, 2012 - 7:35 am
Dear Dr, Muthén,

I'm working with longitudinal data on job performance with workers nested within offices. In particular, I have 7 data points, (1-year spaced), and a mean ICC above .15 (all DIFF are over 2). I would try multilevel LGM with Mplus. In this regard, I have several questions.

1. How we should interpret intercept at the "within" and the "between" level? I mean: as far as I understand, only intercept and slopes at the "between level" could have means.
2. How we should interpret the estimated trajectory in a multilevel LGM? It is related only to the "between level" part of the model?
3. Curran, bauer & Willoughby (2004) (http://www.ncbi.nlm.nih.gov/pubmed/15137890) offered methods to probe the intrecation between predictors and time in LGM. Are these procedures still valid in multilevel LGM?

Thank you in advance for your support.
 Bengt O. Muthen posted on Thursday, November 22, 2012 - 8:38 am
1. The intercept (and slope) growth factor should have a variance on each of the two levels, but a mean on only the between level.

2. The estimated trajectory refers to the estimated means for the outcomes. There is only one mean per outcome even for multilevel data. The fact that the means are reported on the between level is just a convention.

3. With 2-level data you have predictors on 2 levels, so their probing would be a bit different.
 lotti posted on Thursday, November 22, 2012 - 8:51 am
Dear Dr. Muthén,
thank you so much for your quick reply. I have only two minor questions related to point 3 above.
How I should interpret the effect of a covariate on the slope/intercept at the between or within level? Are these effects similar to those in a standard two level model? The fact is that I cannot fully understand the presence of two slopes and intercepts and a single trajectory.

My second question is very minor. Can you suggest a paper (or more) presenting an empirical application of two level LGM? This could help me a lot.
thank you for your assistance.
 Bengt O. Muthen posted on Thursday, November 22, 2012 - 9:19 am
You should think of the slope/intercept as consisting of a part for each of the 2 levels - in your case for workers and for offices. In the unconditional model you estimate the variance corresponding to each of those 2 parts (variance across workers and across offices) and in the conditional model you explain the variation in those 2 parts.

You may want to study the Raudenbush-Bryk (2002) Sage book where Chapter 8 talks about 3-level models (in your case time, worker, office). The section on Studying Individual Change Within Organizations should be just right for you.
 lotti posted on Thursday, November 22, 2012 - 11:19 am
Dear Dr Muthén,

thank you: your comments have been enlightening.
I appreciate very much your prompt availability
 Paul A.Tiffin posted on Saturday, November 24, 2012 - 9:16 am
Dear Mplus Team

I was delighted to see the ability to estimate cross-classified models in Version 7. I am trying to re-estimate a Multi-level logistic regression model (which originally ignored the non-nesting of observations) using this approach. The data is as follows: I am looking at the probability of an application to a University resulting in the offer of a place. Each candidate applies to between 3 and 5 institutions. Thus there are candidate level variables (e.g. academic achievement, sex, age etc) and university level variables (e.g. their admissions policy). However, candidates are not strictly nested within institutions applied to. Also, do I need to use an application level id (e.g. app_id)?
To initially keep it simple, how might I create the model command syntax if 'cand_id' is cluster level id for individuals, 'uni_id' is the university identifier, candidate level variables are , say 'ses' and 'ach'[academic attainment as a z score], 'offer' is a binary variable indicating success of an application event (these are nested within candidates), and 'group' is an ordinal variable relating to the weight placed on an aptitude test by the university applied to? Many thanks for you help.

bw

Paul
 Linda K. Muthen posted on Saturday, November 24, 2012 - 10:41 am
For a categorical dependent variable, cross-classified models are available with the Bayes estimator and probit regression. See Exmaple 9.24.
 Bengt O. Muthen posted on Saturday, November 24, 2012 - 11:20 am
See also the handouts and videos from the Utrecht Version 7 training in August on our web site. The "pupcross" example from Hox' multilevel book that I go through might be helpful.
 Paul A.Tiffin posted on Saturday, November 24, 2012 - 11:31 am
Thanks

I had a look already at ex 9.24 but will have a look at the video material and get back to you if I get stuck

best wishes

Paul
 Tobias Debatin posted on Wednesday, December 17, 2014 - 8:55 am
Dear Mplus Team,

we are doing a longitudinal analysis of language skill development (4 time points). Because of high intraclass correlations we want to use a multilevel LGM. (time, persons, classes) We estimated the unconditional model with free time scores (t1@0 t2 t3 t@1) and we get different "factor loadings"(?) of the within and between slope factors. How do i interpret this? As lotti before i dont understand how to interpret the two slopes (between and within) in multilevel models in general.

Thank you in advance!
 Bengt O. Muthen posted on Thursday, December 18, 2014 - 12:13 pm
If you work with free time scores I think you should hold them equal across Within and Between because otherwise the model will become difficult to interpret (the var-cov structure influenced by a different growth shape than the mean structure).
 Tobias Debatin posted on Thursday, December 18, 2014 - 3:13 pm
Thank you! How do you specify this in the syntax? I tried to look it up but im not sure with the two(three) levels and the | symbol.

What would be your suggestion for an introductory text/ examples for multilevel latent growth models?
 Bengt O. Muthen posted on Thursday, December 18, 2014 - 5:15 pm
Look at slide 62 of our video and handout for our Topic 8 course on our website.
 Tobias Debatin posted on Friday, December 19, 2014 - 6:04 am
Thank you again, i tried it like on the handout before (and now again) and i get the error message that (1) is an unknown variable in a growth statement. I used the alternative syntax now and it seems to work, is this ok?:

MODEL:

%WITHIN%
iw by E_1-E_4@1;
sw by E_1@0;
sw by E_2 (1);
sw by E_3 (2);
sw by E_4@1;

%BETWEEN%
ib by E_1-E_4@1;
sb by E_1@0;
sb by E_2 (1) ;
sb by E_3 (2) ;
sb by E_4@1;
[E_1-E_4@0 ib sb];
 Linda K. Muthen posted on Friday, December 19, 2014 - 6:44 am
You can look at the results to see if you accomplished your goal. I would say:

MODEL:

%WITHIN%
iw by E_1-E_4@1;
sw by E_1@0
E_2 (1)
E_3 (2)
E_4@1;

%BETWEEN%
ib by E_1-E_4@1;
sb by E_1@0;
E_2 (1)
E_3 (2)
E_4@1;
[E_1-E_4@0 ib sb];
 Tobias Debatin posted on Friday, December 19, 2014 - 7:42 am
Im very grateful for your great support! A big compliment to mplus and your work in general!