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?
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.
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
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.
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.