Xu, Man posted on Friday, August 08, 2008 - 9:12 am
Please ignore my last post. I ran a very simple two level model - one dependent variable and two predictors, an individual level predictor and a group level predictor, which is also the group mean of the first predictor (specified to be a BETWEEN variable in the model). I got result from input where I specify the individual predictor to be a WITHIN variable. I also got result from not specifying the individual predictor at any level. The coefficients for the individual level predictor remain the same for results from both inputs. But the coefficients for the between level variable differ from the two results dramatically. How should I understand this? Thanks!
Please see V5 UG ex 9.1 part 1 and part 2. When you don't declare the individual predictor to be WITHIN, the within-level latent variable part of the variable is used as a predictor on the within level. This can be viewed as a latent group-mean centered predictor - see top of page 231. This changes the meaning of the random interept as compared to using the observed individual predictor.
Xu, Man posted on Thursday, August 14, 2008 - 6:49 am
I see. Thanks! I was still using the version 4 manual... I have a few more questions, if you don't mind...
Is this latent group mean procedure in version 5 manual aslo applied in Mplus version 4, or even MLwin??
If I let x to be decomposed at both levels, but not to specify it again as a covariate at %between%, would Mplus still decompose variance of x and use the latent group mean as a latent covariate to explain the intercepts anyways? -I guess this is actually what I did previously in my previous post using Mplus Version 4.
Also, why both models use grandmean cenered X? Does grandmean center give a special meaning for the estimated coefficients for X or W, or it is just to make computation faster??
Sorry for asking so many things and thank you in advance!
Q1. It is part of Mplus 4 as well. It is not in MLwiN as far as I know.
Q2. No, if you don't mention x on between it is not a predictor there.
Q3. For centering, please read the Version 5 UG ex 9.1 and 9.2 (if you don't have the book, it can be found on our web site). Centering is not used to make the computations faster, but is often used to help interpretations.
Xu, Man posted on Thursday, August 21, 2008 - 3:59 am
Thanks! Can I ask in more detail about Q2? In relation to Q2 "If I let x to be decomposed at both levels, but not to specify it again as a covariate at %between%, would Mplus still decompose variance of x and use the latent group mean as a latent covariate to explain the intercepts anyways?" You said it would be a covariate. But:
If I speify x to be a within variable, then the result for this covariate is similar to what I would normally get using a multiple regression. When I don't specify x to be within, and include a variable for group mean x (direct aggregation) on level 2, the result for this covariate I got is quite similar to what I would get using a latent mean x(the latent group-mean centered predictor). Why is this?
About Q3, in Version 5 UG ex 9.1 and 9.2, there isn't a section on grandmean centering... I guess in a multiple regression, grandmean centering just makes the intercept to be value of the mean of x. But in TTPE=TWOLEVEL or any similar multilevel analysis, there is only one intercept estimate at level 2 part of the output, is this intercept also the mean of x as in a multiple regression?
Xu, Man posted on Thursday, August 21, 2008 - 4:03 am
correction to last sentence of my post *You said it would not be a covariate. But: