> --- On Tue, 24/11/09, John Holmes wrote:
>> The texts on LGM suggest that group modelling can be done
>> so you are not simply estimating a single uniform effect
>> on all coefficients from the grouping variable (as you
>> say this is equivalent to including it as a main effect);
>> but instead having two separate but simultaneously
>> estimated models so that in practice each parameter has
>> been given its own individual grouping variable effect.
>
> That sounds exactly like an interaction effect between the
> grouping variable and whatever other variable you are
> interested in. The main effect of the grouping variable
> shifts the curves uniformly up or down, and the interaction
> effects change the slopes of these curves. Together, they
> make sure that each group defined by the grouping variable
> has its own curve, and all this is simultaneously estimated
> in one model.
>
> Hope this helps,
> Maarten
>
> --Maarten
I agree with Maarten--you are describing interactions. The separate
intercepts, separate slopes model is so named because it
simultaneously estimates an intercept and slope for each level of the
grouping variable. I just noted in my previous posting that this model
is equivalent to an typical interaction model that we fit, it just
reparamaterizes the model so that the coefficients represent separate
intercepts and slopes (rather than differences from the constant and
from the main effect of time). The model I described in the previous
post is equivalent to what Mplus would do in a multiple-group analysis
(which by definition estimates separate coefficients -- intercepts and
slopes -- for each level of the grouping factor). If you want the
model where there is no constraints across groups, then you'll want to
use the final model where all the random effects and the residuals
vary across groups.
Hope that helps.
Best,
Scott
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