Within and between-person analyses PreviousNext
Mplus Discussion > Multilevel Data/Complex Sample >
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 Matthew S Kendra posted on Monday, April 09, 2012 - 4:54 pm
I am disentangling within- and between-person effects by running this model:

USEVARIABLES y1 y2
ANALYSIS: TYPE = TWOLEVEL;
MODEL:
%WITHIN%
y1 WITH y2 (gamma10);
%BETWEEN%
y1 WITH y2 (gamma01);
MODEL CONSTRAINT:
NEW(betac);
betac = gamma01 - gamma10;

The model works, but I got curious and ran
it substituting "ON" for "WITH", and the findings are quite disparate. For example, the estimate/SE/p-value for the "BETAC" between-subjects is .692/.146/.000 in the "WITH" model, and .382/.316/.228 in the "ON" model.

(a) Why the large disparity?
(b) Which is more appropriate to use: "WITH" or "ON"?
 Linda K. Muthen posted on Wednesday, April 11, 2012 - 3:41 pm
While the two models are equivalent in terms of the loglikelihood, the betaC parameter is a difference between a covariance in one of the models and a regression coefficient in the other model. The two versions of betaC have no connection as far as I can see. For example significance of BetaC doesn't mean the two variables are correlated in either model - not really sure what meaning is put into betaC. Contextual effects should be examined using ON.
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