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"?
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.