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st: AIC/BIC and "comparison of standardized beta coefficients"


From   "Boecking, Benjamin" <Benjamin.Boecking@iop.kcl.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: AIC/BIC and "comparison of standardized beta coefficients"
Date   Mon, 8 Dec 2008 10:04:13 -0000

Dear colleagues,

I am currently analysing a longitudinal dataset (n = 62, up to 14
measurement occasions per person) using Mixed Models in STATA 10 (as the
n turned out to be too small to use other models and/or programs).

(1) I have a dependent variable A1 (outcome), and an independent
variable A2 (predictor), and control thorughout for time.

(2) Moreover, I lag the dependent variable with various offsets to see
(a) whether I can predict changes in the DV by "previous" predictors and
(b) which "lag" predicts best. 
Outcome_lag1 -> Predictor || Outcome_lag2 -> Predictor || Outcome_lag3
-> Predictor.

(3) Once I have calculated these models, I switch the positions of the
DV and IV and do everything again to maybe get a hint at the
directionality in which these influences work.


Now here are my problems:
(1) When I compare two different models (e.g. M_lag -> Y vs. Y_lag->M)
it happens that - although the beta for one model is smaller - the
corresponding z-value is higher AND the model fit is BETTER (i.e.
smaller).

(1.1) Also, it happens that the model fits the better, the higher the
lag is (although the predictive power decreases of course). However, I
suppose this is mostly due to the decreased number of observations
(depending on the respective lag OR the change of IV and DV), and NOT to
a better model fit as with each lag, betas decrease. 

- So how can I get a "true" model fit, that takes the strength of the
prediction into account? (Keep in mind that a lagged DV and a lagged IV
inevitably produce changed patterns of "deleted" obeservations)
- Is there a way of comparing model fits of different models to make a
comparative statement about the "goodness   of fit"?
- And if not - is there any other way of reasonably comparing the
various lagged models?

(2) I'd like to compare the A1->A2 and the switched-around A2->A1
models. Yet again, as different sets of observations are deleted each
time (i.e. the empty obervations in the dependent variable with the
longestlag which is included in the model), I cannot compare the model
fit indices.

- Is there any test around which tests beta coefficients (of DIFFERENT
models) against each other? 


I apologize to all of my colleagues who think this to be a stupid
question, yet, any help would be appreciated.

Many thanks
Benjamin

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