**=========================================================================
****Date:** Wed, 26 Jul 2006 14:15:22 -0300
**Reply-To:** Hector Maletta <hmaletta@fibertel.com.ar>
**Sender:** "SPSSX(r) Discussion" <SPSSX-L@LISTSERV.UGA.EDU>
**From:** Hector Maletta <hmaletta@fibertel.com.ar>
**Subject:** Re: Addition of covariates in forward regression analyses
**In-Reply-To:** <329A68716B57D54E8D39FD3F8A4A84DF06E0770B@um-mail0136.unimaas.nl>
**Content-Type:** text/plain; charset="us-ascii"
The criteria for inclusion (as explained in the SPSS documentation) are two:
Significance of the new variable (contribution to explaining variance of the
dependent variable) and tolerance (related to colinearity.
The significance criterion is F (additional variance explained relative to
total residual variance from the previous step). It can be fixed as an
absolute F value (default is 3.84) or as a probability (default is 0.05).
The tolerance indicator is the proportion of variance in the new variable
that is NOT explained by other variables in the equation. When the tolerance
indicator is below a certain threshold (default 0.0001) the new variable is
not accepted because it is close to an exact function of the other
variables.
Hector
-----Mensaje original-----
De: SPSSX(r) Discussion [mailto:SPSSX-L@LISTSERV.UGA.EDU] En nombre de
Peters Gj (PSYCHOLOGY)
Enviado el: Wednesday, July 26, 2006 1:24 PM
Para: SPSSX-L@LISTSERV.UGA.EDU
Asunto: Addition of covariates in forward regression analyses

Dear list,

[if this question is inappropriate (as it discusses a topic not limited
to SPSS) please tell me; I could not find rules prohibiting this online]

In forward selection multiple linear regression, which of these factors
influence whether a covariate is added to the model?

- the size of the regression weight the covariate would get
- the standard error of that regression weight
- the complete sample size

I suspect that both the size & standard error of the regression weight
are of influence, and that the sample size influences the standard error
of the regression weight.

If you don't want to know why I'm asking this, you can stop reading now
:-)
In any case thanks in advance :-)

Why I want to know this:

I am conducting several very exploratory regression analyses, regressing
the same covariates on the same criterion in a number of different
subsamples (persons with a different value on a certain variable; in
this case for example ecstasy use status (non-users, users & ex-users)).
I use the forward method to probe which covariates yield a significant
addition to the model. The covariates are placed in six blocks (on the
basis of theoretical proximity to the criterion; the idea is that more
distal covariates only enter the model if they explain a significant
portion of the criterion variance over and above the more proximal
covariates already in the model). P to enter is .05. (peripheral
question: am I correct in assuming that this is the p-value associated
with the t-value of the beta of the relevant covariate?)

The sample sizes of the samples are unequal (e.g., ranging from 200 to
500). I get the strong impression that the number of covariates in the
final model depends on the sample size. This would imply that covariates
with less 'impact' would be added to the model when the model is
developed with a larger sample (e.g., with equal standard errors of the
parameter weight, when a covariate increases 1 standard deviation, an
increase of the criterion of 0.2 * Y's standard deviation could suffice
(lead to inclusion) with n=500, but not with n=200).

If this correct? And if so, is there a way to 'correct' the p-to-enter
for sample size, so that all final models comprise covariates with
roughly equal relevance? (except for selecting sub-subsamples from all
subsamples of the size of the smallest subsample)

My goal in the end is to cursorily compare the models in the different
subsamples (no, sorry, I'm not going to use SEM; given the amount of
potential predictors, the sample sizes are too small). This is not very
'fair' if the model in one subsample has lower thresholds for
'inclusion' than the model in another.

If what I'm trying is completely insade/stupid/otherwise unadvisable,
I'm of course eager to learn :-)

Thanks a lot in advance (if nothing else, for reading this far :-)),

Gjalt-Jorn
_____________________________________
Gjalt-Jorn Ygram Peters

Phd. Student
Department of Experimental Psychology
Faculty of Psychology
University of Maastricht