I am running logistic regression. I have a predictor that was
retained in my main effects model for theoretical (not statistical
reasons). It was not significant in the main effects model. This
predictor however, becomes statistically significant after including
an interaction term with the primary predictor in my model. There is
a good theoretical foundation for exploring this particular
interaction. What to do? Leave them both in? I have heard
differing opinions.

Marc

I am running logistic regression. I have a predictor that was
retained in my main effects model for theoretical (not statistical
reasons). It was not significant in the main effects model. This
predictor however, becomes statistically significant after including
an interaction term with the primary predictor in my model. There is
a good theoretical foundation for exploring this particular
interaction. What to do? Leave them both in? I have heard
differing opinions.

On Jun 27, 3:13 pm, mcap <mca... at (no spam) yahoo.com> wrote:

I am running logisticregression.  I have apredictorthat was
retained in mymaineffectsmodel for theoretical (notstatistical
reasons).  It wasnotsignificantin themaineffectsmodel.  This
predictorhowever, becomes statisticallysignificantafter including
an interaction term with the primarypredictorin my model.  There is
a good theoretical foundation for exploring this particular
interaction.  What to do?  Leave them both in?   I have heard
differing opinions.

Marc

Inregressionmodels with interaction terms, themaineffectsof
terms that are involved in theinteractionsdonothave the usual
simple interpretation. See my May 14, 2008, sci.stat.math post
"Interpretingmaineffectsinregressionmodels withinteractions":
http://groups.google.ca/group/sci.stat.math/browse_frm/thread/
d34056f056466f47#
The comments there are for ordinaryregression, but the ideas apply
equally well to logisticregressionif you change y to logit(p).

On Jun 27, 6:31 pm, Ray Koopman <koop... at (no spam) sfu.ca> wrote:
On Jun 27, 3:13 pm, mcap <mca... at (no spam) yahoo.com> wrote:

I am running logisticregression. I have apredictorthat was
retained in mymaineffectsmodel for theoretical (notstatistical
reasons). It wasnotsignificantin themaineffectsmodel. This
predictorhowever, becomes statisticallysignificantafter including
an interaction term with the primarypredictorin my model. There is
a good theoretical foundation for exploring this particular
interaction. What to do? Leave them both in? I have heard
differing opinions.

Marc

In regression models with interaction terms, the main effects of
terms that are involved in the interactions do not have the usual
simple interpretation. See my May 14, 2008, sci.stat.math post
"Interpretingmaineffectsinregressionmodels withinteractions":
http://groups.google.ca/group/sci.stat.math/browse_frm/thread/
d34056f056466f47#
The comments there are for ordinaryregression, but the ideas apply
equally well to logisticregressionif you change y to logit(p).

Thanks all. I was indeed planning on interpreting the main effects of
the primary predictor with stratified ORs based on the predictor it
interacts with. Thanks for both your responses. I just wonder
whether this is right to do in the face of main effects that are only
weakly related to outcome.

I wonder what the procedure would be in cases where you weren't
forcing predictors. I seemed to have misplaced my Hosmer/Lemeshow.
If you have a predictor that does not make it past the univariate
screening and then even upon re-entry to check for mutlivariate
effects/counfounding, still does not make it, do still test for that
nteraction? I forgot if they did that only for variables in the main
effects model after elimination or used all possible interactions
(even if main effects were not significant). I think at the time I
took the course, there were even differing philosophies between the
two.

Marc

On Jun 29, 10:10 am, mcap <mca... at (no spam) yahoo.com> wrote:





On Jun 27, 6:31 pm, Ray Koopman <koop... at (no spam) sfu.ca> wrote:
On Jun 27, 3:13 pm, mcap <mca... at (no spam) yahoo.com> wrote:

I am running logisticregression.  I have apredictorthat was
retained in mymaineffectsmodel for theoretical (notstatistical
reasons).  It wasnotsignificantin themaineffectsmodel.  This
predictorhowever, becomes statisticallysignificantafter including
aninteractionterm with the primarypredictorin my model.  There is
a good theoretical foundation for exploring this particular
interaction.  What to do?  Leave them both in?   I have heard
differing opinions.

Marc

In regression models withinteractionterms, the main effects of
terms that are involved in the interactions do not have the usual
simple interpretation. See my May 14, 2008, sci.stat.math post
"Interpretingmaineffectsinregressionmodels withinteractions":
http://groups.google.ca/group/sci.stat.math/browse_frm/thread/
d34056f056466f47#
The comments there are for ordinaryregression, but the ideas apply
equally well to logisticregressionif you change y to logit(p).

Thanks all.  I was indeed planning on interpreting the main effects of
the primary predictor with stratified ORs based on the predictor it
interacts with.  Thanks for both your responses.  I just wonder
whether this is right to do in the face of main effects that are only
weakly related to outcome.

There is absolutely nothing wrong with looking at aninteraction
when some or all of the corresponding main effects are absent.



I wonder what the procedure would be in cases where you weren't
forcing predictors.  I seemed to have misplaced my Hosmer/Lemeshow.
If you have a predictor that does not make it past the univariate
screening and then even upon re-entry to check for mutlivariate
effects/counfounding, still does not make it, do still test for that
nteraction?   I forgot if they did that only for variables in the main
effects model after elimination or used all possible interactions
(even if main effects were not significant).  I think at the time I
took the course, there were even differing philosophies between the
two.

Marc

I don't expect there to ever be procedural rules, or even rules of
thumb, that everyone will agree with. No matter what you do, someone
will disapprove, for reasons that are valid given their prior beliefs
about the likelihood of the effects in question being there and their
utility functions for the various possible outcomes. But other people,
with priors and utilities closer to yours, may see nothing wrong.- Hide quoted text -

- Show quoted text -

OK - there is no interaction between the interactions and I can do two
stratified ORs for my primary predictor.  This leads me to a very big
question on effect modification in general.....

-There seems to be a wide variety of opinion on how to handle it.
Hosmer and Lemeshow seem to suggest looking only at plausible
interactions among main effects that you have left in the model
(either statistically or theoretically).  This comes after selection,
scale evaluation and confounding evaluation.

-In Kleinbaum's text, he seems to treat effect modification
differently.  He would have you explore it first and then evaluate
confounding on almost entirely subjective criteria.

-I had an epi teacher that was extremely cautious about looking at
effect modification at all.

So...I am left with this study.   I am looking at job stress and the
effect on work related pain.  Effect modifiers for job strain include
gender and holding an additional job somewhere else.  Both are
plausible for a variety of reasons I don't have the room to go into
here.  Other  predictors to consider are age and hours worked per
week.   Neither is a confounder or effect modifier.

I am left submitting to a journal with a largely clinical audience.  I
would have two stratified ORs for my predictor (male/female) (2nd job/
no 2nd job).   At what point to I have to consider whether it's really
worth it for all of this complexity?  What about overfit?   I don't
gain much in prediction with the extra terms but the ORs are sharpened
and the effect modification does seem clear.

I know there is no absolute answer.  I am just seeking opinions.

Marc

OK - there is no interaction between the interactions and I can do two
stratified ORs for my primary predictor. This leads me to a very big
question on effect modification in general.....

-There seems to be a wide variety of opinion on how to handle it.
Hosmer and Lemeshow seem to suggest looking only at plausible
interactions among main effects that you have left in the model
(either statistically or theoretically). This comes after selection,
scale evaluation and confounding evaluation.

-In Kleinbaum's text, he seems to treat effect modification
differently. He would have you explore it first and then evaluate
confounding on almost entirely subjective criteria.

-I had an epi teacher that was extremely cautious about looking at
effect modification at all.

So...I am left with this study. I am looking at job stress and the
effect on work related pain. Effect modifiers for job strain include
gender and holding an additional job somewhere else. Both are
plausible for a variety of reasons I don't have the room to go into
here. Other predictors to consider are age and hours worked per
week. Neither is a confounder or effect modifier.

I am left submitting to a journal with a largely clinical audience. I
would have two stratified ORs for my predictor (male/female) (2nd job/
no 2nd job). At what point to I have to consider whether it's really
worth it for all of this complexity? What about overfit? I don't
gain much in prediction with the extra terms but the ORs are sharpened
and the effect modification does seem clear.

I know there is no absolute answer. I am just seeking opinions.

On Jul 15, 2:50 am, Ray Koopman <koop... at (no spam) sfu.ca> wrote:
On Jul 14, 3:46 pm, mcap <mca... at (no spam) yahoo.com> wrote:

Thanks again all. Very helpful. Next question. Let's say there
are two plausible and significant interactions. Do I interpret
the primary exposure, stratified for each interaction separately?
Or do I stratify based on both at the same time. Here is how I
have my ORs reported. Assume B and C are the terms that interact
with the primary exposure......

OR - Primary exposure variable when B is -
OR - Primary exposure variable when B is +

OR - Primary exposure varible when C is neg
OR - Primary exposure variable when C is pos

Another method
Primary exposure B- C-
Primary exposure B+ C-
Primary exposure B- C+
Primary exposure B+ C+

Have you checked for a 3-way (primary x B x C) interaction? If
you have and it's negligible, or if it's totally unreasonable on
theoretical grounds, then use method 1. Otherwise use method 2,
presented in a 2 x 2 table, with the method 1 values as marginals.- Hide quoted text -

OK - thanks everyone for your answers. I am still making up my mind.
There was no 3 way interaction. The problem then becomes:

1. OR - Primary exposure variable when B is -
2. OR - Primary exposure variable when B is +

3. OR - Primary exposure varible when C is neg
4. OR - Primary exposure variable when C is pos

By definition and 3 are the same because both b and c are held to
zero.

What to do? It makes for an awkward table even if accurate.

Marc

On Mon, 21 Jul 2008 08:55:55 -0700 (PDT), mcap <mca... at (no spam) yahoo.com
wrote:

OK - thanks everyone for your answers.  I am still making up my mind.
There was no 3 way interaction.  The problem then becomes:

1. OR - Primary exposure variable when B is -
2. OR - Primary exposure variable when B is +

3. OR - Primary exposure varible when C is neg
4. OR - Primary exposure variable when C is pos

By definition and 3 are the same because both b and c are held to
zero.

I thought that B and C were +/-   and never zero.
But that sentence does not parse in English, anyway.

Earlier, you used "2nd job/no"  and male/female.

You can state the this Odds of this outcome (whatever it is -" no
health problems"?), for males compared to females, is (I'm making
up numbers)  3.5  for whose with a 2nd job, and 2.5 for no-2nd-job.  

That takes care of an interaction.  If there is another factor, there
might be an separate description for that one; or another description
of an interaction.  The two effects act "independently"
since there is no 3-way interaction.  

On Jul 21, 2:42 pm, RichUlrich <rich.ulr... at (no spam) comcast.net> wrote:





On Mon, 21 Jul 2008 08:55:55 -0700 (PDT), mcap <mca... at (no spam) yahoo.com
wrote:

OK - thanks everyone for your answers.  I am still making up my mind..
There was no 3 way interaction.  The problem then becomes:

1. OR - Primary exposure variable when B is -
2. OR - Primary exposure variable when B is +

3. OR - Primary exposure varible when C is neg
4. OR - Primary exposure variable when C is pos

By definition and 3 are the same because both b and c are held to
zero.

I thought that B and C were +/-   and never zero.
But that sentence does not parse in English, anyway.

Earlier, you used "2nd job/no"  and male/female.

You can state the this Odds of this outcome (whatever it is -" no
health problems"?), for males compared to females, is (I'm making
up numbers)  3.5  for whose with a 2nd job, and 2.5 for no-2nd-job.  

That takes care of an interaction.  If there is another factor, there
might be an separate description for that one; or another description
of an interaction.  The two effects act "independently"
since there is no 3-way interaction.  

Rich, "setting to 0" refers to setting a variable to its reference
category (when indicator variables are used).  Take the Exposure x Sex
interaction, for example.  One can use either MALE (1=M,0=F) or FEMALE
(1=F,0=M) as the indicator variable for SEX.

If one uses MALE (and Exposure x Male) in the model, Exp(B) for
Exposure gives the odds ratio for females. But if one uses FEMALE (and
Exposure x Female), Exp(B) for Exposure gives the odds ratio for
males.  In general, Exp(B) for Exposure gives the odds ratio for the
reference category of the variable that Exposure interacts with.

As you noted, because there is no 3-way interaction, the two effects
are independent.  I.e., it doesn't matter which category is used as
the referent for the 3rd variable (job)--the Exposure odds ratios will
be the same in either case.

--
Bruce Weaver
bwea... at (no spam) lakeheadu.cawww.angelfire.com/wv/bwhomedir
"When all else fails, RTFM."- Hide quoted text -

- Show quoted text -

On Jul 15, 2:50 am, Ray Koopman <koop... at (no spam) sfu.ca> wrote:
On Jul 14, 3:46 pm, mcap <mca... at (no spam) yahoo.com> wrote:





Thanks again all.  Very helpful.  Next question.  Let's say there
are two plausible and significant interactions.  Do I interpret
the primary exposure, stratified for each interaction separately?
Or do I stratify based on both at the same time.  Here is how I
have my ORs reported.  Assume B and C are the terms that interact
with the primary exposure......

OR - Primary exposure variable when B is -
OR - Primary exposure variable when B is +

OR - Primary exposure varible when C is neg
OR - Primary exposure variable when C is pos

Another method
Primary exposure B-  C-
Primary exposure B+  C-
Primary exposure B-  C+
Primary exposure B+  C+


Have you checked for a 3-way (primary x B x C) interaction? If
you have and it's negligible, or if it's totally unreasonable on
theoretical grounds, then use method 1. Otherwise use method 2,
presented in a 2 x 2 table, with the method 1 values as marginals.- Hide quoted text -

- Show quoted text -

OK - thanks everyone for your answers. I am still making up my mind.
There was no 3 way interaction. The problem then becomes:

1. OR - Primary exposure variable when B is -
2. OR - Primary exposure variable when B is +

3. OR - Primary exposure varible when C is neg
4. OR - Primary exposure variable when C is pos

By definition and 3 are the same because both b and c are held to
zero.

What to do? It makes for an awkward table even if accurate.

Marc