Logistic Regression with Interaction Effects

[Colleen Casey]

Hi-All.

I've already searched through the many postings on logistic regression and interaction effects and
did not see anything (that I recognized) related to this question.

I ran across a 2004 article by Norton et al, about a command in STATA, inteff, specifically
designed to correct for the nonlinear nature of the interaction effects in logistic regression.  I am
interacting two dummy variables and in this article  they argue the parameter estimates and the
direction of the effects, as well as the standard errors may be incorrect, if left unadjusted.  For
two dummys, they argue the interaction effect is the discrete difference, and the standard errors
need to be calculated using the Delta method.

My question--first, is this a debatable topic?  I would guess that it is, and there are differing
perspectives on whether or not this has to occur, or if the parameter estimates can be handled
from a theoretical standpoint like linear interaction effects.

Secondly, is it possible to calculate this using SPSS  (v 16.0) or from the output from the model
estimated in SPSS? Is the discrete difference the same as added the value of the pararmeter of the
variable of interest + your interaction term with this variable,  to get the value for the variable in
which you are interested?

Thanks.

Colleen

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[Bruce Weaver]

Colleen Casey wrote

Hi-All.

I've already searched through the many postings on logistic regression and interaction effects and
did not see anything (that I recognized) related to this question.

I ran across a 2004 article by Norton et al, about a command in STATA, inteff, specifically
designed to correct for the nonlinear nature of the interaction effects in logistic regression.  I am
interacting two dummy variables and in this article  they argue the parameter estimates and the
direction of the effects, as well as the standard errors may be incorrect, if left unadjusted.  For
two dummys, they argue the interaction effect is the discrete difference, and the standard errors
need to be calculated using the Delta method.

My question--first, is this a debatable topic?  I would guess that it is, and there are differing
perspectives on whether or not this has to occur, or if the parameter estimates can be handled
from a theoretical standpoint like linear interaction effects.

Secondly, is it possible to calculate this using SPSS  (v 16.0) or from the output from the model
estimated in SPSS? Is the discrete difference the same as added the value of the pararmeter of the
variable of interest + your interaction term with this variable,  to get the value for the variable in
which you are interested?

Thanks.

Colleen

Is this the article you are referring to?  http://www.stata-journal.com/sjpdf.html?articlenum=st0063

I've not read it carefully, but from a quick skim, it seems to me they are making things more complicated than they need to be.  I suggest that you take a look at James Jaccard's Sage monograph, "Interaction Effects in Logistic Regression".  I also have some notes I could send you.  If you want them, just drop me a line off-list.

--
Bruce Weaver
[e-mail]
http://sites.google.com/a/lakeheadu.ca/bweaver/
"When all else fails, RTFM."

[Hector Maletta]

If you add an interaction between two dummies in the form XZ, this term
would equal 1 when both equal 1, and zero otherwise. The net effect is an
additional effect (positive or negative) when both variables are present, on
top of the separate effect of X and Z taken separately. This effect is
linear in the logit, i.e. it adds a linear term to the exponent, but the
logit is of course nonlinear.
Of course you may posit any other form of interaction you want, to capture
any theoretically foreseeable effect of interactions between X and Z, but
the term would not be a simple product XZ. For instance, suppose there is an
additional (positive or negative) effect only in case X=1 AND Z=0. To
capture this you would need the additional interaction term defined
accordingly; you may define W=(Z=0), where W=1 when Z=0 and conversely, and
use XW as an interaction term. Similar tricks could be used for other
interaction effects.
However, these interactive effects should ideally be theoretically
explicable, rather than simply found to be 'statistically significant' in an
empirical way. What is statistically significant in one sample may not be so
in another, especially in another sample with a different size or coming
from a slightly different population. If one cannot account for the hidden
mechanism producing the interaction effect, exploring interactions at random
is not a fruitful way of advancing knowledge. However you may stumble into
what appears to be a very robust interaction, for instance when exploring
interactions of drugs or treatments, and then it is legitimate to report it,
leaving for others, or for later research, to elicit the mechanism at play.
Hector

-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
Colleen Casey
Sent: 03 July 2009 08:15
To: [hidden email]
Subject: Logistic Regression with Interaction Effects

Hi-All.

I've already searched through the many postings on logistic regression and
interaction effects and
did not see anything (that I recognized) related to this question.

I ran across a 2004 article by Norton et al, about a command in STATA,
inteff, specifically
designed to correct for the nonlinear nature of the interaction effects in
logistic regression.  I am
interacting two dummy variables and in this article  they argue the
parameter estimates and the
direction of the effects, as well as the standard errors may be incorrect,
if left unadjusted.  For
two dummys, they argue the interaction effect is the discrete difference,
and the standard errors
need to be calculated using the Delta method.

My question--first, is this a debatable topic?  I would guess that it is,
and there are differing
perspectives on whether or not this has to occur, or if the parameter
estimates can be handled
from a theoretical standpoint like linear interaction effects.

Secondly, is it possible to calculate this using SPSS  (v 16.0) or from the
output from the model
estimated in SPSS? Is the discrete difference the same as added the value of
the pararmeter of the
variable of interest + your interaction term with this variable,  to get the
value for the variable in
which you are interested?

Thanks.

Colleen

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