Multinomial Logistic Regression Interaction - graph the interaction odds ratios

[SueRichardson]

Hello,

I haven't been able to find a question/solution quite like the problem I
am having, so I'm creating a new thread.
I have a reviewer of a paper who is requesting that I graph a
significant interaction in my multinomial logistic regression
differently than I have been.

To briefly describe the regression, I have three levels of my DV, two
continuous predictors (let's calls them A and B), and the interaction of
those predictors (A*B).

In previous drafts, I've followed the Jaccard (2001) approach by
selecting points of interest for A and B, and used the regression
equation to calculate predicted log odds. Because predicted log odds
could be confusing, I converted these to predicted odds, and graphed those.

While the reviewer acknowledged this was correct, she/he would rather
see me graph the odds ratios instead of odds because of the possible
misinterpretation of the odds as odds ratios.

Where I am stuck is that I understand the "odds ratio" of the
interaction to be the ratio of the odds ratios. So it's not really an
odds ratio, itself.

But I think the spirit of the reviewers question is that they want to see odds ratios, not odds.

I've found guidance in this forum and elsewhere on the web about how to
approach the problem of graphing interactions by manually calculating
odds ratios when the variables are dichotomous to begin with, but not
when the variables are continuous to begin with.

What would work best to describe my interaction in terms of my
hypotheses is to look at 4 levels of A (1,2,3,4) at 2 levels of B (+/-
1SD).

So my question is, how do I calculate the odds ratios for different
combinations of points of interest for my continuous variables?

Can I use the odds ratios from the model I have and take the same
approach as is used for categorical predictor interactions? Do I need to
rerun the model dichotomizing the continuous predictors and their
interaction? Or is there some other step that I am missing?

Thanks for any guidance!

Susan

--
Susan E.V. Richardson
Postdoctoral Associate
Person Environment Zone Project Manager
106 John Dewey Hall
Psychology Department
University of Vermont
Burlington, VT 05405
1-866-532-7183
[hidden email]
[hidden email]

[Bruce Weaver]

Hello Susan.  I assume you are using NOMREG.  Have you taken a look at the /TEST sub-command?  I think it might give you what you're after.  Here is a very quick & dirty example I cobbled together.  Although one can perform several contrasts with one /TEST sub-command (with semicolons separating the various contrasts), I found I could not include labels for the contrasts when I did that; hence the multiple /TEST sub-commands.  You might want to direct the Contrast Results tables to a dataset via OMS to facilitate grabbing the values you want for plotting etc.


GET FILE='C:\SPSSdata\1991 U.S. General Social Survey.sav'.

NOMREG race (BASE=LAST ORDER=ASCENDING) WITH age educ
  /MODEL age educ age*educ
  /STEPWISE=PIN(.05) POUT(0.1) MINEFFECT(0) RULE(SINGLE) ENTRYMETHOD(LR) REMOVALMETHOD(LR)
  /INTERCEPT=INCLUDE
  /PRINT=PARAMETER SUMMARY LRT CPS STEP MFI.

graph histogram age.
graph histogram educ.

* Look at 4 levels of Age (20, 40, 60, 80) and 2 levels of Educ (10, 15).
* I.e., compare 10 and 15 years of education at each of the 4 ages.

NOMREG race (BASE=LAST ORDER=ASCENDING) WITH age educ
  /MODEL age educ age*educ
  /TEST "[1] Age=20, Educ=5"  ALL 1 20  5 100
  /TEST "[2] Age=20, Educ=10" ALL 1 20 10 200
  /TEST "[3] Age=40, Educ=5"  ALL 1 40  5 200
  /TEST "[4] Age=40, Educ=10" ALL 1 40 10 400
  /TEST "[5] Age=60, Educ=5"  ALL 1 60  5 300
  /TEST "[6] Age=60, Educ=10" ALL 1 60 10 600
  /TEST "[7] Age=80, Educ=5"  ALL 1 80  5 400
  /TEST "[8] Age=80, Educ=10" ALL 1 80 10 800
  /TEST "[2]-[1]" ALL 0 0 5 100
  /TEST "[4]-[3]" ALL 0 0 5 200
  /TEST "[6]-[5]" ALL 0 0 5 300
  /TEST "[8]-[7]" ALL 0 0 5 400
  /PRINT=PARAMETER SUMMARY LRT CPS STEP MFI
.

HTH.

SueRichardson wrote

Hello,

I haven't been able to find a question/solution quite like the problem I
am having, so I'm creating a new thread.
I have a reviewer of a paper who is requesting that I graph a
significant interaction in my multinomial logistic regression
differently than I have been.

To briefly describe the regression, I have three levels of my DV, two
continuous predictors (let's calls them A and B), and the interaction of
those predictors (A*B).

In previous drafts, I've followed the Jaccard (2001) approach by
selecting points of interest for A and B, and used the regression
equation to calculate predicted log odds. Because predicted log odds
could be confusing, I converted these to predicted odds, and graphed those.

While the reviewer acknowledged this was correct, she/he would rather
see me graph the odds ratios instead of odds because of the possible
misinterpretation of the odds as odds ratios.

Where I am stuck is that I understand the "odds ratio" of the
interaction to be the ratio of the odds ratios. So it's not really an
odds ratio, itself.

But I think the spirit of the reviewers question is that they want to see odds ratios, not odds.

I've found guidance in this forum and elsewhere on the web about how to
approach the problem of graphing interactions by manually calculating
odds ratios when the variables are dichotomous to begin with, but not
when the variables are continuous to begin with.

What would work best to describe my interaction in terms of my
hypotheses is to look at 4 levels of A (1,2,3,4) at 2 levels of B (+/-
1SD).

So my question is, how do I calculate the odds ratios for different
combinations of points of interest for my continuous variables?

Can I use the odds ratios from the model I have and take the same
approach as is used for categorical predictor interactions? Do I need to
rerun the model dichotomizing the continuous predictors and their
interaction? Or is there some other step that I am missing?

Thanks for any guidance!

Susan

--
Susan E.V. Richardson
Postdoctoral Associate
Person Environment Zone Project Manager
106 John Dewey Hall
Psychology Department
University of Vermont
Burlington, VT 05405
1-866-532-7183
[hidden email]
[hidden email]