Re: Odds Ratios - univariate to multivariate


Hi Bellinda,

It sounds like you have a classical case of suppressor variables. This
can cause coefficients in a multiple or logistic regression to have a
sign opposite the direction of their univariate effect.

Here's a paper that explains the phenomenon:

http://www.visualstatistics.net/Statistics/Suppressor%20Variables/Suppressor.asp

This can happen with multicollinearity, or just because of the nature
of certain variables. In the former case it is more likely to be
spurious.

Suppressor variables can be a problem for model interpretation and/or
validity. For example, it might be difficult to defend inclusion of a
paradoxical predictor variable in a model. Sometimes there might even
be ethical or legal aspects to consider.

For example, in a credit risk model, a variable which, in a univariate
analysis shows positive association with credit reliability, might, in
a multivariate analysis, have a negative sign. If challenged, the
agency might therefore have to defend declining credit based partly on
behavior which, by a priori common sense, indicates a good credit risk.

If the sign of a regression coefficient is opposite the sign of the
univariate correlation of the predictor and the outcome, that is
grounds for caution. It's often hard to defend inclusion of such a
variable in a predictive model unless you can explain the suppressor
effect based on theoretical grounds.

Hope this helps.
--
John Uebersax PhD

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