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Re: st: Interpreting margins results of a non-significant interaction


From   David Hoaglin <dchoaglin@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Interpreting margins results of a non-significant interaction
Date   Fri, 13 Jul 2012 09:20:37 -0400

Dear Antonio,

In the logistic regression, the coefficient of a predictor (e.g.,
income_score) is a slope against that predictor, adjusting for the
contributions of the other predictors in the model.  Those other
predictors are not being held constant at their mean or at any other
value.  Thus, the -margins- command is doing something different from
the -logit- command.

It may be helpful to examine where the point consisting of the means
of those four covariates is located in the 4-dimensional distribution
of those covariates.  If the covariates are essentially uncorrelated,
the mean point should be somewhere in the middle of the "point cloud"
(assuming that the data do not contain outliers or clusters).  If the
covariates are associated in "interesting" ways, the mean point may
have few (or no) covariate points nearby.

Although it will produce considerably more output, you may want to
vary each of the covariates over a meaningful range, so that you have
a grid on the covariates, as well as on income_score.  In that way you
can get a fairly detailed picture of how the log-odds of return is
related to the five variables.  This sort of exploration will be
easier if it is appropriate to simplify the model by removing
predictors that do not make significant contributions.

David Hoaglin

On Fri, Jul 13, 2012 at 8:15 AM, Antonio Silva
<antonio.silva.09@ucl.ac.uk> wrote:
> I'm using the margins command to understand the effect of an
> interaction between two continous variables (perc_catholics and
> income_score) on the binary response using logistic regression. When
> running the logistic regression with other co-variates, both the
> interaction term and one of the variables of this term (income_score)
> are not significant, however when running the margins command I obtain
> a significant relationship for the majority of values of income_score.
> I'm trying to understand how if the overal interaction is not
> significant, there is nevertheless a significant interaction when
> looking at most of the values of income_score. I would appreciate if
> someone has ideas how this may happen.
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