Parameter Sig. vs Effect Sig. & Interaction

My analysis involves a Generalized Estimating Equation --- two binary IVs
predicting a binary DV.  Each binary IV is dummy coded 0-1.

When I run my analyses, the "test of model effects" Wald chi-square
statistic is exactly the same as the "parameter estimate" Wald chi-square
statistic for each predictor.  However, when I add an INTERACTION term to
the model (i.e. I ask SPSS to add it in automatically), this is no longer
the case.  (The Wald statistic for the interaction term matches, but the
statistics for the other parameter estimates don't match the test of model
effects.)

To date, I'm not really clear on why adding the interaction makes this
happen.  I would like to report parameter estimates (odds ratios), but the
significance levels of the parameter estimates change depending on which
group I select for the reference group!  (Just to reiterate, this does not
happen when there is no interaction term.)

Is there a way I can code my data so that this does not occur?

If there's not, what is the appropriate thing to report?

I realize that this is a confusing problem, so I've attached an explanation
of it from a GEE tutorial -- the only mention I could find of it.

"Parameter significance vs. effect significance. Significance levels
reported in the "Parameter Estimates" table also usually repeat significance
levels reported in the "Test of Model Effects" table, but note the two tests
do test different things and a variable effect may be significant while a
corresponding parameter coefficient may be non-significant. If there is a
difference, hypothesis-testing whether the effect of a variable is
significantly different from 0 should use the significance levels reported
in the "Test of Model Effects" table. The "Tests of Model Effects" table
reports Type III (and Type I if requested) Wald chi-square tests for the
null hypothesis that none of the parameter estimates (b coefficients) for a
predictor are different from 0 (a finding of significance means that at
least one of the parameter estimates is significant). In contrast, the Wald
chi-square test in the "Parameter Estimates" table, if significant, means
that that parameter is significantly different from 0. For categorical
variables, the parameter for the reference category is not shown, nor is its
significance, but the reference categories can be switched by changing the
factor order using the Options button under the Predictors tab. For the
variable gender, for instance, the parameter significance level for gender=1
with gender=0 as reference category might be non-significant while the
parameter significance level for gender=0 with gender=1 as reference
category might be significant. This can happen when the model includes
interaction terms (ex., gender*vote). The b coefficient parameters are
partial coefficients, controlling for other terms in the model, so that in
this example, the parameter for gender=1 may be non-significant after
controlling for the interaction terms in the model. If the model only
involves main effects, significance levels in the "Model Effects" table will
correspond to significance levels in the "Parameter Estimates" table for
binary predictors and covariates, but are not directly comparable for
categorical predictors."
http://faculty.chass.ncsu.edu/garson/PA765/gzlm_gee.htm

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[Bruce Weaver]

Simon - [e-mail] wrote

My analysis involves a Generalized Estimating Equation --- two binary IVs
predicting a binary DV.  Each binary IV is dummy coded 0-1.

When I run my analyses, the "test of model effects" Wald chi-square
statistic is exactly the same as the "parameter estimate" Wald chi-square
statistic for each predictor.  However, when I add an INTERACTION term to
the model (i.e. I ask SPSS to add it in automatically), this is no longer
the case.  (The Wald statistic for the interaction term matches, but the
statistics for the other parameter estimates don't match the test of model
effects.)

To date, I'm not really clear on why adding the interaction makes this
happen.  I would like to report parameter estimates (odds ratios), but the
significance levels of the parameter estimates change depending on which
group I select for the reference group!  (Just to reiterate, this does not
happen when there is no interaction term.)

Is there a way I can code my data so that this does not occur?

If there's not, what is the appropriate thing to report?

--- snip ---

Bear in mind that when the product term is included in the model, the parameters for the main effects are really giving you simple main effects .  Suppose your variables are called A and B.  When A*B is also in the model, the parameter for A gives you the effect of A when B is set to its reference level; and the parameter for B gives you the effect of B when A is set to its reference level.  So if you change the reference levels, you'll see different parameter estimates.  The parameter estimate for the A*B product is unaffected by what you choose as the reference categories.

HTH.