I am estimating a multinomial model with two quantitative predictors, X1
and X2, and 3 responses. The responses are called neutral, positive and
negative with neutral being the baseline. There are actually many models
being estimated because I estimate the model over time and also for
various parameter sets but that's not important. When I estimate a
model, since neutral is the baseline and there is no interaction term, I
get back coefficients
X1 negative
X2 negative
X1 positive
X2 positive
Usually the signs of the coefficients are what I would expect. Also,
I've read about Anova so I think that I kind of understand what that is
doing. But, what I'm confused about is the following: In some of the
models, I can get back wald statistics for X1 say, where both the X1
negative Wald stat and the X1 positive Wald stat are not significant.
Yet, the pvalue from the Anova for the X1 variable overall is
significant ? Is this possible ? I think I'm not understanding the
Anova output as well as I thought because, to me, that seems
inconsistent ?
I understand that the Wald statistics for the particular variables are
kind of analogous to the t-stats in a regular regression in that they
are a function of the decrease in deviance conditional on all the rest
of the variables being in the model. The pvalue in the Anova table I
thought was kind of doing the same thing except not differentiating
between the factors and just calculating the decrease in deviance due to
X1 overall without regard to the particular factor response ?
If I'm right in my interpretation of the Anova output, then can that
still happen ?
If I'm wrong about my interpretation, and it can happen, can someone
tell me where to look for an explanation on why that can happen and
possibly explain where my interpretation is wrong ? I just want to
understand my output as best as I can.
If it can't happen, then it's puzzling because it is happening.
Thanks for any insights, comments or references. The output is not
easily reproducible or else I would reproduce it here.
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