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Dear Balazs:
I am not sure I understood your problem specifications correctly.
Chi square does not imply normal distribution, unlike Pearson  R. More 
important, even if you have high dyadic similarity ("goodness of fit"), 
then it is still possible that the whole network R will be virtually 
zero if you have many zeros scattered and network sparseness.
If the attributes are at least ordinal, you can produce dyadic 
dissimilarity between node attributes and then run correlation.  R 
Square should be high then.
If there are two waves only, you can predict "attributes sameness" in 
second wave from first wave attributes in a simple logistic regression.
If you have indeed longitudinal, and you are interested in the 
co-occurrence (or partial dependency, or co-evolution) of attributes and 
relations, use SIENA to decompose attributes similarity from selection 
processes. . 
I hope this would help.

Balazs Vedres wrote:
> *****  To join INSNA, visit http://www.insna.org  *****
>
> Dear Socnetters,
>
> This is a question about model choice with categorical independent
> variables.
>
> I have categorical attributes, and network data.
>
> When I look at the attributes one-by-one, and produce contingency tables
> with the dyadic data, each attribute has a highly significant chi-squared.
>
> When I look at them with QAP multiple regressions approach, the R-squared is
> practically zero. The network is sparse with about a thousand nodes.
>
> Of course, a QAP regression with a binary dependent variables is not really
> appropriate. I think when coefficients are referred to as probabilities in
> the QAP linear regression context, it is not appropriate. Like they are
> referred to here:
>
> http://faculty.ucr.edu/~hanneman/nettext/C18_Statistics.html#tworeg
>
> But even when I calculate geodesics (and have an interval scale dependent
> variable with an approximately normal distribution) I have no R-squared.
>
> So:
>
> Is there a way to model multiple, node level categorical independents, and a
> dyadic dependent variable? 
>
> Log-linear models?
>
> A logistic regression model?
>
> Thanks
> Balazs
>
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