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bob faris wrote:
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> We recognized that it would be impossible to impute their missing
> friendship nominations, but thought that it might be reasonable to impute
> reciprocity--i.e., given that a participating A nominates a missing B, we
> attempt to model whether B reciprocates.
> So we ran a logit on all dyads where there was at least one tie, the
> dependent variable being whether the tie was reciprocated. We included
> in our model various measures of tie strength (emotional closeness,
> frequency of interaction, etc.), the outdegree & indegree of sender, the
> indegree of the recipient, and a measure of transitivity (i.e., how many
> triads would be transitive if B reciprocates).
> Has anyone done something similar to this? Any thoughts?
Aside from the question of estimating the reciprocity rate, a somewhat
more robust procedure would be to use your reciprocity estimates to draw
repeatedly from the set of graphs (conditional on size, observed ties,
and your estimated reciprocity rates), to calculate your quantity of
interest on each draw, and then to study the distribution which results
(instead of any single estimate). If your results hold across the vast
majority of draws (and if you believe the reciprocity model), then you
have some evidence that results would be unlikely to change if you had
the full data. (This can be thought of as multiple imputation, although
one can frame it in other ways if one likes.)
For that matter, though, you might want to consider other, more general
models for the data which incorporate other sorts of structural biases.
Since I think I know the data set to which you refer, I believe that
Jim has already done work on this. Extrapolating p*/ERGM parameters to
graphs of larger size (in order to take draws, which is what you'd
ultimately want to do) is somewhat problematic, but the mean value
parameterization might provide a way around this (especially since
you're not adding all that many vertices). Perhaps Mark or others would
like to chime in here....
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