I think John's suggested approach is good. If you think are thinking of
diminishing returns, you can use quadratic forms. If the number of ballots
ranges from 0 to 3 or so, you can use an indicator variable for each
count.
Kosuke
On Sun, 4 May 2003, John Bright wrote:
Hi Anna,
Have you considered transforming your explanatory variable to linearize the
relationship--something like x'=x^a, where a<1 (since you expect diminishing
returns)? Your "x" is an interval/ratio variable rather than a categorical
or ordinal variable--"one ballot" has an absolute numerical meaning beyond
"different from 0". Therefore, it seems that one possibility is to model the
non-linear relationship between number of ballots and turnout through a
variable transformation.
Best,
John.
On 5/4/03 11:52 AM, "Anna Lorien Nelson" <alnelson(a)fas.harvard.edu>
wrote:
We are modelling the effect of the number of
ballot propositions on voter
turnout. Scholars of ballot propositions have traditionally used OLS
models to estimate this effect, but this seems implausible. It seems
likely that there will be diminishing returns (a/k/a "voter fatigue"), so
that the model should not be linear. For instance, the difference in
turnout for 3 ballot propositions vs. 0 ballot propositions is probably
not equal to the difference in turnout for 6 ballot propositions vs. 3
ballot propositions. How can we estimate these threshholds, or effectly
model this nonlinearly?
I recognize this is a problem of estimating threshholds for an ordered
categorical variable, but I am not sure how to approach it because the
categorical variable at issue is our *explanatory* variable, not our
dependent variable. Any suggestions?
Thanks,
Anna
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