John Kuk writes:
I have taught myself multilevel modeling using your book and read your work with Delia Baldassarri about partisanship and issue alignment. I have a question about related to these two works.
I want to find the level of correlation between partisanship and issues at the state level. Your work with Professor Baldassarri estimated the correlation at the national level, but I want to estimate it at the state level. The problem is that ANES is designed to be a national representative sample, so without using multilevel modeling, the estimated state level correlation is useless.
If I run a varying-intercept, varying-slope model with states as the group variable, I can use these estimates as somewhat comparable to correlation coefficients, though they are not same. If I run a linear regression, I know the coefficient is different with the correlation coefficient as the ratio of standard deviation of x and y. However, even though I understand multilevel model coefficients are the weighted average of the group and the whole coefficients, I don’t know how to compare multilevel coefficients with correlation coefficients.
Given my situation, I have two questions.
1) Is it OK to use estimates from a varying-intercept, varying-slope model to compare the state level correlation of partisanship and issue positions?
2) If no, how can I derive a correlation coefficient to compare state level correlations?
My reply: Yes, I think that rather than modeling correlations, if you’re interested in partisanship and issue attitudes, it would make sense to simply regress issue attitudes on partisanship, with varying intercepts and slopes for states. The varying slopes are what you’re interested in. That said, I’m guessing that ANES won’t have nearly enough data to estimate varying slopes with any level of accuracy. You should pool several years of ANES or else use larger surveys such as Annenberg and Pew as we did for most of our Red State Blue State analysis.