Multi-level linear regression with a time trend?

[Tom Zhang]

I'm trying to replicate the results from an empirical paper (Baldassarri & Gelman 2008). In the paper, the authors ran a multilevel (linear) model with varying intercept and varying slope, in which "the unit of analysis is issue pair × year and the second-level units are issues." In addition, they said that "Rho__it is a correlation between issue i and the measure of partisanship in the year t (i ranges from 1 to 47, while t is time in decades)". The model is:

Rho_{_it} = Alpha__i + Beta__{i *} t + ε_it

It seems that this model has issue-specific constant term and issue-specific time trend. And I had trouble writing the STATA command for it. My attempt is:

mixed Rho t || id:

But it doesn't seem correct to me.

Any help would be greatly appreciated!

[Clyde Schechter]

I'm assuming here that id is a variable that indicates issues. To get the issue-specific time trend you need a cross-level interaction (aka random slope):

mixed Rho t || id: t