The Short Version: Using a school example,  I have a survey that rates both students, and their teachers, at monthly and quarterly intervals. Students are nested in teachers. Months are nested in quarters. The questions are different for each, but everything is measuring the same underlying latent concept (say quality of education in that classroom). I want to generate estimates of latent "quality" at both the student and teacher level every month, and I want to track how that might change over time or in presence of a treatment. What is the proper way to describe this kind of multilevel/multiple measurements design, and how do you estimate it?


The Long Version: A Vietnam era survey measures territorial control over time in 12,000 hamlets nested in 2,500 villages. There was a hamlet-month survey, a hamlet-quarter survey, a village-month survey, and village-quarter survey. Using Irtrees, lme4, and their  documentation, I can put together a model for hamlets and villages separately over time. Two problems, however, stump me.

Responses at different time intervals: Including the extra items for that third month is trivial, but conceptually I don't know what it means for comparing the person parameters over time. Also, some of the quarterly questions are retrospective, providing information about security conditions for the whole quarter.

                           Item 1 Item 2 Item 3 Item 4
Hamlet 1-Jan          A        B         -        -       <- Monthly questionnaire
Hamlet 1-Feb         A        B         -        -       <- Monthly questionnaire
Hamlet 1-March      A        B         C        D    <- Quarterly questionnaire

Questions asked monthly and quarterly about villages, which hamlets were nested into: Ideally, information about the village would propagate down into the thetas for hamlets, and information about the hamlets would propagate up into the thetas for the villages.

                           Item 1 Item 2 Item 3 Item 4
Village 1               A        B         C         B
Hamlet 1               V        V         V        V
Hamlet 2               D        E         C        B
Hamlet 3               V        V         V        V

I appreciate any advice you might have.

Rex W. Douglass
Doctoral Candidate
Department of Politics
Princeton University
rexdouglass@gmail.com






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