Modeling log-linear conditional probabilities for estimation in surveys

Abstract

The Survey of Income and Program Participation (SIPP) is a survey with a longitudinal structure and complex nonignorable design, for which correct estimation requires using the weights. The longitudinal setting also suggests conditional-independence relations between survey variables and early- versus late-wave employment classifications. We state original assumptions justifying an extension of the partially model-based approach of Pfeffermann, Skinner and Humphreys [J. Roy. Statist. Soc. Ser. A 161 (1998) 13–32], accounting for the design of SIPP and similar longitudinal surveys. Our assumptions support the use of log-linear models of longitudinal survey data. We highlight the potential they offer for simultaneous bias-control and reduction of sampling error relative to direct methods when applied to small subdomains and cells. Our assumptions allow us to innovate by showing how to rigorously use only a longitudinal survey to estimate a complex log-linear longitudinal association structure and embed it in cross-sectional totals to construct estimators that can be more efficient than direct estimators for small cells.