Log-linear modeling for estimation of small areas in longitudinal surveys
Jul 25, 15:45
Our objective in this chapter is to review and contribute to the methodology of small-area model-assisted estimation in complex longitudinal surveys. Genuinely longitudinal survey analyses, which address the pattern of behavior of individuals over time, are distinguished from the more common methods based on temporal and spatio-temporal models of data from repeated surveys or repeated cross-sectional waves from longitudinal surveys. We review the estimation of gross flows in longitudinal surveys, dating from early efforts (Fienberg 1980) to define conditional probabilities to parameterize transitions in status. Progress in this area includes the partial model-based approach of Pfeffermann, Skinner, and Humphreys (1998) using logistic regression to discount measurement error. The approach of Thibaudeau, Slud, and Gottschalck (2017) is based on log-linear models with suppressed high-order interactions, parameterized in such a way that design-based estimates suffice for the large-population contingency-table cells but that take full advantage of the model to estimate small cell populations related to uncommon changes in status. The main novelty in the Chapter is to extend the log-linear methodology of Thibaudeau et al. (2017) to small-area estimation from longitudinal surveys, an area where we briefly survey the relatively small body of previous research. The history of log-linear models applied to small area estimation (Purcell and Kish 1979, Marker 1999) and of random effect models in longitudinal surveys (Feder, Nathan, and Pfeffermann 2000) are then recalled, to extend the log-linear models of Thibaudeau et al. (2017) to incorporate geographic-area random effects. The models are further extended to compensate for attrition and multiple irregularly spaced panels within rotational design (following Fienberg and Stasny 1983), in order to present illustrative data analyses from the Current Population Survey (CPS), the official labor force statistical survey in the U.S. We estimate gross flows related to changes in labor force status over multiple months further classified by demographic or coarse occupation-category variables at the regional or state level.
Improvements in sampling error of estimation of small cells are anticipated both from suppressing higher order longitudinal interactions and from borrowing strength across small areas through shared log-linear model parameters. The method mitigates bias by maintaining design-based analyses of marginal counts for large geographies, parameterizing modeled conditional probabilities, and is applicable to general social longitudinal surveys.