Multi-outcome longitudinal small area estimation – a case study

A recent paper [Thibaudeau, Slud, and Gottschalck (2017). Modeling log-linear conditional probabilities for estimation in surveys. The Annals of Applied Statistics, 11, 680–697] proposed a ‘hybrid’ method of survey estimation combining coarsely cross-classified design-based survey-weighted totals in a population with loglinear or generalised-linear model-based conditional probabilities for cells in a finer cross-classification. The models were compared in weighted and unweighted forms on data from the US Survey of Income and Program Participation (SIPP), a large national longitudinal survey. The hybrid method was elaborated in a book-chapter [Thibaudeau, Slud, & Cheng (2019). Small-area estimation of cross-classified gross flows using longitudinal survey data. In P. Lynn (Ed.), Methodology of longitudinal surveys II. Wiley] about estimating gross flows in (two-period) longitudinal surveys, by considering fixed versus mixed effect versions of the conditional-probability models and allowing for 3 or more outcomes in the later-period categories used to define gross flows within generalised logistic regression models. The methodology provided for point and interval small-area estimation, specifically area-level two-period labour-status gross-flow estimation, illustrated on a US Current Population Survey (CPS) dataset of survey respondents in two successive months in 16 states. In the current paper, that data analysis is expanded in two ways: (i) by analysing the CPS dataset in greater detail, incorporating multiple random effects (slopes as well as intercepts), using predictive as well as likelihood metrics for model quality, and (ii) by showing how Bayesian computation (MCMC) provides insights concerning fixed- versus mixed-effect model predictions. The findings from fixed-effect analyses with state effects, from corresponding models with state random effects, and fom Bayes analysis of posteriors for the fixed state-effects with other model coefficients fixed, all confirm each other and support a model with normal random state effects, independent across states.