Pseudo Bayesian Estimation of One-way ANOVA Model in Complex Surveys

TL;DR

This paper introduces survey-weighted pseudo posterior estimators for one-way ANOVA models in complex surveys, providing theoretical guarantees and simulation evidence of their asymptotic unbiasedness, with comparisons to existing frequentist methods.

Contribution

It develops novel pseudo Bayesian estimators for complex survey data in one-way ANOVA models, including theoretical consistency conditions and simulation validation.

Findings

Estimators are asymptotically unbiased under certain conditions.

Theoretical conditions for estimator consistency are provided.

Simulation shows good performance compared to frequentist methods.

Abstract

We devise survey-weighted pseudo posterior distribution estimators under two-stage informative sampling of both primary clusters and secondary nested units for a one-way analysis of variance (ANOVA) population generating model as a simple canonical case where population model random effects are defined to be coincident with the primary clusters, for example student performance based on a survey of schools and students such as the 2000 OECD Programme for International Student Assessment (PISA). We consider estimation on an observed informative sample under both an augmented pseudo likelihood that co-samples the random effects, as well as an integrated likelihood that marginalizes out the random effects from the survey-weighted augmented pseudo likelihood. This paper includes a theoretical exposition that enumerates easily verified conditions for which estimation under the augmented pseudo posterior is guaranteed to be consistent at the true generating parameters. We reveal in simulation that both approaches produce asymptotically unbiased estimation of the generating hyperparameters for the random effects when a key condition on the sum of within cluster weighted residuals is met. We present a comparison with two frequentist alternatives, an expectation-maximization approach and a composite likelihood method that requires pairwise sampling weights.