Sankhya: The Indian Journal of Statistics

1998, Volume 60, Series B, Pt. 1, 101-126

MODELLING DIFFERENTIAL NONRESPONSE IN SAMPLE SURVEYS

By

THOMAS c. LITTLE, Morgan Stanley Dean Witter, New York
and
ANDREW GELMAN, Columbia University, New York

SUMMARY. The standard analysis of unit nonresponse in sample surveys is to assume missing at random -- that is, that the probability a person responds is independent of their response to the question of interest, y, conditional on fully-observed covariates x or on sampling weights w, In this paper, we discuss weakening these assumptions without the use of additional covariates in the special case of a binary outcome variable, y=0 or 1. We note frequentist confidence bounds that do not rely on strong assumptions about the response mechanism. From a Bayesian perspective, we discuss using prior distributions to average over uncertainty in the missing data mechanism. Surprisingly, a natural -looking "noninformative" prior distribution yields unappealing posterior inferences. We discuss methods of constructing porate unequal sampling weights into the model using design-based sampling theory. This is important so that the nonresponse modeling can be an improvement upon rather than merely a replacement for standard weighted analysis of sample surveys. We illustrate the hierarchical model by applying it to the state-level analysis of a series of national pre-election opinion polls. The use of a reasonable prior distribution for the relative response probabilities leads to substantial improvements in coverage of posterior intervals and prediction error of point estimates. We also consider the sensitivity to the prior distribution and the effect of including sampling weights in the analysis.

AMS (1991) subject classification. 62C10.

Key words and phrases. Bayesian inference, hierarchical model, opinion polls, sampling weights.

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