Measurement Error in Small Area Estimation: Functional vs. Structural vs. Naive models


Session:

Miscellanenous (Nonignorability, Measurement Error, Errors in Sampling Variance, Multiple-category Outcome )

Authors:
William R. Bell (U.S. Census Bureau) (Speaker)
Gauri Datta (University of Georgia, U.S. Census Bureau, and RTI International)
Carolina Franco (Center for Statistical Research and Methodology (CSRM), U.S. Census Bureau)
Hee Cheol-Chung (University of Georgia)
Abstract:

Small area estimation using area-level models can sometimes benefit from covariates that are observed subject to random errors. When it is possible to estimate the variances of these errors across small areas, then one can account for the uncertainty in such covariates using measurement error models (e.g., Ybarra and Lohr, 2008). For instance, estimates of the variances of sampling errors are usually available for covariates that are estimates drawn from another survey. Two types of area-level measurement error models have been introduced in the literature to deal with such errors. The functional measurement error model assumes that the underlying true values of the covariate are fixed but unknown quantities. The structural measurement error model assumes that these true values follow a model, formulated as a multivariate model for the covariates and the original dependent variable(s). We compare and contrast these two models under different underlying assumptions. We also explore the consequences for prediction mean squared errors that result from ignoring measurement error when it is present (naïve model), rather than using a functional or structural measurement error model. The comparisons are done both analytically and via simulations.