Double Sampling for Exact Values in Some Multivariate Measurement Error Problems

Abstract

Increasing attention is being given to measurement error models in which the dimension of the proxy or surrogate values is different from that of the missing true values. Even if they are of the same dimension, the error model may not be the simple additive one of observed = true + error, where the error has mean O. The use of broader models relating true and observed values requires the use of external or internal data containing some true values to calibrate/validate the measurement error model. This article considers a multivariate normal framework in which measurement error is allowed in any subset of the variables with a broad class of multivariate regression models relating true and observed values. The classical additive model is a special case. Multiple regression with random regressors (the structural case) is treated within this framework. Correcting for measurement error is made possible through double sampling in which true values are obtained for a randomly chosen subset of the main study units. Maximum likelihood estimators and their asymptotic properties are developed for both unrestricted and restricted models, where the latter arise through specific assumptions about the nature of the measurement error. Detailed results are given for simple linear regression in which case optimal double sampling rates are determined for estimating the slope with minimum variance subject to cost considerations. An example is presented based on the use of infrared measurements as surrogates for characteristics of wheat.

Estimating the polychoric correlation from misclassified data

“…However, similar computational problems will arise because the estimation procedure in Mx is the full information maximum likelihood approach that requires the computation of high-dimensional multiple integrals. It is worth noting that a double sampling scheme that draws n participants randomly from N participants can be regarded as multivariate data missing completely at random (Buonaccorsi, 1990). This is compatible with the Mx program that operates on the assumption that missing data are missing at random.…”

“…The development in Section 2 operates on the assumption that the probabilities t uvj and g hk(uv) which relate to misclassification are known or can be calibrated from available information. When no information is available for calibration, another approach to the analysis of data sets with possible misclassification is double sampling (Buonaccorsi, 1990;Espeland & Odoroff, 1985;Palmgren, 1987;Pepe, 1992;Tenenbein, 1972). In the double sampling scheme, two devices are available for the classification of participants.…”

Bayesian Analysis of Multivariate Probit Models with Surrogate Outcome Data

“…In research studies in which information on the variables of interest is difficult or expensive to obtain, surrogate variables that mimic the variables of interest can be introduced to provide auxiliary information. The use of surrogate variables (Buonaccorsi, 1990;Chen, 2000;Chen, Cai, & Zhou, 2004;Wang & Rao, 2002;Wang & Yu, 2007;Zhou, Chen, & Cai, 2002; among others), however, can lead to responses being misclassified into a category that does not reflect the true state of the respondents. Ignoring such misclassification and employing information from the surrogate variables in analysis will produce results whose reliability is highly dependent on the quality of those variables.…”

Nonparametric regression function estimation with surrogate data and validation sampling

“…The problem with error-in-response has received less attention, mainly because when the measurement error is additive, standard methodology can be used to handle this case. In practice, however, the additive model is often not appropriate, more realistic ones for either the covariate or the response have been considered by Buonaccorsi [2,3], Buonaccorsi and Tosteson [4], Carroll et al [5], Carroll and Stefanski [9]. These methods, however, may be sensitive to the assumed models.…”