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We describe a linear regression model for a spatially correlated dependent variable when a covariate is also spatially correlated and measured with error. Maximum likelihood estimates and likelihood-based confidence intervals for the regression parameters of the linear model are obtained and the method is extended to logistic regression analysis of grouped binomial data by methods analogous to empirical logistic regression. When the independent variable is spatially correlated, the measurement error variance and the other parameters of the regression model can be estimated without additional assumptions or data. The methods are used to characterize the association between outdoor concentrations of volatile organic compounds and respiratory health of school-children attending 73 elementary schools in Kanawha County, West Virginia. Results are compared to those from two-stage estimation procedures in which the dependent variable is regressed on the expectation of the true covariate conditional on the observed covariate values. © 1994 Elsevier Science B.V. All rights reserved.

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