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A0594
Title: A general algorithm for error-in-variables modelling using monte carlo expectation maximization Authors:  Jakub Stoklosa - University of New South Wales (Australia) [presenting]
Abstract: Measurement error models are often needed to correct for uncertainty arising from measurements of covariates in regression modeling. The literature on measurement error modeling is plentiful, however, general algorithms and software for maximum likelihood estimation of models with measurement error are not as readily available, in a form that they can be used by applied researchers without relatively advanced statistical expertise. We develop a novel algorithm for errors-in-variables modeling, which could in principle take any regression model fitted by maximum likelihood, or penalized likelihood, and extend it to account for uncertainty in predictor variables. This is achieved by exploiting an interesting property of the Monte Carlo Expectation-Maximization (MCEM) algorithm, namely that it can be expressed as an iteratively reweighted maximization of complete data likelihoods (formed by imputing the missing values). Thus we can take any regression model for which we have an algorithm for (penalized) likelihood estimation when predictors are error-free, nest it within our proposed iteratively reweighted (MCEM) algorithm, and thus account for uncertainty in predictor variables. The approach is demonstrated in various ecological examples. Because the method uses maximum (penalized) likelihood, it inherits advantageous optimality and inferential properties, as illustrated by simulation. We also study the robustness to some violations in predictor distributional assumptions.