Abstract:
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Count variables often have a fixed set of possible outcomes {0,…,N}. Such variables pose a unique problem when measurement error is present in observed data. Specifically, as both the true count X and the noisy count W lie in the fixed set of values, the typical additive model W = X + U with independent measurement error U is unsuitable. While it is possible to extend misclassification models for categorical variables to the count variable framework, the resulting model is tedious and has a large number of parameters to estimate. We explore how a transformation model W = max(0, min(X+U)) can be used to account for measurement error. In this formulation, the additivity and independence of measurement error can still be utilized. The goal of our study is two-fold: Firstly, we propose discrete parametric distributions for the measurement error U that are symmetric and zero mean. Secondly, we consider the companion problems of estimating the pmf of X based on W data and estimating the conditional mean function E[X|W]. The methodology is illustrated in an application involving the assessment of reading abilities of elementary school children.
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