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    Controlling for individual heterogeneity in longitudinal models, with applications to student achievement

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    Longitudinal data tracking repeated measurements on individuals are highly valued for research because they offer controls for unmeasured individual heterogeneity that might otherwise bias results. Random effects or mixed models approaches, which treat individual heterogeneity as part of the model error term and use generalized least squares to estimate model parameters, are often criticized because correlation between unobserved individual effects and other model variables can lead to biased and inconsistent parameter estimates. Starting with an examination of the relationship between random effects and fixed effects estimators in the standard unobserved effects model, this article demonstrates through analysis and simulation that the mixed model approach has a ``bias compression'' property under a general model for individual heterogeneity that can mitigate bias due to uncontrolled differences among individuals. The general model is motivated by the complexities of longitudinal student achievement measures, but the results have broad applicability to longitudinal modeling.Comment: Published at http://dx.doi.org/10.1214/07-EJS057 in the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org

    ON LIST STRUCTURES AND THEIR USE IN THE PROGRAMMING OF UNIFICATION

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    The notion of list structure is discussed, and a new construct is introduced into LISP which permits the computation of list structures containing cycles without recourse to operations which alter existing structures. It is shown that list structures can be used to represent both finite and “rational” infinite terms. Substitutions (generalized for a term algebra which includes infinite terms) are discussed, “tables” are introduced as an abstract data type, and two methods of representing substitutions by tables, together with their interrelation, are considered. Concise programs are given for a succession of forms of Robinson’s unification algorithm, including one which operates in almost linear time, and for the application of substitutions to terms
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