Anatomy of Correlational Magnitude Transformations in Latency and Discretization Contexts in Monte-Carlo Studies
This chapter is concerned with the assessment of correlational magnitude changes when a subset of the continuous variables that may marginally or jointly follow nearly any distribution in a multivariate setting is dichotomized or ordinalized. Statisticians generally regard discretization as a bad idea on the grounds of power , information , and effect size loss. Despite this undeniable disadvantage and legitimate criticism, its widespread use in social, behavioral, and medical sciences stems from the fact that discretization could yield simpler, more interpretable, and understandable conclusions, especially when large audiences are targeted for the dissemination of the research outcomes. We do not intend to attach any negative or positive connotations to discretization, nor do we take a position of advocacy for or against it. The purpose of the current chapter is providing a conceptual framework and computational algorithms for modeling the correlation transitions under specified distributional assumptions within the realm of discretization in the context of the latency and threshold concepts. Both directions (identification of the pre-discretization correlation value in order to attain a specified post-discretization magnitude, and the other way around) are discussed. The ideas are developed for bivariate settings; a natural extension to the multivariate case is straightforward by assembling the individual correlation entries. The paradigm under consideration has important implications and broad applicability in the stochastic simulation and random number generation worlds. The proposed algorithms are illustrated by several examples; feasibility and performance of the methods are demonstrated by a simulation study.
KeywordsAbsolute Average Deviation Normal Mixture Polychoric Correlation Gaussian Copula Unbiased Measure
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