Globally Optimal Statistical Models, II: Unrestricted Class Variable, Two or More Attributes

Paul R. Yarnold & Robert C. Soltysik

Optimal Data Analysis, LLC

Novometrics—meaning new (Latin: novo) measurement, connotes a newly discovered theoretically-motivated algorithm that explicitly identifies the globally-optimal (GO) statistical model underlying any random statistical sample, indicated as S. Originating from the field of operations research, “optimal” denotes explicitly maximized (weighted) classification accuracy for S: that is, predicting the class category (“dependent variable”) of (weighted) observations in S as accurately as is theoretically possible for S. Novometry identifies the nature and strength of the GO relationship between a class variable and one or more attributes (“independent variables”) for S, where nature and strength are characterized by the number and homogeneity of discrete sample strata which are identified by the GO statistical model. Models maximizing ESS (a normed index of effect strength) and efficiency (ESS/number of strata, a normed index of parsimony) prevent over-fitting and promote cross-generalizability when using the model to classify an independent random S. The present article demonstrates novometry for two applications involving multiple attributes. The first study models a binary measure of patient satisfaction with care received in the Emergency Department (ED) using survey ratings of administration, nurse, physician, lab, and care of family and friends, for 2,198 ED patients. The second study ascertains the effect of atmospheric pressure on fibromyalgia symptoms recorded by a single individual over 297 sequential days.

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