Modeling with Gamuts

Consider predicting a response using an additive model. A gamut is an additional, usually continuous variable that can segment data and any associated estimates; the underlying model varies smoothly. Examples of gamuts: (a) for disease, ages of subjects, their initial severity status, and/or cumulative exposure doses; (b) for learning, measures of cumulative experience and/or engagement; and (c) for economic activity, levels of income and/or spending. In previous work, gamuts have helped identify metric changes, detect coefficient shifts, and formulate statistical narratives. Gamuts can be classified into four types: (1) gamuts exogenously specified and known a priori; (2) those endogenously constructed and therefore latent; (3) gamuts derived from an auxiliary model’s predictions; (4) gamuts chosen to optimize a predictive model. Here we use gamuts of type (3) to parametrize model coefficients. By construction, the in-sample goodness-of-fit is always improved, so we focus on out-ofsample cross-validating methods. We also address computational issues. key words: deconstruction, lowess, nonparametric regression, regression diagnostics, statistical narrative, varying-coefficient models.