Modeling with Gamuts
Abstract
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-of-sample
cross-validating methods. We also address computational issues.
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-of-sample
cross-validating methods. We also address computational issues.
Research Areas
