Estimating Functions of Mixed Ordinal and Categorical Variables Using Adaptive Splines

Abstract

Multivariate adaptive regression splines (MARS) is a methodology for nonparametrically estimating (and interpreting) general functions of a high-dimensional argument given (usually noisy) data. Its basic underlying assumption is that the function to be estimated is locally relatively smooth where smoothness is adaptively defined depending on the local characteristics of the function. The usual definitions of smoothness do not apply to variables that assume unorderable categorical values. After a brief review of the MARS strategy for estimating functions of ordinal variables, alternative concepts of smoothness appropriate for categorical variables are introduced. These concepts lead to procedures that can estimate and interpret functions of many categorical variables, as well as those involving (many) mixed ordinal and categorical variables. They also provide a natural mechanism for modeling and predicting in the presence of missing predictor values (ordinal or categorical).

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1991
Accession Number
ADA590939

Entities

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  • Jerome H. Friedman

Organizations

  • Stanford University

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  • Ground and Sea Platforms

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  • Accuracy
  • Algorithms
  • Applied Mathematics
  • Computational Complexity
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  • Linear Accelerators
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  • Mathematics

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