Polychotomous Regression

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Abstract
An automatic procedure that uses linear splines and their tensor products is proposed for fitting a regression model to data involving a polychotomous response variable and one or more predictors. The fitted model can be used for multiple classification. The automatic fitting procedure involves maximum likelihood estimation, stepwise addition, stepwise deletion, and model selection by the Akaike information criterion, cross-validation, or an independent test set. A modified version of the algorithm has been constructed that is applicable to large datasets, and it is illustrated using a phoneme recognition dataset with 250,000 cases, 45 classes, and 63 predictors.