Monotone Spline Transformations for Dimension Reduction | Psychometrika | Cambridge Core (original) (raw)

Abstract

Consider a set of data consisting of measurements of n objects with respect to p variables displayed in an n × p matrix. A monotone transformation of the values in each column, represented as a linear combination of integrated basis splines, is assumed determined by a linear combination of a new set of values characterizing each row object. Two different models are used: one, an Eckart-Young decomposition model, and the other, a multivariate normal model. Examples for artificial and real data are presented. The results indicate that both methods are helpful in choosing dimensionality and that the Eckart-Young model is also helpful in displaying the relationships among the objects and the variables. Also, results suggest that the resulting transformations are themselves illuminating.

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