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THE REDUCED‐RANK GROWTH CURVE MODEL FOR DISCRIMINANT ANALYSIS OF LONGITUDINAL DATA
Author(s) -
Albert Jeffrey M.,
Kshirsagar Anant M.
Publication year - 1993
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1993.tb01342.x
Subject(s) - discriminant , rank (graph theory) , linear discriminant analysis , discriminant function analysis , growth curve (statistics) , curse of dimensionality , multivariate statistics , statistics , mathematics , computer science , longitudinal data , artificial intelligence , pattern recognition (psychology) , data mining , combinatorics
Summary This paper presents a method of discriminant analysis especially suited to longitudinal data. The approach is in the spirit of canonical variate analysis (CVA) and is similarly intended to reduce the dimensionality of multivariate data while retaining information about group differences. A drawback of CVA is that it does not take advantage of special structures that may be anticipated in certain types of data. For longitudinal data, it is often appropriate to specify a growth curve structure (as given, for example, in the model of Potthoff & Roy, 1964). The present paper focuses on this growth curve structure, utilizing it in a model‐based approach to discriminant analysis. For this purpose the paper presents an extension of the reduced‐rank regression model, referred to as the reduced‐rank growth curve (RRGC) model. It estimates discriminant functions via maximum likelihood and gives a procedure for determining dimensionality. This methodology is exploratory only, and is illustrated by a well‐known dataset from Grizzle & Allen (1969).