The Reduced‐rank Growth Curve Model for Discriminant Analysis of Longitudinal Data

Abstract

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).

A multivariate reduced-rank growth curve model with unbalanced data

“…Albert and Kshirsagar (1993) and Reinsel and Velu (1998, pp. 171-176) proposed a special case of (1) under the same terminology.…”

Estimation of Growth Curve Models with Structured Error Covariances by Generalized Estimating Equations

“…For instance, reduced-rank restrictions such as rank(AB) ≤ min (D,P ) (Albert & Kshirsagar, 1993;Reinsel & Velu, 1998, pp. 171-176) may be imposed on the method.…”

An Extended Multivariate Random-Effects Growth Curve Model

“…For instance, reduced-rank restrictions may be imposed on the method, motivated by the fact that the mathematical structure of the growth curve model is akin to that of the reduced-rank regression model (Albert & Kshirsagar, 1993;Hwang & Takane, 2004;Reinsel & Velu, 1998, pp. 171-176).…”