Non-Null Distributions of the Wald's Criteria in Random Effects Growth Curve Models

SYNOPTIC ABSTRACT

This paper deals with profile analysis in two extended growth curve models. The first is a growth curve model with parallel mean profiles, which has a random effects covariance structure based on a single response variable; the second is a multivariate growth curve model with parallel mean profiles, which has a multivariate random effects covariance structure based on several response variables. For testing “no condition variation” and “level” hypotheses concerning parallel mean profiles of several groups, we obtain the Wald's criteria (Trans. Amer. Math. Soc. 54 (1943) 426–482) and their asymptotic non-null distributions. A numerical example is also given.

Key Words and Phrases:

• Growth curves
• non-null distribution
• parallel profiles
• random effects covariance structure
• repeated measurements
• Wald's criterion