Project/Area Number  09640280 
Research Category 
GrantinAid for Scientific Research (C)

Section  一般 
Research Field 
General mathematics (including Probability theory/Statistical mathematics)

Research Institution  Kumamoto University 
Principal Investigator 
YOKOYAMA Takahisa Faculty of Engineering, Assistant Prof., 工学部, 講師 (20240864)

CoInvestigator(Kenkyūbuntansha) 
NAKAMURA Takashi Okayama University of Science, Faculty of Informatics, Prof., 総合情報学部, 教授 (20069074)
TAKADA Yoshikazu Faculty of Science, Associates Prof., 理学部, 助教授 (70114098)
SAKATA Toshio Faculty of Engineering, Associates Prof., 工学部, 助教授 (20117352)

Project Fiscal Year 
1997 – 1998

Project Status 
Completed(Fiscal Year 1998)

Budget Amount *help 
¥1,200,000 (Direct Cost : ¥1,200,000)
Fiscal Year 1998 : ¥500,000 (Direct Cost : ¥500,000)
Fiscal Year 1997 : ¥700,000 (Direct Cost : ¥700,000)

Keywords  Repeated Measures / Random Effects / Covariance Structure / Growth Curve Model / 経時測定 / ランダム効果 / 共分散構造 / 成長曲線モデル 
Research Abstract 
First we propose test statistics for a general hypothesis concerning the adequacy of multivariate randomeffects covariance structures in a multivariate growth curve model with differing numbers of random effects. Since the exact likelihood ratio (LR) statistic for the hypothesis is complicated, it is suggested to use a modified LR statistic. An asymptotic expansion of the null distribution of the statistic is obtained. The exact LR statistic is also discussed (Yokoyama, T., J.Statist. Plann. inference 65 (1997) 281 292). Next we consider profile analysis in two extended growth curve models. The first is a growth curve model with parallel mean profiles, which has a randomeffects covariance structure based on a single response variable ; the second is a multivariate growth curve model with parallel mean profiles, which has a multivariate randomeffects 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 criteria proposed by Wald along with their asymptotic null distributions. We give a numerical example of these asymptotic results (Yokoyama, T., Hiroshima Math. J.28 (1998) 345  354).
