Analysis of multivariate longitudinal data using quasi-least squares

In this paper we consider the analysis of multivariate longitudinal data assuming a scale multiple of Kronecker product correlation structure for the covariance matrix of the observations on each subject. The method used for the estimation of the parameters is the quasi-least squares method developed in the following three papers: Chaganty (J. Statist. Plann. Inference 63 (1997) 39), Shults and Chaganty (Biometrics 54 (1998) 1622) and Chaganty and Shults (J. Statist. Plann. Inference 76 (1999) 145). We show that the estimating equations for the correlation parameters in the quasi-least-squares method are optimal unbiased estimating equations if the data is from a normal population. An algorithm for computing the estimates is provided and implemented on a real life data set. The asymptotic joint distribution of the estimators of the regression and correlation parameters is derived and used for testing a linear hypothesis on the regression parameters.

[1]  C. Heyde,et al.  Quasi-likelihood and its application , 1997 .

[2]  J. Shults.  Modeling the correlation structure of data that have multiple levels of association , 2000 .

[3]  N. Rao Chaganty,et al.  Analysis of Serially Correlated Data Using Quasi-Least Squares , 1998 .

[4]  Martin Crowder,et al.  On the use of a working correlation matrix in using generalised linear models for repeated measures , 1995 .

[5]  A. Zellner.  An Efficient Method of Estimating Seemingly Unrelated Regressions and Tests for Aggregation Bias , 1962 .

[6]  A. Zellner.  Estimators for Seemingly Unrelated Regression Equations: Some Exact Finite Sample Results , 1963 .

[7]  V. P. Godambe.  An Optimum Property of Regular Maximum Likelihood Estimation , 1960 .

[8]  R. Serfling.  Approximation Theorems of Mathematical Statistics , 1980 .

[9]  J. Shults,et al.  On eliminating the asymptotic bias in the quasi-least squares estimate of the correlation parameter , 1999 .

[10]  Robert J. Boik,et al.  Scheffés mixed model for multivariate repeated measures:a relative efficiency evaluation , 1991 .

[11]  L. Imhof.  Matrix Algebra and Its Applications to Statistics and Econometrics , 1998 .

[12]  Dayanand N. Naik,et al.  Analysis of multivariate repeated measures data with a Kronecker product structured covariance matrix , 2001 .

[13]  W. Hauck,et al.  Wald's Test as Applied to Hypotheses in Logit Analysis , 1977 .

[14]  Kalyan Das,et al.  Miscellanea. On the efficiency of regression estimators in generalised linear models for longitudinal data , 1999 .

[15]  S. Zeger,et al.  Longitudinal data analysis using generalized linear models , 1986 .

[16]  R. G. Cornell,et al.  Modern Statistical Methods in Chronic Disease Epidemiology. , 1988 .

[17]  J. Shults,et al.  Use of Quasi–Least Squares to Adjust for Two Levels of Correlation , 2002, Biometrics.

[18]  N. Rao Chaganty,et al.  An alternative approach to the analysis of longitudinal data via generalized estimating equations , 1997 .

[19]  Andrzej T. Galecki,et al.  General class of covariance structures for two or more repeated factors in longitudinal data analysis , 1994 .

[20]  N. H. Timm.  2 Multivariate analysis of variance of repeated measurements , 1980 .