A MATRIX HANDLING OF PREDICTIONS UNDER A GENERAL LINEAR RANDOM-EFFECTS MODEL WITH NEW OBSERVATIONS

作者：Tian, Yongge^*

来源：Electronic Journal of Linear Algebra, 2015, 29(1): 30-45.

DOI：10.13001/1081-3810.2895

• Linear random-effects model
• Quadratic matrix-valued function
• Lowner partial ordering
• BLUP
• BLUE
• Covariance matrix

Linear regression models that include random effects are commonly used to analyze longitudinal and correlated data. Assume that a general linear random-effects model gamma = X beta + epsilon with beta = A alpha + gamma is given, and new observations in the future follow the linear model y(f) = X-f beta + epsilon(f). This paper shows how to establish a group of matrix equations and analytical formulas for calculating the best linear unbiased predictor (BLUP) of the vector phi = F alpha + G gamma + H epsilon + E-f epsilon(f) of all unknown parameters in the two models under a general assumption on the covariance matrix among the random vectors gamma, epsilon and epsilon(f) via solving a constrained quadratic matrix-valued function optimization problem. Many consequences on the BLUPs of phi and their covariance matrices, as well as additive decomposition equalities of the BLUPs with respect to its components are established under various assumptions.

• 出版日期2015
• 单位中央财经大学