Using SEM Algorithm to Obtain Asymptotic Variance-Covariance Matrices in Linear Mixed Models

• Main Authors: Te-Yu Lin, 林德育
• Other Authors: Miao-Yu Tsai
• Format: Others
• Language: zh-TW
• Published: 2007
• Online Access: http://ndltd.ncl.edu.tw/handle/85552240423820117147

碩士 === 國立彰化師範大學 === 統計資訊研究所 === 95 === The purpose of the thesis is to obtain the maximum likelihood estimators (MLEs) of parameters through use of the EM algorithm and compute their asymptotic variance-covariance matrices via the supplemented EM algorithm (SEM algorithm) in linear mixed models (LMMs). Besides, we compare the asymptotic variance-covariance matrices of MLEs using the SEM algorithm with that derived by the profiled likelihood. We consider an application for illustrations. The example concerns the growth data (Potthoff and Roy, 1964) where the response variable is the distance from the center of the pituitary to the pterygomaxillary fissure of 27 children. The results show that the sex and age are important factors associated with the distance and the variance estimator of the random intercept is large implying substantial individual heterogeneity. In addition, we find that the asymptotic variance-covariance matrix of MLEs for variance components via the SEM algorithm is slightly smaller than that derived by profiled likelihood. Finally, for SEM computations, choosing reasonable and accurate initial values can reduce the number of iterations and improve the symmetry of the resulting variance-covariance matrix.