系数随机的多元线性回归模型的参数估计

ESTIMATION OF PARAMETERS IN RANDOM COEFFICIENT MULTIVARIATE LINEAR REGRESSION MODELS

对一般系数随机的带有相关因子的多元线性回归模型的参数进行估计。估计值是用EM算法给出的极大似然估计或约束的极大似然估计。给出了EM算法的具体公式,并利用bootstrap方法估算出这些估计值的精确度。最后通过一判别儿童总体中是否存在Catch-Up生长的例子以解释给出的方法。

EM algorithm is employed to find maximum likelihood estimates or restricted maximum likelihood estimates for parameters in the general multivariate linear regression models while incorporating related covariates. Detailed EM algorithm is derived, while the accuracy of these estimates can be approximated by using bootstrap method. One example from the growth studies is used to illustrate the method. The results answer the question of whether or not catch-up growth is present in the population.