Zerbe G O, Wu M C, Zucker D M
Division of Biometrics, University of Colorado Health Sciences Center, Denver 820262.
Stat Med. 1994;13(5-7):759-68. doi: 10.1002/sim.4780130536.
Blomqvist's problem of studying the relationship between change and initial value in a linear growth curve setting is reformulated from a random effects model perspective. First, a maximum likelihood estimate of the between-individual covariance matrix for a simple linear regression model with stochastic parameters is obtained via an EM algorithm as discussed by Laird and Ware. Second, the regression coefficient of the individual-specific slopes on the individual-specific intercepts is estimated as a ratio of elements of the between-individual covariance matrix as discussed by Zucker et al. Then a Fieller's type confidence interval for this ratio is proposed. Discussion is facilitated by recognizing the Laird-Ware model as a special case of a more general model discussed by Hocking.
布洛姆奎斯特在线性增长曲线设定中研究变化与初始值之间关系的问题，从随机效应模型的角度进行了重新阐述。首先，如莱尔德和韦尔所讨论的，通过期望最大化（EM）算法获得具有随机参数的简单线性回归模型的个体间协方差矩阵的最大似然估计。其次，如祖克等人所讨论的，将个体特定斜率对个体特定截距的回归系数估计为个体间协方差矩阵元素的比率。然后针对该比率提出了费勒尔型置信区间。通过将莱尔德 - 韦尔模型识别为霍金所讨论的更一般模型的特殊情况，有助于展开讨论。
