Estimation of interclass correlations in familial data
家族数据中类间相关系数的估计AI 解读 ↓
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家族数据中类间相关系数的估计
- 研究问题
- 当不同家庭的子女数量不等时，如何估计父母与子女之间的类间相关，并构造计算简便的零相关检验？
- 方法与思路
- 作者提出只需求解一个方程的最大似然估计途径，以及两套更易计算的替代估计，并据此构造使用已知分布的检验。
- 材料陈述的贡献
- 摘要称简化了不等家庭规模下的相关参数估计，并给出使用普通 Student t 分布检验类间相关为零的方法。
- 阅读关注点
- 应核对家庭数据模型、单方程求解的性质、替代估计的统计表现，以及 t 检验成立的条件与自由度计算方式。
- 阅读边界
- 仅据所给 OpenAlex 索引摘要，稿件版本未注明；摘要未交代分布假设或检验适用条件，不能推断任意家族数据均适用。
原文摘要
SUMMARY The maximum likelihood estimates of the parent-child interclass correlation and other parameters from familial data when the families have unequal numbers of offspring is given. Also given are two alternative sets of estimates which are easier to compute than the maximum likelihood estimates. Using these estimates, a test for the interclass correlation to be zero requires only the ordinary Student's t-distribution. Similarly other tests use only known distributions. In the analysis of familial data the degree of mother-sib resemblance is measured by the interclass correlation, the correlation between two different types of family member. Several estimates of this correlation have been proposed in the literature; see Rosner, Donner & Hennekens (1977) for details and their Monte Carlo comparisons of mean squared errors. In particular, they gave maximum likelihood estimates when the sib sizes are equal. However, when the sib sizes are not equal, Rosner (1979) proposed an algorithm for finding the maximum likelihood estimates which involves iterative maximization of an implicit function of two parameters. This algorithm is difficult to implement and may not even converge for some sets of data. Recently Mak & Ng (1981) used the linear model approach of Kempthorne & Tandan (1953) to obtain the maximum likelihood estimates. This reduces the problem to iterative maximization of a function of one parameter. However, nothing is known about the convergence of the procedure. Another iterative method of finding the maximum likelihood estimates has been given by Smith (1980). In this paper, an alternative approach is given which requires solving only one equation. Also, two alternative sets of estimates are given. These estimates are easier to compute than the maximum likelihood estimates. Using these estimates, a test for the interclass correlation to be zero is given; it requires only the ordinary Student's t distribution. Similarly, other tests use only known results.