Cholesky problems
Cholesky problems
复制标题
DOI：
10.1007/s10519-005-5355-9
复制
发表时间：
2005-09-01
影响因子：
2.6
通讯作者：
Carey, G
中科院分区：
文献类型：
--
作者：
Carey, G
行为遗传学家通常将遗传或环境协方差矩阵参数化为下对角矩阵乘以其转置的乘积--这种技术通常被称为“拟合乔莱斯基”。“在这里，模拟表明这个过程有时是有效的，但在其他时候：（1）可能不会产生以chi（2）分布的拟合统计量;或者（2）如果拟合统计量的分布是chi（2）停止，那么自由度（df）并不总是一般模型中的参数数量减去约束模型中的参数数量之间的差异。假设这个问题与Cholesky参数化要求乘积形成的协方差矩阵是正定或奇异的这一事实有关。即使人口协方差矩阵可能是正定的，抽样误差和遗传和环境矩阵的派生性质（而不是直接派生）的组合允许矩阵是负（半）定的。当这种情况发生时，拟合Cholesky限制了搜索的数值范围，并损害了目前在行为遗传学中使用的最大似然理论。在理解这种现象的原因并开发出令人满意的解决方案之前，拟合Cholesky矩阵的人面临着证明其拟合统计量和模型比较的df的有效性的负担。提出了一种临时补救措施-拟合无约束模型和Cholesky模型，如果两者不同，则报告拟合统计量和参数估计值的差异。乔莱斯基问题是一个程度问题，而不是种类问题。因此，一些乔列斯基解与无约束解的差别很小，问题的重要性必须根据这两种解导致对结果的不同实质性解释的频率来评估。如果遵循，拟议的临时补救措施将开发一个机构的经验数据，以评估在何种程度上乔莱斯基问题是重要的实质性问题与统计好奇心。
Behavioral geneticists commonly parameterize a genetic or environmental covariance matrix as the product of a lower diagonal matrix postmultiplied by its transpose-a technique commonly referred to as "fitting a Cholesky." Here, simulations demonstrate that this procedure is sometimes valid, but at other times: (1) may not produce fit statistics that are distributed as a chi(2); or (2) if the distribution of the fit statistic is chi(2) stop, then the degrees of freedom (df) are not always the difference between the number of parameters in the general model less the number of parameters in a constrained model. It is hypothesized that the problem is related to the fact that the Cholesky parameterization requires that the covariance matrix formed by the product be either positive definite or singular. Even though a population covariance matrix may be positive definite, the combination of sampling error and the derived-as opposed to directly observed-nature of genetic and environmental matrices allow matrices that are negative (semi) definite. When this occurs, fitting a Cholesky constrains the numerical area of search and compromises the maximum likelihood theory currently used in behavioral genetics. Until the reasons for this phenomenon are understood and satisfactory solutions are developed, those who fit Cholesky matrices face the burden of demonstrating the validity of their fit statistics and the df for model comparisons. An interim remedy is proposed-fit an unconstrained model and a Cholesky model, and if the two differ, then report the difference in fit statistics and parameter estimates. Cholesky problems are a matter of degree, not of kind. Thus, some Cholesky solutions will differ trivially from the unconstrained solutions, and the importance of the problems must be assessed by how often the two lead to different substantive interpretation of the results. If followed, the proposed interim remedy will develop a body of empirical data to assess the extent to which Cholesky problems are important substantive issues versus statistical curiosities.