Testing covariance structure in multivariate models: Application to family disease data

• 成果类型: Article
• 署名作者: Whittemore, AS; Halpern, J; Gong, G
• 署名单位: Stanford University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• 发表日期: 1998
• 页码: 518-525
• 关键词: ovarian-cancer; regression; traits

摘要

Recent interest in modeling multivariate responses for members of groups has emphasized the need for testing goodness of fit. Here we describe a way to test the covariance structure of a multivariate distribution parameterized by a vector theta. The idea is to extend this distribution, the null distribution, to a more general distribution that depends on theta, an additional scalar gamma, and a specific quadratic function of the response vector chosen to capture features of an alternative covariance structure. When gamma = 0, the more general distribution reduces to the null one. Standard likelihood theory yields a score test for gamma = 0; that is, a test of fit of the null distribution. The score statistic is the standardized difference between observed and expected values of the quadratic function, where the expectation is taken with respect to the null distribution, with theta replaced by its maximum likelihood estimate. Applying the methods to case-control data on familial cancers of the ovary and breast, we illustrate their use with nonrandomly sampled groups, with censored response data, and with complex multivariate distributions. The application shows that this kind of model extension can succeed where more obvious approaches fail.