Testing the Independence Assumption in Linear Models
提出利用近重复失拟检验来检验线性模型中观测值是否独立，通过构造合理子组识别相关性，帮助判断模型假设是否成立。
Abstract We propose using an existing set of statistical tools in a new way that allows one to test the independence assumption in standard normal theory linear models. The set of tools is near-replicate lack-of-fit tests. The classical lack-of-fit test requires a linear model in which some rows of the model matrix are repeated. Near-replicate lack-of-fit tests were developed to mimic the behavior of the classical test by identifying clusters of rows in the design matrix that are similar, though not necessarily exact replications. We argue that meaningful clusters can be formed more generally by constructing rational subgroups of data collected under similar circumstances. As such, observations in the same subgroup may be more highly correlated than observations in different subgroups. We investigate the behavior of these tests when used to identify lack of independence.