Limited- and full-information estimation and goodness-of-fit testing in 2n contingency tables: A unified framework

• 成果类型: Article
• 署名作者: Maydeu-Olivares, A; Joe, H
• 署名单位: University of Barcelona; IE University; University of British Columbia
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/016214504000002069
• 发表日期: 2005
• 页码: 1009-1020
• 关键词: pessimism; models

摘要

High-dimensional contingency tables tend to be sparse, and standard goodness-of-fit statistics such as X-2 cannot be used without pooling categories. As an improvement on arbitrary pooling, for goodness of fit of large 2(n) contingency tables, we propose classes of quadratic form statistics based on the residuals of margins or multivariate moments up to order r. These classes of test statistics are asymptotically chi-squared distributed under the null hypothesis. Further, the marginal residuals are useful for diagnosing lack of fit of parametric models. We show that when r is small (r = 2, 3), the proposed statistics have better small-sample properties and are asymptotically more powerful than X-2 for some useful multivariate binary models. Related to these test statistics is a class of limited-information estimators based on low-dimensional margins. We show that these estimators have high efficiency for one commonly used latent trait model for binary data.