Generalised bilinear regression

• 成果类型: Article
• 署名作者: Gabriel, KR
• 署名单位: University of Rochester
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/85.3.689
• 发表日期: 1998
• 页码: 689700
• 关键词: Principal component analysis; linear-models; multiplicative models; least-squares; 2-way tables; matrices; approximation; parameters; biplot

摘要

This paper discusses the application of generalised linear methods to bilinear models by criss-cross regression. It proposes an extension to segmented bilinear models in which the expectation matrix is linked to a sum in which each segment has specified row and column covariance matrices as well as a coefficient parameter matrix that is specified only by its rank. This extension includes a variety of biadditive models including the generalised Tukey degree of freedom for non-additivity model that consists of two bilinear segments, one of which is constant. The extension also covers a variety of other models for which least squares fits had not hitherto been available, such as higher-way layouts combined into the rows and columns of a matrix, and a harmonic model which can be reparameterised so a lower rank fit is equivalent to a constant phase parameter. A number of practical applications are provided,including displaying fits by biplots and using them to diagnose models.