THE ESTIMATION AND COMPARISON OF RESIDUAL REGRESSIONS WHERE THERE ARE 2 OR MORE RELATED SETS OF OBSERVATIONS
成果类型：
Article
署名作者：
CARTER, AH
刊物名称：
BIOMETRIKA
ISSN/ISSBN：
0006-3444
DOI：
10.1093/biomet/36.1-2.26
发表日期：
1949
页码：
2646
关键词：
摘要：
The problem investigated concerns a series of parallel samples of multivariate observations where corresponding members of the several samples have elements in common. It is assumed, however, that there is no interaction of this correlated effect with the sample effect. Max. likelihood estimates of the partial regression coeffs. in each sample are given. An exact test of the homogeneity, between samples, of the regression coeffs. is obtained by introducing dummy variates into the test of a general linear hypothesis given by Kolodziejczyk (Biometrika, 1935). Using the same approach, a test of the significance of the difference between any two comparable regression estimates is derived. The cases of two or more bivariate samples, of two q-variate samples, and of independent samples are considered in detail and two numerical illustrations are given. Yates (Proc. Roy. Soc. Edinb., 1939) considered the problem of comparing regression coeffs. from two correlated samples when interaction may be present and obtained an approx. test for the hypothesis of equality. In the first example, both tests are applied and the differences noted.[long dash]Leo Katz.