Analysis of paired ordered categorical data in a factorial design
作者:
H. L. Patel,
K. T. Tsai,
期刊:
Journal of Biopharmaceutical Statistics
(Taylor Available online 1996)
卷期:
Volume 6,
issue 1
页码: 15-36
ISSN:1054-3406
年代: 1996
DOI:10.1080/10543409608835119
出版商: Marcel Dekker, Inc.
关键词: Pairs of discordant vectors;Lehmann alternative;Proportional odds model;Marginal homogeneity
数据来源: Taylor
摘要:
In clinical trials and behavioral sciences, there exist situations where paired responses are obtained from each subject on an ordinal scale. Existing methods for analyzing such data in a factorial design are reviewed and new methods are developed with a special emphasis on pre-and post-treatment responses. The distribution of a square table is decomposed into successively independent pairs of discordant vectors, and assuming a logistic model, a statistics is computed to measure the shift in the marginal distributions. The approach is similar to McCullagh's approach (1). Two other criteria are proposed, one based on a Lehmann alternative used for comparing two distribution functions and the other based on a proportional odds model. These criteria are applied to the marginal distributions of a square table. For each case, a statistic measuring lack of marginal homogeneity and its variance are computed for each independent square table of a factorial design. Given such statistics, one can estimate a set of linear contrasts and compute its dispersion matrix for making inference. A numerical example is given.
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