On the Partitioning of Goodness-of-Fit Statistics for Multivariate Categorical Response Models
作者:
JosephB. Lang,
期刊:
Journal of the American Statistical Association
(Taylor Available online 1996)
卷期:
Volume 91,
issue 435
页码: 1017-1023
ISSN:0162-1459
年代: 1996
DOI:10.1080/01621459.1996.10476972
出版商: Taylor & Francis Group
关键词: Asymptotic independence;Constraint equation;Generalized log-linear model;Independent hypotheses;Separable hypotheses;Simultaneous model
数据来源: Taylor
摘要:
Numerical and asymptotic stochastic partitioning of goodness-of-fit statistics are considered for a broad class of simultaneous multivariate categorical response models. These simultaneous models impose constraints on the joint and marginal distributions of categorical response variables. Under certain conditions, the tenability of the corresponding simultaneous hypothesis can be assessed by separately testing the two subhypotheses: one regarding the joint distributions and the other regarding the marginal distributions. Specifically, easily verifiable sufficient conditions are introduced that allow us to partition the overall goodness-of-fit statistic into two interesting goodness-of-fit statistics: one for testing whether the joint distribution model holds and the other for testing whether the marginal distribution model holds. Moreover, it is proven that when the sufficient conditions hold and the simultaneous hypothesis is true, the two component goodness-of-fit statistics are asymptotically independent. These results are illustrated through several examples.
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