Inequality constrained analysis of variance: A Bayesian approach
Inequality constrained analysis of variance: A Bayesian approach
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DOI：
10.1037/1082-989x.10.4.477
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发表时间：
2005-12-01
影响因子：
7
通讯作者：
Hoijtink, H
中科院分区：
文献类型：
--
作者：
Klugkist, I;Laudy, O;Hoijtink, H
研究者通常有一个或多个理论或期望关于他们的实证研究的结果。当研究人员谈论如果某个理论是正确的，变量之间的预期关系时，他们的陈述通常是根据一个或多个参数预期大于或小于一个或多个其他参数。换句话说，他们的陈述经常使用不等式约束来制定。在这篇文章中，贝叶斯方法来评估方差分析或协方差分析模型的不等式约束（调整）的手段。这种评估包含两个问题：估计的参数给定的限制使用吉布斯采样器和模型选择使用贝叶斯因素的情况下，竞争理论。文章最后用两个例子：一个单向协方差分析和一个三向有序平均值表的分析。
Researchers often have one or more theories or expectations with respect to the outcome of their empirical research. When researchers talk about the expected relations between variables if a certain theory is correct, their statements are often in terms of one or more parameters expected to be larger or smaller than one or more other parameters. Stated otherwise, their statements are often formulated using inequality constraints. In this article, a Bayesian approach to evaluate analysis of variance or analysis of covariance models with inequality constraints on the (adjusted) means is presented. This evaluation contains two issues: estimation of the parameters given the restrictions using the Gibbs sampler and model selection using Bayes factors in the case of competing theories. The article concludes with two illustrations: a one-way analysis of covariance and an analysis of a three-way table of ordered means.