Consonni Guido, Paroli Roberta
Università Cattolica del Sacro Cuore, Milan, Italy.
Psychometrika. 2017 Sep;82(3):589-609. doi: 10.1007/s11336-016-9516-y. Epub 2016 Oct 4.
In the social sciences we are often interested in comparing models specified by parametric equality or inequality constraints. For instance, when examining three group means [Formula: see text] through an analysis of variance (ANOVA), a model may specify that [Formula: see text], while another one may state that [Formula: see text], and finally a third model may instead suggest that all means are unrestricted. This is a challenging problem, because it involves a combination of nonnested models, as well as nested models having the same dimension. We adopt an objective Bayesian approach, requiring no prior specification from the user, and derive the posterior probability of each model under consideration. Our method is based on the intrinsic prior methodology, suitably modified to accommodate equality and inequality constraints. Focussing on normal ANOVA models, a comparative assessment is carried out through simulation studies. We also present an application to real data collected in a psychological experiment.
在社会科学中，我们常常对比较由参数等式或不等式约束所指定的模型感兴趣。例如，在通过方差分析（ANOVA）检验三个组均值[公式：见正文]时，一个模型可能指定[公式：见正文]，而另一个模型可能表明[公式：见正文]，最后第三个模型可能反而暗示所有均值不受限制。这是一个具有挑战性的问题，因为它涉及非嵌套模型以及具有相同维度的嵌套模型的组合。我们采用一种客观贝叶斯方法，无需用户事先指定，并推导出所考虑的每个模型的后验概率。我们的方法基于内在先验方法，并进行了适当修改以适应等式和不等式约束。聚焦于正态ANOVA模型，通过模拟研究进行了比较评估。我们还展示了该方法在一项心理实验中收集的实际数据上的应用。
