With the growing popularity of spatial mixture models in cluster analysis, model selection criteria have become an established tool in the search for parsimony. However, the label-switching problem is often inherent in Bayesian implementation of mixture models and a variety of relabeling algorithms have been proposed. We use a space-time mixture of Poisson regression models with homogeneous covariate effects to illustrate that the best model selected by using model selection criteria does not always support the model that is chosen by the optimal relabeling algorithm. The results are illustrated for real and simulated datasets. The objective is to make the reader aware that if the purpose of statistical modeling is to identify clusters, applying a relabeling algorithm to the model with the best fit may not generate the optimal relabeling.

中文翻译：

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时空混合模型：重新标记算法和模型选择问题

随着空间混合模型在聚类分析中的日益流行，模型选择标准已成为寻求简约的既定工具。然而，标签切换问题通常是混合模型的贝叶斯实现中固有的，并且已经提出了各种重新标记算法。我们使用具有同质协变量效应的泊松回归模型的时空混合来说明使用模型选择标准选择的最佳模型并不总是支持最佳重新标记算法选择的模型。结果针对真实和模拟数据集进行了说明。目的是让读者意识到，如果统计建模的目的是识别集群，则将重新标记算法应用于具有最佳拟合的模型可能不会生成最佳重新标记。