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Model Selection for Poisson Regression via Association Rules Analysis

机译：通过关联规则分析的泊松回归模型选择

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摘要

This study integrates association rules analysis, a methodology for selecting potential interactions, with Poisson regression modeling. Though typically ignored in conventional Poisson regression, interactions are very common in practice. However, selecting a Poisson regression model when many main effects and interactions are involved is problematic. In this study, we develop a model selection framework to address this problem. Specifically, we focus on building an optimal Poisson regression model by (1) discretizing the response and quantitative attributes into levels; (2) exploring via association rules analysis combinations of input variables that have a significant impact on response; (3) selecting potential (low- and high-order) interactions; (4) converting these potential interactions into new variables; and (5) selecting variables from all the input variables and the newly created variables (interactions) to build the optimal Poisson regression model. Our model selection procedure is the first approach to enable a global search for potential interactions and the first to establish the optimal combination of main effects and interaction effects in the Poisson regression model. A real-life example is given for illustration. It is shown that the proposed method finds the optimal model including important interactions that cannot be found by other existing methods.
机译：本研究与泊松回归建模相结合了关联规则分析，一种选择潜在相互作用的方法。虽然通常在传统的泊松回归中被忽略，但在实践中相互作用非常常见。然而，当涉及许多主要效果和相互作用时，选择泊松回归模型是有问题的。在本研究中，我们开发了一个模型选择框架来解决这个问题。具体而言，我们专注于建立最佳泊松回归模型（1）将响应和定量属性离散到水平中; （2）通过关联规则探索对响应产生重大影响的输入变量的组合; （3）选择潜力（低阶和高阶）相互作用; （4）将这些潜在的相互作用转换为新变量; （5）从所有输入变量和新创建的变量（交互）选择变量以构建最佳泊松回归模型。我们的模型选择程序是启用全球搜索潜在交互的方法，以及第一个在泊松回归模型中建立主要效果和交互效应的最佳组合。提供了现实生活的例子。结果表明，所提出的方法找到最佳模型，包括其他现有方法无法找到的重要交互。

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