Lin Ting Hsiang, Tsai Min-Hsiao
Department of Statistics, National Taipei University, New Taipei City, Taiwan.
J Appl Stat. 2021 May 26;49(11):2953-2963. doi: 10.1080/02664763.2021.1929875. eCollection 2022.
Inflated data and over-dispersion are two common problems when modeling count data with traditional Poisson regression models. In this study, we propose a latent class inflated Poisson (LCIP) regression model to solve the unobserved heterogeneity that leads to inflations and over-dispersion. The performance of the model estimation is evaluated through simulation studies. We illustrate the usefulness of introducing a latent class variable by analyzing the Behavioral Risk Factor Surveillance System (BRFSS) data, which contain several excessive values and characterized by over-dispersion. As a result, the new model we proposed displays a better fit than the standard Poisson regression and zero-inflated Poisson regression models for the inflated counts.
在使用传统泊松回归模型对计数数据进行建模时，数据膨胀和过度离散是两个常见问题。在本研究中，我们提出了一种潜在类别膨胀泊松（LCIP）回归模型，以解决导致数据膨胀和过度离散的未观察到的异质性问题。通过模拟研究对模型估计的性能进行了评估。我们通过分析行为风险因素监测系统（BRFSS）数据来说明引入潜在类别变量的有用性，该数据包含几个极值且具有过度离散的特征。结果表明，对于膨胀计数，我们提出的新模型比标准泊松回归模型和零膨胀泊松回归模型具有更好的拟合度。
