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.

使用传统泊松回归模型对计数数据进行建模时，数据膨胀和过度分散是两个常见问题。在这项研究中，我们提出了一个潜在类别膨胀泊松（LCIP）回归模型来解决导致膨胀和过度分散的未观察到的异质性。通过模拟研究评估模型估计的性能。我们通过分析行为风险因素监视系统 (BRFSS) 数据来说明引入潜在类变量的有用性，这些数据包含几个过高的值并以过度分散为特征。因此，我们提出的新模型比标准泊松回归和膨胀计数的零膨胀泊松回归模型更适合。