Department of Statistical Data Science, Institute of Statistical Mathematics, Tachikawa, Tokyo, Japan.
Department of Statistical Modeling, Institute of Statistical Mathematics, Tachikawa, Tokyo, Japan.
PLoS One. 2022 Jan 7;17(1):e0260836. doi: 10.1371/journal.pone.0260836. eCollection 2022.
In the era of open data, Poisson and other count regression models are increasingly important. Still, conventional Poisson regression has remaining issues in terms of identifiability and computational efficiency. Especially, due to an identification problem, Poisson regression can be unstable for small samples with many zeros. Provided this, we develop a closed-form inference for an over-dispersed Poisson regression including Poisson additive mixed models. The approach is derived via mode-based log-Gaussian approximation. The resulting method is fast, practical, and free from the identification problem. Monte Carlo experiments demonstrate that the estimation error of the proposed method is a considerably smaller estimation error than the closed-form alternatives and as small as the usual Poisson regressions. For counts with many zeros, our approximation has better estimation accuracy than conventional Poisson regression. We obtained similar results in the case of Poisson additive mixed modeling considering spatial or group effects. The developed method was applied for analyzing COVID-19 data in Japan. This result suggests that influences of pedestrian density, age, and other factors on the number of cases change over periods.
在开放数据时代，泊松和其他计数回归模型变得越来越重要。然而，传统的泊松回归在可识别性和计算效率方面仍然存在问题。特别是，由于识别问题，泊松回归在零较多的小样本中可能不稳定。针对这一问题，我们提出了一种包含泊松可加混合模型的过离散泊松回归的闭式推断。该方法是通过基于模式的对数高斯逼近得到的。所得方法快速、实用，且不存在识别问题。蒙特卡罗实验表明，与闭式替代方法相比，该方法的估计误差要小得多，与常用的泊松回归相当。对于零较多的计数，我们的逼近具有比传统泊松回归更好的估计精度。在考虑空间或组效应的泊松可加混合模型的情况下，我们得到了类似的结果。所开发的方法用于分析日本的 COVID-19 数据。结果表明，行人密度、年龄等因素对病例数量的影响随时间变化。
