Poisson regression assumes variance = mean; real count data usually over-disperse (variance > mean). This tool fits Poisson, the negative binomial NB2 (its dispersion α estimated by profile likelihood, variance μ + αμ²), and zero-inflated versions where a separate structural-zero probability absorbs excess zeros — fitted by EM, the count arm re-weighted each round.
The Poisson fit reports Pearson χ²/df: values well above 1 signal overdispersion and point to the negative binomial. Model choice should be driven by AIC and the zero counts, not just significance.
Frequently asked questions
When is zero-inflation warranted?
When zeros come from two different processes — "never happens" and "happened but recorded zero" (insurance claims, fishing catches). If the Poisson/NB already predicts your zero count well, ZIP adds parameters without adding fit.
How do I read α?
α = 0 collapses to Poisson. Larger α means more overdispersion; the variance formula μ + αμ² shows the extra spread growing with the square of the mean.
中文说明
泊松回归假设方差等于均值；真实计数数据通常过散（方差 > 均值）。本工具拟合泊松、负二项 NB2（离散参数 α 由剖面似然估计，方差 μ + αμ²），以及用 EM 拟合的零膨胀版本——一个独立的结构零概率吸收多余的零，计数部分逐轮重加权。
泊松结果会报告 Pearson χ²/自由度：明显高于 1 提示过散、应改用负二项。模型选择看 AIC 与零的个数，而不只是显著性。
常见问题
什么时候该用零膨胀？
当零来自两个过程——“从不发生”与“发生但记为零”（保险理赔、渔获）。若泊松/负二项已能预测零的个数，ZIP 只是加参数不加拟合。
α 怎么读？
α = 0 退化为泊松；α 越大过散越强。方差公式 μ + αμ² 表明额外离散度随均值平方增长。