Tests of Hypotheses in Overdispersed Poisson Regression and other Quasi-Likelihood Models
过度离散泊松回归及其他拟似然模型中的假设检验AI 解读 ↓
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过度离散泊松回归及其他拟似然模型中的假设检验
- 研究问题
- 当计数数据存在过度离散且方差参数需要估计时，如何检验新增回归变量的显著性，并获得可靠的标准误与检验水平？
- 方法与思路
- 作者结合矩估计方差参数与拟似然估计回归系数，比较采用模型协方差和经验协方差的 Wald、得分检验，并开展模拟。
- 材料陈述的贡献
- 摘要称相关检验与估计方程可推广至一般拟似然模型；模拟中模型协方差方法表现较好，经验方法更依赖较大样本。
- 阅读关注点
- 应核对均值与方差设定所需条件、估计方差参数对检验的影响，以及经验协方差有效性的渐近依据和模拟样本规模。
- 阅读边界
- 仅据 OpenAlex 索引摘要，稿件版本未注明。模拟表现不能推广至任意过度离散机制；摘要未给出完整正则条件，不能推断刊本变化。
原文摘要
Test statistics for evaluating the significance of added variables in a regression equation are developed for mixed Poisson models, where the structural parameter φ that determines the mean/variance relationship var(μ; φ) = μ + φ · μ 2 is estimated by the method of moments and the regression coefficients are estimated by quasi-likelihood. The formulas presented for test statistics and related estimating equations are applicable generally to quasi-likelihood models specified by an arbitrary mean value function μ(x; β), together with a variance function V(μ; φ) that contains one or more unknown parameters. Two versions of the Wald and score tests are investigated—one calculated from the usual model-based covariance matrix whose validity depends on correct specification of the variance function, and another using an “empirical” covariance matrix that has a more general asymptotic justification. Monte Carlo simulations demonstrate that the quasi-likelihood/method of moments (QL/M) procedures yield approximately unbiased estimates of regression coefficients and their standard errors and that model-based Wald, score, and deviance tests approximate the nominal size at the 5% level for moderate sample sizes. The simpler Poisson analysis also produces approximately unbiased regression coefficients, even though the overdispersion is not accounted for. Although tests and standard errors based on Poisson theory are seriously in error in the presence of overdispersion, the empirical standard errors and especially the empirical score test obtained in conjunction with the Poisson analysis perform reasonably well with overdispersed data provided the sample size is sufficiently large. They perform less well in small samples than do the model-based QL/M procedures, probably because of the lack of precision in the empirical variances. These methods have important applications in epidemiology, toxicology, and related areas.