四川大学学报（自然科学版）2026，Vol.63Issue(3)：566-573,8.DOI:10.19907/j.0490-6756.250195
纵向零膨胀计数数据的多参数联合回归模型
Multi-parameter joint regression model for longitudinal zero-inflated count data
摘要
Abstract
Longitudinal zero-inflated count data are gathered from a series of measurements of experimental individuals at multiple time points and possess the very characteristics of longitudinal data,count data and zero-inflated data simultaneously.The number of zeros contained in count data far exceeds that randomly gen-erated by classical discrete distributions such as Poisson and negative binomial distributions.In the regression analysis of longitudinal zero-inflated count data,the data are generally assumed to consist of zero-inflated com-ponents and random sampling components,and the mean,zero-inflation rate and dispersion are three main characteristic parameters of the data.Nowadays,most regression models for zero-inflated data only consider the influence of covariates on the mean and zero-inflation rate and the dispersion is unfortunately igored or set to a fixed value.As a result,these models cannot be applied to the situations where dispersion at different ob-servation time points dynamically changes with time or other covariates.For the count data following the zero-inflated negative binomial distribution,a generalized regression model is develpoed to describe the relation-ship between all three data characteristics and the covariates.The maximum likelihood estimate of the regres-sion coefficients is obtained by using the EM(Expectation-Maximization)algorithm to simultaneously the three regression coefficients.Theoretical analysis shows that,in comparison with the two-parameter regres-sion model estimation,the proposed likelihood estimator is consistent and asymptotically normal,enabling ac-curate simultaneous estimation of the three regression coefficients.Finally,simulation results demonstrate that the proposed model is more accurate and effective than the regression models that do not consider time-varying dispersion.关键词
纵向零膨胀计数数据/联合建模/零膨胀负二项回归/EM算法Key words
longitudinal zero-inflated count data/joint modeling/zero-inflated negative binomial regression/EM algorithm分类
数理科学引用本文复制引用
余静,吕晨洁,陈晨,刘华仙..纵向零膨胀计数数据的多参数联合回归模型[J].四川大学学报（自然科学版）,2026,63(3):566-573,8.基金项目
重庆市教委科学技术研究项目(KJQN202301156) （KJQN202301156）
重庆理工大学研究生教育高质量发展项目(gzlcx20245278) （gzlcx20245278）
四川省科技计划重点研发项目(2025YFHZ0025) （2025YFHZ0025）
