基于EM算法的多水平零膨胀负二项混合效应回归模型的参数估计
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摘要
计数数据广泛应用于医疗、生物和保险等诸多领域.泊松回归模型与负二项回归模型是分析这类离散型数据的重要模型.在实际计数中往往会出现相对于泊松分布或负二项分布过多的零,称之为零膨胀现象.分析此类数据的常见方法是零膨胀泊松(ZIP)回归模型和零膨胀负二项(ZINB)回归模型.但是,如果非零观测值过度分散并且具有相关性,则参数估计可能会出现严重偏差,导致传统的ZINB模型不能对其进行很好的拟合.提出了一种具有随机效应的多水平零膨胀负二项混合效应回归模型,并利用极大似然估计的EM算法对多水平零膨胀负二项混合效应回归模型进行参数估计.
Counting data are widely used in medicine,biology,insurance and many other fields.Poisson regression model and negative binomial regression model are important models for analyzing such discrete data.In actual counting,there are often too many zeros relative to Poisson distribution or negative binomial distribution,which are called zero inflation phenomenon.The common methods for analyzing such data are zero inflation Poisson(ZIP)regression model and zero inflation negative binomial(ZINB)regression model.However,if the non-zero observations are over-dispersed and correlated,the parameter estimation may be seriously biased,which results in the incompatibility of traditional ZINB model.A multi-level zero inflation negative binomial mixed regression model with random effects is proposed,and EM algorithm with maximum likelihood estimation is used to estimate the parameters of the multi-level zero inflation negative binomial mixed regression model.
Counting data are widely used in medicine,biology,insurance and many other fields.Poisson regression model and negative binomial regression model are important models for analyzing such discrete data.In actual counting,there are often too many zeros relative to Poisson distribution or negative binomial distribution,which are called zero inflation phenomenon.The common methods for analyzing such data are zero inflation Poisson(ZIP)regression model and zero inflation negative binomial(ZINB)regression model.However,if the non-zero observations are over-dispersed and correlated,the parameter estimation may be seriously biased,which results in the incompatibility of traditional ZINB model.A multi-level zero inflation negative binomial mixed regression model with random effects is proposed,and EM algorithm with maximum likelihood estimation is used to estimate the parameters of the multi-level zero inflation negative binomial mixed regression model.
引文
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[12]Wang K,Yau K K W,Lee A H.A zero-inflated Poisson mixed model to analyze diagnosis related groups with majority of same-day hospital stays[J].Computer Methods and Programs in Biomedicine,2002(68):195-203
[2]Greene W.Accounting for excess zeros and sample selection in Poisson and Negative Binomial Regression models[J].Working Paper,1994:EC-94-10
[3]HallDB.Zero-inflatedPoissonandbinomialregressionwithrandomeffects:acasestudy[J].Biometrics,2000(56):1030-1039
[4]Yau K K W,Lee A H.Zero-inflated Poisson regression with random effects to evaluate an occupational injury prevention program[J].Statistics in Medicine,2001(20):2907-2920
[5]Ridout M,Hinde J,DemtrioC G B.A score test for testing zero inflated Poisson regression model against zero inflated negative binomial alternatives[J].Biometrics,2001(57):219-223
[6]Yau K K W.Multilevel models for survival analysis with random effects[J].Biometrics,2001(57):96-102
[7]Xiang L,Lee A H,Yau K K W,et al.A score test for zero-inflation in correlated count data[J].Statistics in Medicine,2006(25):1660-1671
[8]Moghimbeigi A,Eshaghian M R,Mohammad K,et al.A score test for zero inflation in multilevel count data[J].Computational Statistics and Data Analysis,2008(53):1239-1248
[9]解锋昌,韦博成,林金官.ZI数据的统计分析综述[M].应用统计概率,2009,25(6):659-667
[10]Robinson G K.The BLUP is a good thing:the estimation of random effects[J].Statistical Science,1991(6):15-32
[11]McLachlan G J.On the EM algorithm for overdispersed count data[J].Statistical Methods in Medical Research,1997(6):76-98
[12]Wang K,Yau K K W,Lee A H.A zero-inflated Poisson mixed model to analyze diagnosis related groups with majority of same-day hospital stays[J].Computer Methods and Programs in Biomedicine,2002(68):195-203