Objective Sub-health status has progressively gained more attention from both medical professionals and the publics. Treating the number of sub-health symptoms as count data rather than dichotomous data helps to compl...Objective Sub-health status has progressively gained more attention from both medical professionals and the publics. Treating the number of sub-health symptoms as count data rather than dichotomous data helps to completely and accurately analyze findings in sub-healthy population. This study aims to compare the goodness of fit for count outcome models to identify the optimum model for sub-health study.Methods The sample of the study derived from a large-scale population survey on physiological and psychological constants from 2007 to 2011 in 4 provinces and 2 autonomous regions in China. We constructed four count outcome models using SAS: Poisson model, negative binomial (NB) model, zero-inflated Poisson (ZIP) model and zero-inflated negative binomial (ZINB) model. The number of sub-health symptoms was used as the main outcome measure. The alpha dispersion parameter and O test were used to identify over-dispersed data, and Vuong test was used to evaluate the excessive zero count. The goodness of fit of regression models were determined by predictive probability curves and statistics of likelihood ratio test.Results Of all 78 307 respondents, 38.53% reported no sub-health symptoms. The mean number of sub-health symptoms was 2.98, and the standard deviation was 3.72. The statistic O in over-dispersion test was 720.995 (P<0.001); the estimated alpha was 0.618 (95% CI: 0.600-0.636) comparing ZINB model and ZIP model; Vuong test statistic Z was 45.487. These results indicated over-dispersion of the data and excessive zero counts in this sub-health study. ZINB model had the largest log likelihood (-167 519), the smallest Akaike’s Information Criterion coefficient (335 112) and the smallest Bayesian information criterion coefficient (335455),indicating its best goodness of fit. The predictive probabilities for most counts in ZINB model fitted the observed counts best. The logit section of ZINB model analysis showed that age, sex, occupation, smoking, alcohol drinking, ethnicity and obesity were determinants for presence of sub-health symptoms; the binomial negative section of ZINB model analysis showed that sex, occupation, smoking, alcohol drinking, ethnicity, marital status and obesity had significant effect on the severity of sub-health.Conclusions All tests for goodness of fit and the predictive probability curve produced the same finding that ZINB model was the optimum model for exploring the influencing factors of sub-health symptoms.展开更多
This paper discusses the estimation of parameters in the zero-inflated Poisson (ZIP) model by the method of moments. The method of moments estimators (MMEs) are analytically compared with the maximum likelihood estima...This paper discusses the estimation of parameters in the zero-inflated Poisson (ZIP) model by the method of moments. The method of moments estimators (MMEs) are analytically compared with the maximum likelihood estimators (MLEs). The results of a modest simulation study are presented.展开更多
Zero-Inflated Poisson model has found a wide variety of applications in recent years in statistical analyses of count data, especially in count regression models. Zero-Inflated Poisson model is characterized in this p...Zero-Inflated Poisson model has found a wide variety of applications in recent years in statistical analyses of count data, especially in count regression models. Zero-Inflated Poisson model is characterized in this paper through a linear differential equation satisfied by its probability generating function [1] [2].展开更多
The present paper proposes a new robust estimator for Poisson regression models. We used the weighted maximum likelihood estimators which are regarded as Mallows-type estimators. We perform a Monte Carlo simulation st...The present paper proposes a new robust estimator for Poisson regression models. We used the weighted maximum likelihood estimators which are regarded as Mallows-type estimators. We perform a Monte Carlo simulation study to assess the performance of a suggested estimator compared to the maximum likelihood estimator and some robust methods. The result shows that, in general, all robust methods in this paper perform better than the classical maximum likelihood estimators when the model contains outliers. The proposed estimators showed the best performance compared to other robust estimators.展开更多
Often the lifecycle data occur as count of the vital events and are recorded as integers.The purpose of this article is to model the fertility behavior based on religious,educational,economic,and occupational characte...Often the lifecycle data occur as count of the vital events and are recorded as integers.The purpose of this article is to model the fertility behavior based on religious,educational,economic,and occupational characteristics.The responses of classified groups according to these determinants are examined for significant influence on fertility using Poisson regression model(PRM) based on the National Family Health Survey-3 dataset.The observed and predicted probabilities under PRM indicate modal value of two children for the Poisson distribution modeled data.Presence of dominance of two child in the data motivates the authors to adopt multinomial regression model(MRM) in order to link fertility with various socioeconomic indicators responsible for fertility variation.Choice of the explanatory factors is limited to the availability of data.Trends and patterns of preference for birth counts suggest that religion,caste,wealth,female education,and occupation are the dominant factors shaping the observed birth process.Empirical analysis suggests that both the models used in the study perform similarly on the sample data.However,fitting of MRM by taking birth count of two as comparison category shows improved Akaike information criterion and consistent Akaike information criterion values.Current work contributes to the existing literature as it attempts to provide more insight into the determinants of Indian fertility using Poisson and MRM.展开更多
Many researchers have discussed zero-inflated univariate distributions. These univariate models are not suitable, for modeling events that involve different types of counts or defects. To model several types of defect...Many researchers have discussed zero-inflated univariate distributions. These univariate models are not suitable, for modeling events that involve different types of counts or defects. To model several types of defects, multivariate Poisson model is one of the appropriate model. This can further be modified to incorporate inflation at zero and we can have multivariate zero-inflated Poisson distribution. In the present article, we introduce a new Bivariate Zero Inflated Power Series Distribution and discuss inference related to the parameters involved in the model. We also discuss the inference related to Bivariate Zero Inflated Poisson Distribution. The model has been applied to a real life data. Extension to k-variate zero inflated power series distribution is also discussed.展开更多
Count data with excess zeros encountered in many applications often exhibit extra variation. There- fore, zero-inflated Poisson （ZIP） model may fail to fit such data. In this paper, a zero-inflated double Poisson mo...Count data with excess zeros encountered in many applications often exhibit extra variation. There- fore, zero-inflated Poisson （ZIP） model may fail to fit such data. In this paper, a zero-inflated double Poisson model （ZIDP）, which is generalization of the ZIP model, is studied and the score tests for the significance of dis- persion and zero-inflation in ZIDP model are developed. Meanwhile, this work also develops homogeneous tests for dispersion and/or zero-inflation parameter, and corresponding score test statistics are obtained. One numer- ical example is given to illustrate our methodology and the properties of score test statistics are investigated through Monte Carlo simulations.展开更多
目的介绍应用修正poisson回归模型计算常见结局事件的前瞻性研究中暴露因素的调整相对危险度的精确区间估计值。方法应用稳健误差方差估计法(sandwich variance esti mator)来校正相对危险度(RR)的估计方差,并通过SAS程序中GENMOD过程的...目的介绍应用修正poisson回归模型计算常见结局事件的前瞻性研究中暴露因素的调整相对危险度的精确区间估计值。方法应用稳健误差方差估计法(sandwich variance esti mator)来校正相对危险度(RR)的估计方差,并通过SAS程序中GENMOD过程的REPEATED语句实现修正poisson回归。此外,采用不同的统计方法对5个虚拟的研究数据进行了分析比较。结果以分层的Mantel-Haenszel法为标准参照,修正poisson回归对aRR点和区间估计均较为理想,普通poisson回归的aRR区间估计偏于保守。而logistic回归得到的aOR值明显偏离真实的RR值。结论修正poisson回归模型适合于处理常见结局事件的前瞻性研究资料。展开更多
基金supported by the Basic Performance Key Project,the Ministry of Science and Technology of the People’s Republic of China(No.2006FY110300)
文摘Objective Sub-health status has progressively gained more attention from both medical professionals and the publics. Treating the number of sub-health symptoms as count data rather than dichotomous data helps to completely and accurately analyze findings in sub-healthy population. This study aims to compare the goodness of fit for count outcome models to identify the optimum model for sub-health study.Methods The sample of the study derived from a large-scale population survey on physiological and psychological constants from 2007 to 2011 in 4 provinces and 2 autonomous regions in China. We constructed four count outcome models using SAS: Poisson model, negative binomial (NB) model, zero-inflated Poisson (ZIP) model and zero-inflated negative binomial (ZINB) model. The number of sub-health symptoms was used as the main outcome measure. The alpha dispersion parameter and O test were used to identify over-dispersed data, and Vuong test was used to evaluate the excessive zero count. The goodness of fit of regression models were determined by predictive probability curves and statistics of likelihood ratio test.Results Of all 78 307 respondents, 38.53% reported no sub-health symptoms. The mean number of sub-health symptoms was 2.98, and the standard deviation was 3.72. The statistic O in over-dispersion test was 720.995 (P<0.001); the estimated alpha was 0.618 (95% CI: 0.600-0.636) comparing ZINB model and ZIP model; Vuong test statistic Z was 45.487. These results indicated over-dispersion of the data and excessive zero counts in this sub-health study. ZINB model had the largest log likelihood (-167 519), the smallest Akaike’s Information Criterion coefficient (335 112) and the smallest Bayesian information criterion coefficient (335455),indicating its best goodness of fit. The predictive probabilities for most counts in ZINB model fitted the observed counts best. The logit section of ZINB model analysis showed that age, sex, occupation, smoking, alcohol drinking, ethnicity and obesity were determinants for presence of sub-health symptoms; the binomial negative section of ZINB model analysis showed that sex, occupation, smoking, alcohol drinking, ethnicity, marital status and obesity had significant effect on the severity of sub-health.Conclusions All tests for goodness of fit and the predictive probability curve produced the same finding that ZINB model was the optimum model for exploring the influencing factors of sub-health symptoms.
文摘This paper discusses the estimation of parameters in the zero-inflated Poisson (ZIP) model by the method of moments. The method of moments estimators (MMEs) are analytically compared with the maximum likelihood estimators (MLEs). The results of a modest simulation study are presented.
文摘Zero-Inflated Poisson model has found a wide variety of applications in recent years in statistical analyses of count data, especially in count regression models. Zero-Inflated Poisson model is characterized in this paper through a linear differential equation satisfied by its probability generating function [1] [2].
文摘The present paper proposes a new robust estimator for Poisson regression models. We used the weighted maximum likelihood estimators which are regarded as Mallows-type estimators. We perform a Monte Carlo simulation study to assess the performance of a suggested estimator compared to the maximum likelihood estimator and some robust methods. The result shows that, in general, all robust methods in this paper perform better than the classical maximum likelihood estimators when the model contains outliers. The proposed estimators showed the best performance compared to other robust estimators.
基金supported by R&D Grant from University of DelhiDU-DST PURSE GrantICMR Grant No.3/1/3/JRF-2010/HRD-122(35831)
文摘Often the lifecycle data occur as count of the vital events and are recorded as integers.The purpose of this article is to model the fertility behavior based on religious,educational,economic,and occupational characteristics.The responses of classified groups according to these determinants are examined for significant influence on fertility using Poisson regression model(PRM) based on the National Family Health Survey-3 dataset.The observed and predicted probabilities under PRM indicate modal value of two children for the Poisson distribution modeled data.Presence of dominance of two child in the data motivates the authors to adopt multinomial regression model(MRM) in order to link fertility with various socioeconomic indicators responsible for fertility variation.Choice of the explanatory factors is limited to the availability of data.Trends and patterns of preference for birth counts suggest that religion,caste,wealth,female education,and occupation are the dominant factors shaping the observed birth process.Empirical analysis suggests that both the models used in the study perform similarly on the sample data.However,fitting of MRM by taking birth count of two as comparison category shows improved Akaike information criterion and consistent Akaike information criterion values.Current work contributes to the existing literature as it attempts to provide more insight into the determinants of Indian fertility using Poisson and MRM.
文摘Many researchers have discussed zero-inflated univariate distributions. These univariate models are not suitable, for modeling events that involve different types of counts or defects. To model several types of defects, multivariate Poisson model is one of the appropriate model. This can further be modified to incorporate inflation at zero and we can have multivariate zero-inflated Poisson distribution. In the present article, we introduce a new Bivariate Zero Inflated Power Series Distribution and discuss inference related to the parameters involved in the model. We also discuss the inference related to Bivariate Zero Inflated Poisson Distribution. The model has been applied to a real life data. Extension to k-variate zero inflated power series distribution is also discussed.
基金Supported in part by the National Natural Science Foundation of China under Grant No.11271193 and 11571073the Natural Science Foundation of Jiangsu Province under Grant No.BK20141326
文摘Count data with excess zeros encountered in many applications often exhibit extra variation. There- fore, zero-inflated Poisson （ZIP） model may fail to fit such data. In this paper, a zero-inflated double Poisson model （ZIDP）, which is generalization of the ZIP model, is studied and the score tests for the significance of dis- persion and zero-inflation in ZIDP model are developed. Meanwhile, this work also develops homogeneous tests for dispersion and/or zero-inflation parameter, and corresponding score test statistics are obtained. One numer- ical example is given to illustrate our methodology and the properties of score test statistics are investigated through Monte Carlo simulations.
文摘目的介绍应用修正poisson回归模型计算常见结局事件的前瞻性研究中暴露因素的调整相对危险度的精确区间估计值。方法应用稳健误差方差估计法(sandwich variance esti mator)来校正相对危险度(RR)的估计方差,并通过SAS程序中GENMOD过程的REPEATED语句实现修正poisson回归。此外,采用不同的统计方法对5个虚拟的研究数据进行了分析比较。结果以分层的Mantel-Haenszel法为标准参照,修正poisson回归对aRR点和区间估计均较为理想,普通poisson回归的aRR区间估计偏于保守。而logistic回归得到的aOR值明显偏离真实的RR值。结论修正poisson回归模型适合于处理常见结局事件的前瞻性研究资料。
