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
In this paper, the frequency of an earthquake occurrence and magnitude relationship has been modeled with generalized linear models for the set of earthquake data of Nepal. A goodness of fit of a statistical model is ...In this paper, the frequency of an earthquake occurrence and magnitude relationship has been modeled with generalized linear models for the set of earthquake data of Nepal. A goodness of fit of a statistical model is applied for generalized linear models and considering the model selection information criterion, Akaike information criterion and Bayesian information criterion, generalized Poisson regression model has been selected as a suitable model for the study. The objective of this study is to determine the parameters (a and b values), estimate the probability of an earthquake occurrence and its return period using a Poisson regression model and compared with the Gutenberg-Richter model. The study suggests that the probabilities of earthquake occurrences and return periods estimated by both the models are relatively close to each other. The return periods from the generalized Poisson regression model are comparatively smaller than the Gutenberg-Richter model.展开更多
The purpose of this article is to investigate approaches for modeling individual patient count/rate data over time accounting for temporal correlation and non</span><span style="font-family:Verdana;"...The purpose of this article is to investigate approaches for modeling individual patient count/rate data over time accounting for temporal correlation and non</span><span style="font-family:Verdana;">-</span><span style="font-family:Verdana;">constant dispersions while requiring reasonable amounts of time to search over alternative models for those data. This research addresses formulations for two approaches for extending generalized estimating equations (GEE) modeling. These approaches use a likelihood-like function based on the multivariate normal density. The first approach augments standard GEE equations to include equations for estimation of dispersion parameters. The second approach is based on estimating equations determined by partial derivatives of the likelihood-like function with respect to all model parameters and so extends linear mixed modeling. Three correlation structures are considered including independent, exchangeable, and spatial autoregressive of order 1 correlations. The likelihood-like function is used to formulate a likelihood-like cross-validation (LCV) score for use in evaluating models. Example analyses are presented using these two modeling approaches applied to three data sets of counts/rates over time for individual cancer patients including pain flares per day, as needed pain medications taken per day, and around the clock pain medications taken per day per dose. Means and dispersions are modeled as possibly nonlinear functions of time using adaptive regression modeling methods to search through alternative models compared using LCV scores. The results of these analyses demonstrate that extended linear mixed modeling is preferable for modeling individual patient count/rate data over time</span><span style="font-family:Verdana;">,</span><span style="font-family:Verdana;"> because in example analyses</span><span style="font-family:Verdana;">,</span><span style="font-family:Verdana;"> it either generates better LCV scores or more parsimonious models and requires substantially less time.展开更多
Malaria is a major cause of morbidity and mortality in Apac district, Northern Uganda. Hence, the study aimed to model malaria incidences with respect to climate variables for the period 2007 to 2016 in Apac district....Malaria is a major cause of morbidity and mortality in Apac district, Northern Uganda. Hence, the study aimed to model malaria incidences with respect to climate variables for the period 2007 to 2016 in Apac district. Data on monthly malaria incidence in Apac district for the period January 2007 to December 2016 was obtained from the Ministry of health, Uganda whereas climate data was obtained from Uganda National Meteorological Authority. Generalized linear models, Poisson and negative binomial regression models were employed to analyze the data. These models were used to fit monthly malaria incidences as a function of monthly rainfall and average temperature. Negative binomial model provided a better fit as compared to the Poisson regression model as indicated by the residual plots and residual deviances. The Pearson correlation test indicated a strong positive association between rainfall and malaria incidences. High malaria incidences were observed in the months of August, September and November. This study showed a significant association between monthly malaria incidence and climate variables that is rainfall and temperature. This study provided useful information for predicting malaria incidence and developing the future warning system. This is an important tool for policy makers to put in place effective control measures for malaria early enough.展开更多
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In this paper, the frequency of an earthquake occurrence and magnitude relationship has been modeled with generalized linear models for the set of earthquake data of Nepal. A goodness of fit of a statistical model is applied for generalized linear models and considering the model selection information criterion, Akaike information criterion and Bayesian information criterion, generalized Poisson regression model has been selected as a suitable model for the study. The objective of this study is to determine the parameters (a and b values), estimate the probability of an earthquake occurrence and its return period using a Poisson regression model and compared with the Gutenberg-Richter model. The study suggests that the probabilities of earthquake occurrences and return periods estimated by both the models are relatively close to each other. The return periods from the generalized Poisson regression model are comparatively smaller than the Gutenberg-Richter model.
文摘The purpose of this article is to investigate approaches for modeling individual patient count/rate data over time accounting for temporal correlation and non</span><span style="font-family:Verdana;">-</span><span style="font-family:Verdana;">constant dispersions while requiring reasonable amounts of time to search over alternative models for those data. This research addresses formulations for two approaches for extending generalized estimating equations (GEE) modeling. These approaches use a likelihood-like function based on the multivariate normal density. The first approach augments standard GEE equations to include equations for estimation of dispersion parameters. The second approach is based on estimating equations determined by partial derivatives of the likelihood-like function with respect to all model parameters and so extends linear mixed modeling. Three correlation structures are considered including independent, exchangeable, and spatial autoregressive of order 1 correlations. The likelihood-like function is used to formulate a likelihood-like cross-validation (LCV) score for use in evaluating models. Example analyses are presented using these two modeling approaches applied to three data sets of counts/rates over time for individual cancer patients including pain flares per day, as needed pain medications taken per day, and around the clock pain medications taken per day per dose. Means and dispersions are modeled as possibly nonlinear functions of time using adaptive regression modeling methods to search through alternative models compared using LCV scores. The results of these analyses demonstrate that extended linear mixed modeling is preferable for modeling individual patient count/rate data over time</span><span style="font-family:Verdana;">,</span><span style="font-family:Verdana;"> because in example analyses</span><span style="font-family:Verdana;">,</span><span style="font-family:Verdana;"> it either generates better LCV scores or more parsimonious models and requires substantially less time.
文摘Malaria is a major cause of morbidity and mortality in Apac district, Northern Uganda. Hence, the study aimed to model malaria incidences with respect to climate variables for the period 2007 to 2016 in Apac district. Data on monthly malaria incidence in Apac district for the period January 2007 to December 2016 was obtained from the Ministry of health, Uganda whereas climate data was obtained from Uganda National Meteorological Authority. Generalized linear models, Poisson and negative binomial regression models were employed to analyze the data. These models were used to fit monthly malaria incidences as a function of monthly rainfall and average temperature. Negative binomial model provided a better fit as compared to the Poisson regression model as indicated by the residual plots and residual deviances. The Pearson correlation test indicated a strong positive association between rainfall and malaria incidences. High malaria incidences were observed in the months of August, September and November. This study showed a significant association between monthly malaria incidence and climate variables that is rainfall and temperature. This study provided useful information for predicting malaria incidence and developing the future warning system. This is an important tool for policy makers to put in place effective control measures for malaria early enough.
