Spatio-temporal modelling of tick life-stage count data with spatially varying coefficients

There is a vast amount of geo-referenced data in many fields of study including ecological studies. Geo-referencing is usually by point referencing; that is, latitudes and longitudes or by areal referencing, which includes districts, counties, states, provinces and other administrative units. The availability of large geo-referenced datasets for modelling has necessitated the development and application of spatial statistical methods. However, spatial varying coefficients models exploring the abundance of tick counts remain limited. In this study we used data that was collected and prepared by researchers in the Department of Biological Sciences from the Old Dominion University, Virginia, USA. We modelled tick life-stage counts and abundance variability from 12 sampling locations, with 5 different habitats (numbered 1-5), three habitat types; namely: woods, edges and grass; collected monthly from May 2009 through December 2018. Spatio-temporal Poisson and spatio-temporal negative binomial (NB) count data models were fitted to the data and compared using the deviance information criteria (DIC). The NB model outperformed the Poisson models with all its DIC values being smaller than those of the Poisson model. Results showed that the covariates varied spatially across counties. There was a decreasing time (in years) effect over the study period. However, even though the time effect was decreasing over the study period, space-time interaction effects were seen to be increasing over time in York County.

Download Full-text

Modeling the Frequency of Auto Insurance Claims by Means of Poisson and Negative Binomial Models

Annals of the Alexandru Ioan Cuza University - Economics ◽

10.1515/aicue-2015-0011 ◽

2015 ◽

Vol 62 (2) ◽

pp. 151-168 ◽

Cited By ~ 3

Author(s):

Mihaela David ◽

Dănuţ-Vasile Jemna

Keyword(s):

Risk Factors ◽

Count Data ◽

Negative Binomial ◽

Information Criteria ◽

Count Data Models ◽

Auto Insurance ◽

Insurance Portfolio ◽

Negative Binomial Models ◽

Degree Of Risk ◽

Binomial Models

Abstract Within non-life insurance pricing, an accurate evaluation of claim frequency, also known in theory as count data, represents an essential part in determining an insurance premium according to the policyholder’s degree of risk. Count regression analysis allows the identification of the risk factors and the prediction of the expected frequency of claims given the characteristics of policyholders. The aim of this paper is to verify several hypothesis related to the methodology of count data models and also to the risk factors used to explain the frequency of claims. In addition to the standard Poisson regression, Negative Binomial models are applied to a French auto insurance portfolio. The best model was chosen by means of the log-likelihood ratio and the information criteria. Based on this model, the profile of the policyholders with the highest degree of risk is determined

Download Full-text

Comparison of Different Count Models for Investigation of Some Environmental Factors Affecting Stillbirth in Holsteins

Indian Journal of Animal Research ◽

10.18805/ijar.bf-1415 ◽

2022 ◽

Author(s):

Y. Gevrekçi ◽

Ö.İ. Güneri ◽

Ç. Takma ◽

A. Yeşilova

Keyword(s):

Regression Model ◽

Count Data ◽

Negative Binomial ◽

Information Criteria ◽

Parameter Estimates ◽

Count Data Models ◽

Factors Affecting ◽

Independent Variables ◽

Gender Parity ◽

Hurdle Regression

Background: The objective of this study is comparing different count data models for stillbirth data. In modeling this type of data, Poisson regression or alternative models can be preferred. Methods: The poisson, negative binomial, zero-inflated poisson, zero-inflated negative binomial, poisson-logit hurdle and negative binomial-logit hurdle regressions were compared and used to examine the effects of the gender, parity and herd-year-season independent variables on stillbirth. Furthermore, the Log-Likelihood statistics, Akaike Information Criteria, Bayesian Information Criteria and rootogram graphs were used as comparison criteria for performance of the models. According to these criteria, Negative Binomial-Logit Hurdle Regression model was chosen as the best model. Result: The parameter estimates obtained by Negative Binomial-Logit Hurdle Regression model in relation to the effects of the gender, parity and herd-year-season independent variables on stillbirth were found to be significant (p less than 0.01). It was found that while stillbirth incidence was higher in males than females, it was found to decrease as the parity increased. As a result, the Negative Binomial Logit Hurdle model was found the best model for stillbirth count data with overdispersion.

Download Full-text

Comparing Bayesian Spatial Conditional Overdispersion and the Besag–York–Mollié Models: Application to Infant Mortality Rates

Mathematics ◽

10.3390/math9030282 ◽

2021 ◽

Vol 9 (3) ◽

pp. 282

Author(s):

Mabel Morales-Otero ◽

Vicente Núñez-Antón

Keyword(s):

Infant Mortality ◽

Count Data ◽

Spatial Dependence ◽

Poisson Model ◽

Mortality Rates ◽

Estimation Methods ◽

Neighborhood Structure ◽

Specific Context ◽

Count Data Models ◽

Conditional Mean

In this paper, we review overdispersed Bayesian generalized spatial conditional count data models. Their usefulness is illustrated with their application to infant mortality rates from Colombian regions and by comparing them with the widely used Besag–York–Mollié (BYM) models. These overdispersed models assume that excess of dispersion in the data may be partially caused from the possible spatial dependence existing among the different spatial units. Thus, specific regression structures are then proposed both for the conditional mean and for the dispersion parameter in the models, including covariates, as well as an assumed spatial neighborhood structure. We focus on the case of response variables following a Poisson distribution, specifically concentrating on the spatial generalized conditional normal overdispersion Poisson model. Models were fitted by making use of the Markov Chain Monte Carlo (MCMC) and Integrated Nested Laplace Approximation (INLA) algorithms in the specific context of Bayesian estimation methods.

Download Full-text

Beta-binomial models for meta-analysis with binary outcomes: Variations, extensions, and additional insights from econometrics

Research Methods in Medicine & Health Sciences ◽

10.1177/2632084321996225 ◽

2021 ◽

pp. 263208432199622

Author(s):

Tim Mathes ◽

Oliver Kuss

Keyword(s):

Simulation Study ◽

Count Data ◽

Negative Binomial ◽

Meta Analysis ◽

Negative Binomial Regression ◽

Binary Outcomes ◽

Small Scale ◽

Panel Count Data ◽

Count Data Models ◽

Meta Analyses

Background Meta-analysis of systematically reviewed studies on interventions is the cornerstone of evidence based medicine. In the following, we will introduce the common-beta beta-binomial (BB) model for meta-analysis with binary outcomes and elucidate its equivalence to panel count data models. Methods We present a variation of the standard “common-rho” BB (BBST model) for meta-analysis, namely a “common-beta” BB model. This model has an interesting connection to fixed-effect negative binomial regression models (FE-NegBin) for panel count data. Using this equivalence, it is possible to estimate an extension of the FE-NegBin with an additional multiplicative overdispersion term (RE-NegBin), while preserving a closed form likelihood. An advantage due to the connection to econometric models is, that the models can be easily implemented because “standard” statistical software for panel count data can be used. We illustrate the methods with two real-world example datasets. Furthermore, we show the results of a small-scale simulation study that compares the new models to the BBST. The input parameters of the simulation were informed by actually performed meta-analysis. Results In both example data sets, the NegBin, in particular the RE-NegBin showed a smaller effect and had narrower 95%-confidence intervals. In our simulation study, median bias was negligible for all methods, but the upper quartile for median bias suggested that BBST is most affected by positive bias. Regarding coverage probability, BBST and the RE-NegBin model outperformed the FE-NegBin model. Conclusion For meta-analyses with binary outcomes, the considered common-beta BB models may be valuable extensions to the family of BB models.

Download Full-text

Comparing of Car-Bym, Generalized Poisson dan Negative Binomial on Tuberculosis Data in Banyumas Districs

Indonesian Journal of Statistics and Its Applications ◽

10.29244/ijsa.v5i1p130-140 ◽

2021 ◽

Vol 5 (1) ◽

pp. 130-140

Author(s):

Jajang Jajang ◽

Budi Pratikno ◽

Mashuri Mashuri

Keyword(s):

Parameter Estimation ◽

Maximum Likelihood ◽

Count Data ◽

Degrees Of Freedom ◽

Negative Binomial ◽

Likelihood Estimation ◽

Poisson Model ◽

Generalized Poisson ◽

Central Java ◽

Area Data

In 2019 the number of people with TB (Tuberculosis) in Banyumas, Central Java, is high (1,910 people have been detected with TB). The number of people infected Tuberculosis (TB) in Banyumas is the count data and it is also the area data. In modeling, the parameter estimation and characteristic of the data need to be considered. Here, we studied comparing Generalized Poisson (GP), negative binomial (NB), and Poisson and CAR.BYM model for TB cases in Banyumas. Here, we use two methods for parameter estimation, maximum likelihood estimation (MLE) and Bayes. The MLE is used for GP and NB models, whereas Bayes is used for Poisson and CAR-BYM. The results showed that Poisson model detected overdispersion where deviance value is 67.38 for 22 degrees of freedom. Therefore, ratio of deviance to degrees of freedom is 3.06 (>1). This indicates that there was overdispersion. The folowing GP, NB, Poisson-Bayes and CAR-BYM are used to modeling TB data in Banyumas and we compare their RMSE. With refer to RMES criteria, we found that CAR-BYM is the best model for modeling TB in Banyumas because its RMSE is smallest.

Download Full-text

Distributions You Can Count On …But What’s the Point?

Econometrics ◽

10.3390/econometrics8010009 ◽

2020 ◽

Vol 8 (1) ◽

pp. 9 ◽

Cited By ~ 1

Author(s):

Brendan P. M. McCabe ◽

Christopher L. Skeels

Keyword(s):

Count Data ◽

Negative Binomial ◽

Broad Class ◽

Poisson Model ◽

Econometric Analysis ◽

Discrete Distributions ◽

Optimal Test ◽

Score Tests ◽

Optimal Tests ◽

Over Dispersion

The Poisson regression model remains an important tool in the econometric analysis of count data. In a pioneering contribution to the econometric analysis of such models, Lung-Fei Lee presented a specification test for a Poisson model against a broad class of discrete distributions sometimes called the Katz family. Two members of this alternative class are the binomial and negative binomial distributions, which are commonly used with count data to allow for under- and over-dispersion, respectively. In this paper we explore the structure of other distributions within the class and their suitability as alternatives to the Poisson model. Potential difficulties with the Katz likelihood leads us to investigate a class of point optimal tests of the Poisson assumption against the alternative of over-dispersion in both the regression and intercept only cases. In a simulation study, we compare score tests of ‘Poisson-ness’ with various point optimal tests, based on the Katz family, and conclude that it is possible to choose a point optimal test which is better in the intercept only case, although the nuisance parameters arising in the regression case are problematic. One possible cause is poor choice of the point at which to optimize. Consequently, we explore the use of Hellinger distance to aid this choice. Ultimately we conclude that score tests remain the most practical approach to testing for over-dispersion in this context.

Download Full-text

Using Count Data Models to Predict Epiphytic Bryophyte Recruitment in Schima superba Gardn. et Champ. Plantations in Urban Forests

Forests ◽

10.3390/f11020174 ◽

2020 ◽

Vol 11 (2) ◽

pp. 174

Author(s):

Dexian Zhao ◽

Zhenkai Sun ◽

Cheng Wang ◽

Zezhou Hao ◽

Baoqiang Sun ◽

...

Keyword(s):

Count Data ◽

Human Disturbance ◽

Negative Binomial ◽

Urban Environments ◽

Tree Planting ◽

Count Data Models ◽

Urban Tree ◽

Schima Superba ◽

Hurdle Models ◽

Positive Effects

Epiphytic bryophytes are known to perform essential ecosystem functions, but their sensitivity to environmental quality and change makes their survival and development vulnerable to global changes, especially habitat loss in urban environments. Fortunately, extensive urban tree planting programs worldwide have had a positive effect on the colonization and development of epiphytic bryophytes. However, how epiphytic bryophytes occur and grow on planted trees remain poorly known, especially in urban environments. In the present study, we surveyed the distribution of epiphytic bryophytes on tree trunks in a Schima superba Gardn. et Champ. urban plantation and then developed count data models, including tree characteristics, stand characteristics, human disturbance, terrain factors, and microclimate to predict the drivers on epiphytic bryophyte recruitment. Different counting models (Poisson, Negative binomial, Zero-inflated Poisson, Zero-inflated negative binomial, Hurdle-Poisson, Hurdle-negative binomial) were compared for a data analysis to account for the zero-inflated data structure. Our results show that (i) the shaded side and base of tree trunks were the preferred locations for bryophytes to colonize in urban plantations, (ii) both hurdle models performed well in modeling epiphytic bryophyte recruitment, and (iii) both hurdle models showed that the tree height, diameter at breast height (DBH), leaf area index (LAI), and altitude (ALT) promoted the occurrence of epiphytic bryophytes, but the height under branch and interference intensity of human activities opposed the occurrence of epiphytic bryophytes. Specifically, DBH and LAI had positive effects on the species richness recruitment count; similarly, DBH and ALT had positive effects on the abundance recruitment count, but slope had a negative effect. To promote the occurrence and growth of epiphytic bryophytes in urban tree planting programs, we suggest that managers regulate suitable habitats by cultivating and protecting large trees, promoting canopy closure, and controlling human disturbance.

Download Full-text

Using Poisson Class Regression To Analyze Count Data in Correctional and Forensic Psychology

Criminal Justice and Behavior ◽

10.1177/0093854807307030 ◽

2007 ◽

Vol 34 (12) ◽

pp. 1659-1674 ◽

Cited By ~ 40

Author(s):

Glenn D. Walters

Keyword(s):

Count Data ◽

Negative Binomial ◽

Forensic Psychology ◽

Poisson Model ◽

Negative Binomial Regression ◽

Ordinary Least Squares ◽

Statistical Procedure ◽

Least Squares Regression ◽

Binomial Regression ◽

Censored Models

The benchmark model for count data is the Poisson distribution, and the standard statistical procedure for analyzing count data is Poisson regression. However, highly restrictive assumptions lead to frequent misspecification of the Poisson model. Alternate approaches, such as negative binomial regression, zero modified procedures, and truncated and censored models are consequently required to handle count data in many social science contexts. Empirical examples from correctional and forensic psychology are provided to illustrate the importance of replacing ordinary least squares regression with Poisson class procedures in situations when count data are analyzed.

Download Full-text

Approaches for dealing with various sources of overdispersion in modeling count data: Scale adjustment versus modeling

Statistical Methods in Medical Research ◽

10.1177/0962280215588569 ◽

2015 ◽

Vol 26 (4) ◽

pp. 1802-1823 ◽

Cited By ~ 13

Author(s):

Elizabeth H Payne ◽

James W Hardin ◽

Leonard E Egede ◽

Viswanathan Ramakrishnan ◽

Anbesaw Selassie ◽

...

Keyword(s):

Error Estimates ◽

Standard Error ◽

Count Data ◽

Poisson Regression ◽

Negative Binomial ◽

Rank Order ◽

Good Practice ◽

Information Criteria ◽

Population Heterogeneity ◽

Count Response

Overdispersion is a common problem in count data. It can occur due to extra population-heterogeneity, omission of key predictors, and outliers. Unless properly handled, this can lead to invalid inference. Our goal is to assess the differential performance of methods for dealing with overdispersion from several sources. We considered six different approaches: unadjusted Poisson regression (Poisson), deviance-scale-adjusted Poisson regression (DS-Poisson), Pearson-scale-adjusted Poisson regression (PS-Poisson), negative-binomial regression (NB), and two generalized linear mixed models (GLMM) with random intercept, log-link and Poisson (Poisson-GLMM) and negative-binomial (NB-GLMM) distributions. To rank order the preference of the models, we used Akaike's information criteria/Bayesian information criteria values, standard error, and 95% confidence-interval coverage of the parameter values. To compare these methods, we used simulated count data with overdispersion of different magnitude from three different sources. Mean of the count response was associated with three predictors. Data from two real-case studies are also analyzed. The simulation results showed that NB and NB-GLMM were preferred for dealing with overdispersion resulting from any of the sources we considered. Poisson and DS-Poisson often produced smaller standard-error estimates than expected, while PS-Poisson conversely produced larger standard-error estimates. Thus, it is good practice to compare several model options to determine the best method of modeling count data.

Download Full-text

Robustness of Poisson Mixture models in identifying risk factors for Under-Five mortality in Nigeria

Annals of Health Research ◽

10.30442/ahr.0402-6-17 ◽

2018 ◽

Vol 4 (2) ◽

pp. 141-154

Author(s):

Kolawole S. Oritogun ◽

Elijah A. Bamgboye

Keyword(s):

Risk Factors ◽

Birth Order ◽

Mixture Models ◽

Maternal Education ◽

Negative Binomial ◽

National Level ◽

Poisson Model ◽

Information Criteria ◽

Poisson Mixture ◽

Under Five

Background: Estimates of Under-Five mortality (U5M) have taken advantage of indirect methods but U5M risk factors have been identified using fixed statistical models with little considerations for the potentials of mixture models. Mixture models such as Poisson-Mixture models exhibit flexibility tendency, which is an attribute of robustness lacking in fixed models. Objective: To examine the robustness of Poisson-Mixture models in identifying reliable determinants of U5M. Methods: The data on 18,855 women used in this study were obtained from the 2008 Nigeria Demographic and Health Survey (NDHS). Six different Poisson-Mixture models namely: Poisson (PO), Zero-Inflated Poisson (ZIP), Poisson Hurdle (PH), Negative Binomial (NBI), Zero-Inflated Negative Binomial (ZINBI) and Negative Binomial Hurdle (NBIH) were fitted separately to the data. The Akaike Information Criteria (AIC) and diagnostic check for normality were used to select robust models. All tests were conducted at p = 0.05. Results: The models and AIC values for U5M were: 38763.47 (PO), 38654.55 (ZIP), 44270.77 (PH), 38526.26 (NBI), 38513.71 (ZINBI) and 44269.30 (NBIH). The PO, ZIP, PH and NBIH met normality test criteria, and the ZIP model was of best fit. The model identified breastfeeding, paternal education, toilet type, maternal education, place of delivery, birth-order and antenatal-visits as significant determinants of U5M at the national level. Conclusion: The Zero-Inflated Poisson model provided the best robust estimates of Under-five Mortality in Nigeria, while maternal education and birth-order were identified as the most important determinants. The Poisson-mixture models are recommended for modelling Under-five Mortality in Nigeria.

Download Full-text