scholarly journals On Predictive Distribution of K-Inflated Poisson Models with and Without Additional Information

2020 ◽  
Vol 43 (2) ◽  
pp. 173-182
Author(s):  
Abdolnasser Sadeghkhani ◽  
S. Ejaz Ahmed
Keyword(s):  
Count Data ◽  
Poisson Model ◽  
Random Variable ◽  
Simulation Method ◽  
Predictive Distribution ◽  
Bayesian Estimator ◽  
Additional Information ◽  
Poisson Models ◽  
Model Independent

This   paper   addresses  different   approaches  in  finding   the   Bayesian predictive distribution of a random  variable from a Poisson  model that  can handle  count data  with an inflated  value  of K ∈ N, known as the KIP  model. We explore  how we can  use  other  source  of additional information to  find such  an estimator. More specifically, we find a Bayesian estimator of future density of random  variable Y1 , based  on observable X1  from the K1 IP(p1 , λ1 ) model, with and without assuming that  there exists  another random  variable X2 , from the K2 IP(p2 , λ2 ) model, independent of X1 , provided λ1  ≥ λ2 , and compare their  performance using  simulation method.

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

Mathematics ◽  
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.

scholarly journals Flexible models for overdispersed and underdispersed count data

2021 ◽  
Author(s):  
Dexter Cahoy ◽  
Elvira Di Nardo ◽  
Federico Polito
Keyword(s):  
Poisson Distribution ◽  
Count Data ◽  
Hypergeometric Functions ◽  
Natural Generalization ◽  
Model Parameters ◽  
Probability Models ◽  
Limiting Behavior ◽  
Poisson Models ◽  
Special Cases ◽  
Flexible Models

AbstractWithin the framework of probability models for overdispersed count data, we propose the generalized fractional Poisson distribution (gfPd), which is a natural generalization of the fractional Poisson distribution (fPd), and the standard Poisson distribution. We derive some properties of gfPd and more specifically we study moments, limiting behavior and other features of fPd. The skewness suggests that fPd can be left-skewed, right-skewed or symmetric; this makes the model flexible and appealing in practice. We apply the model to real big count data and estimate the model parameters using maximum likelihood. Then, we turn to the very general class of weighted Poisson distributions (WPD’s) to allow both overdispersion and underdispersion. Similarly to Kemp’s generalized hypergeometric probability distribution, which is based on hypergeometric functions, we analyze a class of WPD’s related to a generalization of Mittag–Leffler functions. The proposed class of distributions includes the well-known COM-Poisson and the hyper-Poisson models. We characterize conditions on the parameters allowing for overdispersion and underdispersion, and analyze two special cases of interest which have not yet appeared in the literature.

scholarly journals An Application Comparison of Two Poisson Models on Zero Count Data

2021 ◽  
Vol 1818 (1) ◽  
pp. 012165
Author(s):  
L. H. Hashim ◽  
K. H. Hashim ◽  
Mushtak A. K. Shiker
Keyword(s):  
Count Data ◽  
Poisson Models

PARAMETER ESTIMATION ON HURDLE POISSON REGRESSION MODEL WITH CENSORED DATA

2012 ◽  
Vol 57 (1) ◽  
Author(s):  
SEYED EHSAN SAFFAR ◽  
ROBIAH ADNAN ◽  
WILLIAM GREENE
Keyword(s):  
Regression Model ◽  
Count Data ◽  
Poisson Regression ◽  
Goodness Of Fit ◽  
Poisson Model ◽  
Likelihood Method ◽  
Poisson Regression Model ◽  
Response Variable ◽  
The Mean ◽  
Over Dispersion

A Poisson model typically is assumed for count data. In many cases, there are many zeros in the dependent variable and because of these many zeros, the mean and the variance values of the dependent variable are not the same as before. In fact, the variance value of the dependent variable will be much more than the mean value of the dependent variable and this is called over–dispersion. Therefore, Poisson model is not suitable anymore for this kind of data because of too many zeros. Thus, it is suggested to use a hurdle Poisson regression model to overcome over–dispersion problem. Furthermore, the response variable in such cases is censored for some values. In this paper, a censored hurdle Poisson regression model is introduced on count data with many zeros. In this model, we consider a response variable and one or more than one explanatory variables. The estimation of regression parameters using the maximum likelihood method is discussed and the goodness–of–fit for the regression model is examined. We study the effects of right censoring on estimated parameters and their standard errors via an example.

scholarly journals Geostatistical prediction of clay percentage based on soil survey data

2002 ◽  
Vol 11 (4) ◽  
pp. 381-390
Author(s):  
A. TALKKARI ◽  
L. JAUHIAINEN ◽  
M. YLI-HALLA
Keyword(s):  
Soil Properties ◽  
Spatial Variation ◽  
Survey Data ◽  
Clay Content ◽  
Spherical Model ◽  
Simulation Method ◽  
Soil Survey ◽  
Management Zones ◽  
Additional Information ◽  
Clay Percentage

In precision farming fields may be divided into management zones according to the spatial variation in soil properties. Clay content is an important soil characteristic, because it is associated with other soil properties that are important in management. Soil survey data from 150 sampling sites taken from an area of 218 ha were used to predict the spatial variation of clay percentage geostatistically in an agricultural soil in Jokioinen, Finland. The exponential and spherical models with a nugget component were fitted to the experimental variogram. This indicated that the medium-range pattern could be modelled, but the short-range variation could not, due to sparsity of sample points at short distances. The effect of sampling density on the kriging error was evaluated using the random simulation method. Kriging with a spherical model produced a map with smooth variation in clay percentage. The standard error of kriging estimates decreased only slightly when the density of samples was increased. The predictions were divided into three classes based on the clay percentage. Areas with clay content below 30%, between 30% and 60% and over 60% belong to non-clay, clay and heavy clay zones, respectively. With additional information from the soil samples on the contents of nutrients and organic matter these areas can serve as agricultural management zones.;

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

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.

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

Econometrics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 9 ◽  
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.

Missing value imputation for physical activity data measured by accelerometer

2016 ◽  
Vol 27 (2) ◽  
pp. 490-506 ◽  
Author(s):  
Jung Ae Lee ◽  
Jeff Gill
Keyword(s):  
Physical Activity ◽  
Count Data ◽  
R Package ◽  
Predictive Distribution ◽  
Epidemiological Studies ◽  
Accelerometer Data ◽  
Activity Data ◽  
Health And Nutrition ◽  
Log Normal ◽  
Over Dispersion

An accelerometer, a wearable motion sensor on the hip or wrist, is becoming a popular tool in clinical and epidemiological studies for measuring the physical activity. Such data provide a series of activity counts at every minute or even more often and displays a person’s activity pattern throughout a day. Unfortunately, the collected data can include irregular missing intervals because of noncompliance of participants and therefore make the statistical analysis more challenging. The purpose of this study is to develop a novel imputation method to handle the multivariate count data, motivated by the accelerometer data structure. We specify the predictive distribution of the missing data with a mixture of zero-inflated Poisson and Log-normal distribution, which is shown to be effective to deal with the minute-by-minute autocorrelation as well as under- and over-dispersion of count data. The imputation is performed at the minute level and follows the principles of multiple imputation using a fully conditional specification with the chained algorithm. To facilitate the practical use of this method, we provide an R package accelmissing. Our method is demonstrated using 2003−2004 National Health and Nutrition Examination Survey data.

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

2007 ◽  
Vol 34 (12) ◽  
pp. 1659-1674 ◽  
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.

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