Generalized Poisson Model Research Articles

Can Generalized Poisson model replace any other count data models? An evaluation

BackgroundCount data represents the number of occurrences of an event within a fixed period of time. In count data modelling, overdispersion is inevitable. Sometimes, this overdispersion may not be just due to the excess zeros but may be due to the presence of two or more mixtures. Hence the main objective is to examine for the presence of mixtures if any, with excess zeros and compare Generalized Poisson model, Mixture models with other count data models using real time and simulated data. MethodsThree real time over-dispersed datasets were used for the comparison of the models. The real time data models were compared using information criteria like AIC and BIC and regression coefficients. Data was also simulated using mixture Poisson with excess zeros. The simulation was repeated for different sample sizes were used to identify the better model. ResultsGeneralized Poisson showed consistently lower bias and MSE when compared to the other models for varying sample of sizes. AIC and BIC values were almost similar for Generalized Poisson, ZIP and Mixture Poisson model. Similar findings were also obtained from real time data. ConclusionGeneralized Poisson models provides a better fit for overdispersed data due to excess zeros, consistently in real time and simulated with varying sample sizes. Negative Binomial models can be redistricted or re-evaluated against Generalized Poisson model.

Estimation of safety performance functions for urban intersections using various functional forms of the negative binomial regression model and a generalized Poisson regression model

Intersections are established dangerous entities of a highway system due to the challenging and unsafe roadway environment they are characterized for drivers and other road users. In efforts to improve safety, an enormous interest has been shown in developing statistical models for intersection crash prediction and explanation. The selection of an adequate form of the statistical model is of great importance for the accurate estimation of crash frequency and the correct identification of crash contributing factors. Using a six-year crash data, road infrastructure and geometric design data, and traffic flow data of urban intersections, we applied three different functional forms of negative binomial models (i.e., NB-1, NB-2, NB-P) and a generalized Poisson (GP) model to develop safety performance functions (SPF) by crash severity for signalized and unsignalized intersections. This paper presents the relationships found between the explanatory variables and the expected crash frequency. It reports the comparison of different models for total, injury & fatal, and property damage only crashes in order to obtain ones with the maximum estimation accuracy. The comparison of models was based on the goodness of fit and the prediction performance measures.The fitted models showed that the traffic flow and several variables related to road infrastructure and geometric design significantly influence the intersection crash frequency. Further, the goodness of fit and the prediction performance measures revealed that the NB-P model outperformed other models in most crash severity levels for signalized intersections. For the unsignalized intersections, the GP model was the best performing model. When only the NB models were compared, the functional form NB-P performed better than the traditional NB-1 and, more specifically, the NB-2 models. In conclusion, our findings suggest a potential improvement in the estimation accuracy of the SPFs for urban intersections by applying the NB-P and GP models.

An Application of the Generalized Poisson Model for Over Dispersion Data on The Number of Strikes Between 1984 and 2017

Poisson regression analysis is widely used in many studies including count data. Poisson regression analysis is based on the assumption of equal mean and variance. However, this assumption is quite difficult in regression models. In cases where the assumption is not provided, over dispersion or under dispersion occurs. Over dispersion in data occurs when the variance of the dependent variable is greater than the average. This results in lower estimates than the standard errors. The generalized Poisson regression model is one of the methods used in case of over dispersion. This model is a generalization of Poisson regression. In this study, Poisson regression and generalized Poisson regression methods were used in the modeling of count data for determinants of strikes between 1984 and 2017. According to empirical results, while all explanatory variables of the Poisson regression model were significant, the unemployment rate was found to be insignificant for the generalized Poisson regression model. This result was evaluated considering the structure of the data.

Assessing farmers' contribution to greenhouse gas\xa0emission and the impact of adopting climate-smart agriculture on mitigation

BackgroundThe adoption of climate-smart agricultural (CSA) practices is expected to improve farmers’ adaptation to climate change and also increase yields while simultaneously curbing greenhouse gas (GHG) emissions. This paper explores the determinants of smallholder farmers’ participation in GHG-emitting activities. It also estimates the impact of CSA activities on reducing GHG emissions.MethodsThe findings are based on survey data obtained from 350 smallholder farmers in the East Gonja district of Northern Ghana. We adopted the generalized Poisson regression model in identifying factors influencing farmers’ participation in the GHG emission practices and inverse-probability-weighted regression adjustment (IPWRA) to estimate the impact of CSA adoption on GHG emissions.ResultsMost farming households engaged in at least one emission activity. The findings of the generalized Poisson model found that wealthier households, higher education, and households with access to extension services were less likely to participate in GHG emission activities. There was also evidence that CSA adoption significantly reduces GHG emissions.ConclusionAdvocacy in CSA adoption could be a necessary condition for environmental protection through the reduction of GHG emissions.

Modeling Burglar Incidents Data Using Generalized and Quasi Poisson Regression Models: A Case Study of Nairobi City County, Kenya

Serious violent crimes including Burglary, dangerous drug trafficking and sexual offenses make up the bulk of incidents filed at police stations daily. These crimes related activities poses a serious threat to the peace and serenity of a nation as far as safety is concerned. Burglar incidents data are often discrete and do not conform to the general assumptions of the linear model and its variants. Ordinarily, such data could be modeled using a linear regression approach to derive the relationship between the response variable to the underlying covariates. However, the narrowing of the gap between city and suburban burglar crime rates brings about variability invalidating the application of Ordinary linear regression approaches. The main objective of this study focused on the comparative use of Generalized Poisson and Quasi-Poisson models as an alternative to the classical linear regression approach in modeling Burglar incidents in Nairobi City County, Kenya. The prime advantage of applying Quasi Poisson in count data analysis is that it fixes the basic fallacy of assuming homogeneity in data and allows estimation of dispersion. The study used secondary data covering Eight (8) Nairobi's Administrative Divisions from the National Crime Research Center (NCRC) for the period 2016-2018. The comparison criteria were the Akaike Information (AIC) Criterion and Deviance Information Criterion (DIC) alongside other model diagnostics tests. Application of this results in burglar events revealed that the number of incidents in the study area are Under-dispersed with the risks of experiencing Burglar crime being above 5% in all the locations surveyed. In an attempt to explore Burglar to location relationship, results from study proved that Generalized Poisson Model performed better than the Quasi Poisson model having posted the lowest AIC value.

GEE-based zero-inflated generalized Poisson model for clustered over or under-dispersed count data

ABSTRACTThe zero-inflated regression models such as zero-inflated Poisson (ZIP), zero-inflated negative binomial (ZINB) or zero-inflated generalized Poisson (ZIGP) regression models can model the count data with excess zeros. The ZINB model can handle over-dispersed and the ZIGP model can handle the over or under-dispersed count data with excess zeros as well. Moreover, the count data may be correlated because of data collection procedure or special study design. The clustered sampling approach is one of the examples in which the correlation among subjects could be defined. In such situations, a marginal model using generalized estimating equation (GEE) approach can incorporate these correlations and lead up to the relationships at the population level. In this study, the GEE-based zero-inflated generalized Poisson regression model was proposed to fit over and under-dispersed clustered count data with excess zeros.

Multiple subscriptions to mobile networks and consumer satisfaction

The objective of this study is to analyze the determinants of the use of several telecommunication networks on the satisfaction of subscribers in Cameroon. To achieve this goal, a dual approach is adopted. Firstly, a mobilization of the different theories concerned within the framework of this study is carried out in order to expose the hypotheses of research. The second step is the organization and use of field survey data to test the assumptions made. At the end of the study, the Generalized Poisson model reveals that the individual's entourage, network problems, the use of promotional offers and the characteristics of the networks exert a significant influence on the multiple subscriptions. Moreover, gender, the age of the individual and his level of education are also significant. In addition, the ordered Simultaneous Bivariate Probit model indicates that multiple subscriptions improves individual's satisfaction. Indeed, as the number of networks used increases, there is an improvement in overall satisfaction, although the addition of a fourth network is a saturation point for individuals.

How many want to drive the bus? Analyzing the number of bids for public transport bus contracts

This paper examines how different factors related to contract characteristics and the operational and tender environments affect the number of unique bidders placing bids in tenders for bus contracts. A generalized Poisson model is used with a comprehensive data set containing most of the recently tendered bus contracts in Sweden, spanning the period 2007–2015.The main finding from the analysis is that most contract characteristics change participation in tenders by approximately 0.1–0.5 bidders. Operator-restricting measures such as special requirements on buses have a similar limited effect. Further, the number of tenders that are open at the same time as a specific tender was shown to reduce participation by almost two bidders. Finally, there is evidence that the local competitive environment is of importance, and the public transport authorities therefore need to be concerned with entry barriers in their tenders.

Modelling auto insurance claims in Singapore

Claim frequency data in general insurance may not follow the traditional Poisson distribution when there are many zeros. When the number of observed zeros exceeds the number of expected zeros under the Poisson distribution, extra dispersion appears. This paper summarizes several dispersed and zero-inflated count data models, which are used to handle dispersion and excess zeros. We model the insurance claim count data with excess zeros with these models. We use chi-square goodness-of-fit, to test the validity of the assumption of the count data distribution and fit count data regression model with predictors. We compare the fits through AIC and BIC. The generalized Poisson model and Negative binomial model provide a good fit to the data.

Marginalized zero-inflated generalized Poisson regression

ABSTRACTThe generalized Poisson (GP) regression model has been used to model count data that exhibit over-dispersion or under-dispersion. The zero-inflated GP (ZIGP) regression model can additionally handle count data characterized by many zeros. However, the parameters of ZIGP model cannot easily be used for inference on overall exposure effects. In order to address this problem, a marginalized ZIGP is proposed to directly model the population marginal mean count. The parameters of the marginalized zero-inflated GP model are estimated by the method of maximum likelihood. The regression model is illustrated by three real-life data sets.

Identification and estimation of a bidding model for electronic auctions

Because of discrete bid increments, bidders at electronic auctions engage in shading instead of revealing their valuations, which would occur under the commonly assumed second‐price rule. We demonstrate that misspecifying the pricing rule can lead to biased estimates of the latent valuation distribution, and then explore identification and estimation of a model with a correctly specified pricing rule. A further challenge to econometricians is that only a lower bound on the number of participants at each auction is observed. From this bound, however, we establish nonparametric identification of the arrival process of bidders—the process that matches potential buyers to auction listings—which then allows us to identify the latent valuation distribution without imposing functional‐form assumptions. We propose a computationally tractable, sieve‐type estimator of the latent valuation distribution based on B‐splines, and then compare two parametric models of bidder participation, finding that a generalized Poisson model cannot be rejected by the empirical distribution of observables. Our structural estimates enable us to explore information rents and optimal reserve prices on eBay. eBay electronic auctions bid increments pricing rule D44 C72

Religion and Fertility in East Asia: Evidence from the East Asian Social Survey

AbstractThis article analyses the effect of religious affiliation on fertility in Japan, Korea and the Republic of China (Taiwan). It adds to the sparse empirical evidence on the effects of religious affiliation on fertility in East Asia, for both Christian and other religions. It uses an identity‐economic model and analyses prescriptions among the different religions to derive testable hypotheses. In the empirical section, the East Asian Social Survey and a generalized Poisson model are used to estimate the effects of different religions on fertility. In line with theoretical predictions, the empirical results suggest that a positive effect of Catholicism on fertility is still present in East Asia. In line with the sparse previous empirical evidence on Buddhism, it seems to have no effect on fertility.

Test Statistics for Dispersion Parameter in Poisson Regression and Generalized Poisson Regression Models

Two symmetrical distributed test statistics, called Zm and Z0_New are proposed and their goodness-of-fit tests are compared with other available five test statistics: Wald-t, Score test, Z μ, ZY, and Z0, for overdispersion in Poisson regression model versus generalized Poisson model. Five thousand data sets in each condition of overdispersion parameters and sample sizes are simulated to perform the assessment of the models’ fits using those statistics, concerning the coverage probability and power of tests. Results show that the Zm test performs closely as good a Zμ and ZYtests but it tend to be better than the others when the sample size is large. Even if the Z0_New test has the largest power; however, in consideration for coverage probability and power of tests, the Zm test probably be more reliable. The Zm test statistic is interesting not only in its simplest form, with the reasonable coverage probability and power but also in its robust property of using median that needs fewer assumptions for its parent distribution.

Modeling crash frequency and severity with spatiotemporal dependence

This study proposes a novel multinomial generalized Poisson model with error components and spatiotemporal dependence (ST-EMGP) to analyze multi-period crash frequency and severity data. The proposed model not only simultaneously models crash frequency and severity, but also accommodates spatial and temporal dependence (spatiotemporal dependence) by specifying a spatiotemporal function. To demonstrate the applicability of the proposed model, a case study is conducted on five consecutive years׳ (2004–2008) crash data of Taiwan׳s Freeway No. 1. Estimation results show that ST-EMGP model performs better than the models without considering spatiotemporal dependence in terms of adjusted likelihood ratio index, consistent Akaike information criterion and log–likelihood test. Additionally, the estimated ST-EMGP model shows that spatial and temporal dependences exist and correlate mutually. Spatial dependence may overstate its impact magnitude, but underestimate its impact range when temporal dependence is ignored. According to the distribution and regression results of spatiotemporal effects, temporal effects are higher in crash frequency and are mainly affected by traffic characteristics; while spatial effects are higher in severe crash severity levels and are mainly affected by geometric configuration. Obviously, the proposed model can successfully elucidate the sources of spatiotemporal dependence as well as their effects on crash frequency and severity.

Semi Varying Coefficient Zero-Inflated Generalized Poisson Regression Model

In this paper, the semi varying coefficient zero-inflated generalized Poisson model is discussed based on penalized log-likelihood. All the coefficient functions are fitted by penalized spline (P-spline), and Expectation-maximization algorithm is used to drive these estimators. The estimation approach is rapid and computationally stable. Under some mild conditions, the consistency and the asymptotic normality of these resulting estimators are given. The score test statistics about dispersion parameter is discussed based on the P-spline estimation. Both simulated and real data example are used to illustrate our proposed methods.

WemIQ: an accurate and robust isoform quantification method for RNA-seq data.

The deconvolution of isoform expression from RNA-seq remains challenging because of non-uniform read sampling and subtle differences among isoforms. We present a weighted-log-likelihood expectation maximization method on isoform quantification (WemIQ). WemIQ integrates an effective bias removal with a weighted expectation maximization (EM) algorithm to distribute reads among isoforms efficiently. The weight represents the oversampling or undersampling of sequence reads and is estimated through a generalized Poisson model without any presumption on the bias sources and formats. WemIQ significantly improves the quantification of isoform and gene expression as well as the derived exon inclusion rates. It provides robust expression estimates across different laboratories and protocols, which is valuable for the integrative analysis of RNA-seq. For the recent single-cell RNA-seq data, WemIQ also provides the opportunity to distinguish bias heterogeneity from true biological heterogeneity and uncovers smaller cell-to-cell expression variability.

Modeling time series of counts with COM-Poisson INGARCH models

Frequently count time series exhibit overdispersion, but the opposite phenomenon of underdispersion is well documented in some situations, thus may be encountered in real applications. The INGARCH model is a popular tool for modeling time series of counts. The Poisson and negative binomial models can only deal with overdispersion, and the double Poisson and generalized Poisson models can treat both of them, but the latter two models have some shortcomings or limitations. The revived COM-Poisson distribution is flexible in modeling a wide range of overdispersion and underdispersion with only two parameters, while possessing properties that make it methodologically appealing and useful in practice, thus we introduce a new INGARCH model based on this distribution. We give an approximate condition for stationarity and expressions for mean, variance and autocorrelation function and test the accuracy of these expressions via simulations and real examples. We discuss the maximum likelihood estimation procedure for the parameters of interest. In addition, we also try to find influences of different distributions on INGARCH models using three real data sets. The results show that the generalized Poisson and COM-Poisson models perform well in most cases and the COM-Poisson model is a powerful competitor compared with the generalized Poisson model.

What Else do Epileptic Data Reveal

Problem statement: Aggregating and analyzing data of all patients using statistical methodologies as often done in macro sense would be not useful when physician’s professional interest was only to provide the best medical care to the patient. For this purpose, individual data of the involved patient should be analyzed and modeled in a micro sense for the physician to notice whether the treatment was helping the particular patient as demonstrated in this article. Understandably, a medical treatment would work in some patients but not in all patients. The physician would be more helped to know whether the treatment worked in a patient. Otherwise, the physician might switch to another treatment for the patient. No appropriate methodology existed in the literature to perform such a profile analysis. Hence, this article introduced a new statistical methodology and demonstrated the methodology using epileptic data. Approach: A probabilistic approach was necessary, as the number of epilepsy seizure in a patient happened to involve a degree of uncertainty. In some patient, the chance for a large number of seizures might be more depending on his/her proneness. The proneness would be a latent and non-measurable factor and hence, it could be captured only as a parameter. The traditional Poisson distribution was not suitable as it assumed homogeneous patients with respect to the proneness. The probability model should match the reality. A generalized Poisson model with an additional parameter to describe individual patient’s proneness was necessary as the article demonstrated. The author introduced such a model and investigated several statistical properties before in another article A new methodology with that probability was devised in this article for assessing the efficacy of a treatment for a chosen patient in epilepsy study. Results: Physicians pondered over whether epilepsy seizure incidences data support their hunch that their treatment was successful for a patient. This kind of case-by-case profiling was necessary to exercise the option of switching to another treatment for the patient. Aggregated medical data analysis of all patients did not help in making decision for a particular patient. The results of this article demonstrated about how the new methodology worked in epilepsy data to confirm when the treatment was successful. Patients, nurses and physicians were eager to develop an early warning system about how successful the treatment was in a patient. Such an early warning system was feasible, after finding the probability pattern of the data, because of the new methodology in this article. The discussions in this article could be emulated for other medical data analysis to address patient’s profile. Conclusions/Recommendations: As demonstrated with an example using epilepsy data, other medical data could be fit, analyzed and interpreted using the incidence rate restricted Poisson model. Not only the incidence rate but also the restriction level on the incidence rate due to the treatment could be estimated and tested. The proximity of the patients could then be identified using the indices based on mapping the principal components of their data as demonstrated in the article.

A two-parameter generalized Poisson model to improve the analysis of RNA-seq data

Deep sequencing of RNAs (RNA-seq) has been a useful tool to characterize and quantify transcriptomes. However, there are significant challenges in the analysis of RNA-seq data, such as how to separate signals from sequencing bias and how to perform reasonable normalization. Here, we focus on a fundamental question in RNA-seq analysis: the distribution of the position-level read counts. Specifically, we propose a two-parameter generalized Poisson (GP) model to the position-level read counts. We show that the GP model fits the data much better than the traditional Poisson model. Based on the GP model, we can better estimate gene or exon expression, perform a more reasonable normalization across different samples, and improve the identification of differentially expressed genes and the identification of differentially spliced exons. The usefulness of the GP model is demonstrated by applications to multiple RNA-seq data sets.

Score Tests for Zero-Inflation in Overdispersed Count Data

The negative binomial (NB) model and the generalized Poisson (GP) model are common alternatives to Poisson models when overdispersion is present in the data. Having accounted for initial overdispersion, we may require further investigation as to whether there is evidence for zero-inflation in the data. Two score statistics are derived from the GP model for testing zero-inflation. These statistics, unlike Wald-type test statistics, do not require that we fit the more complex zero-inflated overdispersed models to evaluate zero-inflation. A simulation study illustrates that the developed score statistics reasonably follow a χ2 distribution and maintain the nominal level. Extensive simulation results also indicate the power behavior is different for including a continuous variable than a binary variable in the zero-inflation (ZI) part of the model. These differences are the basis from which suggestions are provided for real data analysis. Two practical examples are presented in this article. Results from these examples along with practical experience lead us to suggest performing the developed score test before fitting a zero-inflated NB model to the data.