Count Data Models Research Articles

New biased estimators for the Conway–Maxwell-Poisson Model

Recent studies focus on modelling count data, which often shows overdispersion or underdispersion. The Conway–Maxwell–Poisson (COMP) regression model effectively handles such dispersion. However, multicollinearity can negatively impact the maximum likelihood estimator (MLE) by increasing variance. To address this, biased estimators like the ridge estimator have been suggested to mitigate multicollinearity effects. This research proposes a new COMP hybrid estimator to further address multicollinearity issues. Theoretical comparisons between the COMP hybrid estimator, MLE, and other COMP estimators reveal that the hybrid estimator reduces mean squared error. Monte Carlo simulations and practical applications confirm that these proposed estimators outperform both MLE and existing COMP estimators.

Efficient Analysis of Overdispersed Data Using an Accurate Computation of the Dirichlet Multinomial Distribution.

Modeling count data using suitable statistical distributions has been instrumental for analyzing the patterns it conveys. However, failing to address critical aspects, like overdispersion, jeopardizes the effectiveness of such an analysis. In this paper, overdispersed count data is modeled using the Dirichlet Multinomial (DM) distribution by maximizing its likelihood using a fixed-point iteration algorithm. This is achieved by estimating the DM distribution parameters while comparing the recent Languasco-Migliardi (LM), and the Yu-Shaw (YS) procedures, which address the well-known computational difficulties of evaluating its log-likelihood. Experiments were conducted using multiple datasets from different domains spanning polls, images, and IoT network traffic. They all showed the superiority of the LM procedure as it succeeded at estimating the DM parameters at the designated level of accuracy in all experiments, while the YS procedure failed to produce sufficiently accurate results (or any results at all) in several experiments. Moreover, the LM procedure achieved a speedup that ranged from 2-fold to 20-fold over YS.

Traffic count data analysis using mixtures of Kato–Jones distributions

Abstract We discuss the modelling of traffic count data that show the variation of traffic volume within a day. For the modelling, we apply mixtures of Kato–Jones distributions in which each component is unimodal and affords a wide range of skewness and kurtosis. We consider two methods for parameter estimation, namely, a modified method of moments and the maximum-likelihood method. These methods were seen to be useful for fitting the proposed mixtures to our data. As a result, the variation in traffic volume was classified into the morning and evening traffic whose distributions have different shapes, particularly different degrees of skewness and kurtosis.

Good: An R package for modelling count data

Abstract Organisms‐related data often appear as counts. The Poisson distribution is the most popular choice for modelling count data, but this distribution assumes equidispersion, which is usually not satisfied in real‐world data. Deviations from the Poisson assumption lead to discrete‐valued distributions that can fit over‐ and/or underdispersion. Although models for count data with over‐dispersion have been widely considered in the literature, models for underdispersion—the opposite phenomenon—have received less attention because underdispersion is relatively common only in certain research fields, including ecology. The Good distribution is a flexible option for modelling count data with over‐dispersion or underdispersion, although no R packages are available so far offering functionalities such as calculating quantiles, probabilities, etc., of a Good distribution or providing a method for modelling a Good‐distributed output based on a number of potential predictors. This paper presents the R package good, which computes the standard probabilistic functions, generates random samples from a population following a Good distribution and estimates the Good regression.

On the Conflation of Negative Binomial and Logarithmic Distributions

In recent decades, the study of discrete distributions has received increasing attention in the field of statistics, mainly because discrete distributions can model a wide range of count data. One common distribution used for modeling count data, for instance, is the negative binomial distribution (NBD), which performs well with over-dispersed data. In this paper, a new count distribution is introduced, called the conflation of negative binomial and logarithmic distributions, which is formed by conflating the negative binomial and logarithmic distributions, resulting in a distribution that possesses some of the properties of negative binomial and logarithmic distributions. The distribution has two parameters and is verified by a positive integer. Two modifications are proposed to the distribution, which includes zero as a support point. The new distribution is valuable from a theoretical perspective since it is a member of the weighted negative binomial distribution family. In addition, the distribution differs from the NBD in the sense that the probability of lower counts is inflated. This study discusses the characteristics of the proposed distribution and its modified versions, such as moments, probability generating functions, likelihood stochastic ordering, log-concavity, and unimodality properties. Real-world data are used to evaluate the performance of the proposed models against other models. All computations shown in this paper were produced using the R programming language.

Physical aspects of quantile residual lifetime sequence

Abstract The modeling of count data is found in many fields, such as statistical physics, public health, medicine, epidemiology, applied science, sociology, and agriculture. In many physical situations, it has been observed that many times in the real world, the original variables may be continuous in nature, but discrete by observation. In this study, the α {\rm{\alpha }} -quantile residual life function for discrete lifetime models is defined and some attributes are investigated. The relation between this measure and the hazard rate function is studied. We discuss how this measure could be useful for finding the burn-in time of a lifetime dataset. Then, a new stochastic order based on the α {\rm{\alpha }} -quantile residual life is proposed and studied.

Nonstationary longitudinal autoregressive mixed model for count data with measurement error in covariates: Estimation and asymptotics

Several methods have been proposed in the literature for computing unbiased and efficient estimates of the parameters of generalized linear models when the covariates are measured with error. However, to our knowledge, no documented research on computational techniques for parameter estimation currently exist in the literature when the data is a longitudinal count data influenced by an unobservable latent variable and observable covariates that are measured with error. In this paper, we propose a nonstationary conditionally Poisson mixed model for such data and develop unbiased estimating equations with iterative methods for computing estimates of the effect of the covariates, variance of the latent variable, and the correlation index parameter. The performance of the iterative methods is examined through extensive simulation studies. The results show that the methods performed well when the magnitude of the measurement error is not so large as to dominate or mask the effect of the true covariates. Using observed longitudinal count data on the number of patents awarded to 168 firms in the United States from 1974 to 1979 along with associated covariate information on the type of firm, log of the book value of capital in 1972 and research and development (R & D) expenditures we have demonstrated how the methods proposed in this paper can be applied to a real data. In addition, we derive the influence function of the estimator of the covariate effect and discuss the asymptotic properties of the estimator. Journal of Statistical Research 2024, Vol. 58, No. 1, pp. 151-180.

Location dynamics of coworking spaces in China: insights from Beijing metropolitan

ABSTRACT This paper explores the location determinants of coworking spaces (CSs) in the Chinese capital of Beijing, thus filling the gap in the literature about CS location in urban China. The study applies a count data model (CDM) to the data collected in 2022 to answer three research questions: (1) Where are CSs located and what are the location determinants? (2) How does Beijing’s urban structure affect CS location determinants? (3) What role do creative industry specialisation, variety, government facilities and incentives play in CS location? The findings reveal that CSs in Beijing – most of them promoted by public authorities – tend to cluster in the central city where there is a high diversity of knowledge-intensive and creative industries. The semi-polycentric urban structure of Beijing affects the location of CSs by creating localised activity hubs. Furthermore, the study finds evidence that creative industry specialisation and variety are crucial factors in CS location. In addition, government facilities and incentives play a key role in driving their locations.

A novel model for count data: zero-inflated Probit Bell model with applications

A novel model for count data is proposed in this work. This new model is briefly called the Zero-Inflated Probit Bell (ZIPBell) model. The ZIPBell model can be used to simulate and analyze traditional count data and can be used well in the simulation and analysis of count data with the phenomenon that the frequency for zero occupies a very high percentage. In the scope of this study, we first provide the general formula, functions or related equations for the ZIPBell model. The results of asymptotic inferences for the ZIPBell model are also given in this work. Maximum likelihood estimator (MLE) is used to check its performance of the proposed model. According to the numerical illustrations via several simulation researches and the analysis of a practical data set, it has been seen that the MLE method has offered correct and reliable inferences. Finally, the inferences and conclusions of this study are mentioned.

Core functions, visitor friendliness and digitalisation: a comparative analysis of corporate museums’ performance

We exploit a rich dataset on Italian museums to investigate whether corporate museums’ service provision is quantitatively different from the provision by the rest of private museums and by the three different types of Italian publicly owned museums (whose classification is by organisational mode: traditional, autonomous, and outsourced). We consider service provision in the dimensions of core museum functions (research, collection management, dissemination) and visitor friendliness, and we also focus on digital services. We use count data models estimation methods and include controls referring to museums’ characteristics and contextual factors to account for possible confounding effects. Our analysis reveals that corporate museums do not provide more core services than other museums, as expected given the public good component of this category of services. Contrary to expectations, we find that corporate museums are not among the museums providing the largest number of services enhancing visitor friendliness. Finally, corporate museums provide more digital services than traditional public museums and private museums owned by churches, and not less than other museum types. We argue that this latter evidence may come from their interaction with the parent firm. Corporate museums’ higher levels of digitalisation may be seen as the effect of a knowledge spillover between the more profit-oriented business world and the non-profit cultural sector.

ANALYSIS OF TRAFFIC ACCIDENTS AND THE DEPLOYMENT OF THE FIRE RESCUE SERVICE IN THE CZECH REPUBLIC

Traffic accidents remain a topical safety issue. The aim of this article is to use the statistical apparatus to describe a random variable, the daily number of accidents, and to model it. The data on traffic accidents for the period 2012–2021, including time and location information, came from the database of the Fire Rescue Service of the Czech Republic. The study utilised an analysis of variance for statistical analysis with a count variable, following a Poisson distribution. One-factor and two-factor analyses are used to describe the dependence of the daily number of accidents involving the deployment of the fire rescue service on the day of the week, and month. The use of generalised linear model for count data to analyse the number of traffic accidents is unique in the Czech Republic.

What are the key drivers of Fraud reporting in Takaful insurance? Evidence from count data models

Purpose This study aims at investigating the effect of corporate governance attributes on the Fraud disclosure of Takaful insurance companies in Saudi Arabia from 2014 to 2022. Design/methodology/approach This study uses a self-constructed disclosure index to quantify the level of fraud information using content analysis. The count regression (Poisson and negative binomial) models in panel data modeling are used to check the interdependence relationship between the Fraud disclosure and the corporate governance structure of 26 Takaful insurers. Findings The findings confirm the negative effect of ownership structure and the board size on the Fraud disclosure. However, the high proportion of independent board members, the audit board committee and the size of the risk board committee positively affect the extent of Fraud disclosure. Finally, this study provide evidence that large size of Shariah board is associated with a lower level of voluntary Fraud disclosure. Research limitations/implications Both economics-based theories and social exchange theory provide a better basis upon which to understand mechanisms by which board of directors in Takaful insurance provides external stakeholders with valuable information about corporate fraud. Practical implications It seems important to equip audit and Shariah board committee with the tools to give them an operational content that focus systematically on the “tone at the top” in investigating fraud, including disclosure and discipline. Originality/value Corporate governance is rapidly changing in Saudi Arabia and it is unclear whether adopting a corporate governance practices in financial institutions is appropriate for Islamic insurance companies.

A double Pólya-Gamma data augmentation scheme for a hierarchical Negative Binomial - Binomial data model

A double Pólya-Gamma data augmentation scheme is developed for posterior sampling from a Bayesian hierarchical model of total and categorical count data. The scheme applies to a Negative Binomial - Binomial (NBB) hierarchical regression model with logit links and normal priors on regression coefficients. The approach is shown to be very efficient and in most cases out-performs the Stan program. The hierarchical modeling framework and the Pólya-Gamma data augmentation scheme are applied to human mitochondrial DNA data.

An examination of trends in U.S. orange and grapefruit juice consumption

AbstractThe average U.S. consumer has been drinking less orange and less grapefruit juice over time. Per capita consumption is down more than 50% since the mid‐2000s. In this study, we propose and estimate a count data model. The number of times an adult consumes 100% orange or 100% grapefruit juice over a 2‐day period is modeled as a function of income, product prices, and some characteristics of the consumer such as level of education, being on a diet, and taking nutrient supplements that proxy for health concerns and nutrition knowledge. Data used in the study were collected between January 2005 and March 2020 on over 30,000 adult consumers. Tests for overdispersion favor a negative binomial model instead of the more restrictive Poison regression model. Estimation results confirm that rising juice product prices and concern over product healthfulness have been contributing to long run trends in orange and grapefruit juice consumption. Prices for these citrus juices have increased in recent years due in part to the citrus greening disease and hazardous weather in Florida. Trends in orange and grapefruit juice consumption can impact consumer diet quality, fruit growers, and agribusiness firms responsible for transforming raw fruit into juice and juice products. [EconLit Citations: D12, Q13].

Semi-parametric approach for modelling overdispersed count data with application to Industry 4.0

The paper deals with a test for the goodness-of-fit of a model for count data, in the framework of Generalized Linear Models. The motivating example concerns the study on the effectiveness of policy incentives for the adoption of 4.0 technologies by Small and Medium Enterprises. According to the literature, openness to Industry 4.0 should be measured in terms of the number of 4.0 technologies adopted, represented by a count variable. To investigate the effectiveness of public policy interventions to encourage the adoption of 4.0 technologies, we propose the application of a model for count data with a permutation ANOVA to test the goodness-of-fit and for the model selection. When the distribution of the response is neither Poisson nor Negative Binomial, and in the quite common situation in which the response variance is much greater than the mean, the classic Poisson regression and Negative Binomial regression are not valid. The proposed testing method is based on the combination of permutation tests on the significance of the regression coefficient estimates. The power behaviour of the proposed semi-parametric solution is investigated through a comparative Monte Carlo simulation study. The performance of such a method is compared to those of the two main parametric competitors. The application of the permutation test to an interesting case study is presented. The dataset is original, and related to a sample survey carried out in Italy, about the adoption of Industry 4.0 technologies by Italian enterprises.

The geography of the craft beer scene in Budapest

PurposeThis paper aims to investigate the locational determinants of the craft beer industry in Budapest, Hungary, between 2009 and 2022.Design/methodology/approachThe authors use various count data models to determine the relationship between the number of microbreweries and locational factors.FindingsThe authors find that demand and supply-side factors, including income, unemployment, level of education, population density and the number of local businesses, affect the number of craft breweries. Whilst agglomeration effects proxied by breweries per capita in a district have a positive coefficient, the number of breweries in neighbouring districts is not significant. In addition, the authors do not observe any negative impact of COVID-19-related restrictions. The picture of a still-evolving, resilient craft beer sector emerges from our analysis.Originality/valueTo the best of the authors’ knowledge, this is one of the first specific studies on the craft beer sector in the Central and Eastern European region and the first to evaluate the location choices of craft breweries in Hungary within a municipality using an up-to-date data set. The authors’ analysis covers 14 years, from the early stages of craft brewery proliferation in Budapest until 2022, testing several hypotheses with respect to the location choices of these businesses.

A flexible time-varying coefficient rate model for panel count data.

Panel count regression is often required in recurrent event studies, where the interest is to model the event rate. Existing rate models are unable to handle time-varying covariate effects due to theoretical and computational difficulties. Mean models provide a viable alternative but are subject to the constraints of the monotonicity assumption, which tends to be violated when covariates fluctuate over time. In this paper, we present a new semiparametric rate model for panel count data along with related theoretical results. For model fitting, we present an efficient EM algorithm with three different methods for variance estimation. The algorithm allows us to sidestep the challenges of numerical integration and difficulties with the iterative convex minorant algorithm. We showed that the estimators are consistent and asymptotically normally distributed. Simulation studies confirmed an excellent finite sample performance. To illustrate, we analyzed data from a real clinical study of behavioral risk factors for sexually transmitted infections.

A new poisson-exponential-gamma distribution for modelling count data with applications

A new poisson-exponential-gamma distribution for modelling count data with applications

A double generally weighted moving average control chart for monitoring zero-inflated Poisson processes

. The zero-inflated Poisson (ZIP) distribution is used to model count data with an excessive number of zeros. In this article, we present a double generally weighted moving average control chart for monitoring ZIP processes (regarded as ZIP-DGWMA chart). The run-length distribution of the proposed chart is evaluated by performing Monte Carlo simulations. A comparison study with the ZIP-GWMA chart indicates that the ZIP-DGWMA chart is more effective for shifts in the zero-inflated parameter p and for small shifts in both of the zero-inflated and Poisson parameters. The proposed chart is also applied on an example to demonstrate its application.

Improved estimators in bell regression model with application

In this paper, we propose the application of shrinkage strategies to estimate coefficients in the Bell regression models when prior information about the coefficients is available. The Bell regression models are well-suited for modelling count data with multiple covariates. Furthermore, we provide a detailed explanation of the asymptotic properties of the proposed estimators, including asymptotic biases and mean squared errors. To assess the performance of the estimators, we conduct numerical studies using Monte Carlo simulations and evaluate their simulated relative efficiency. The results demonstrate that the suggested estimators outperform the unrestricted estimator when prior information is taken into account. Additionally, we present an empirical application to demonstrate the practical utility of the suggested estimators.