Count Data Models Research Articles

A new improvement Liu-type estimator for the Bell regression model

The Poisson Regression Model (PRM) is a well-known model in applications when the response variable consists of count data. However, Bell Regression Model (BRM) is proposed recently as an alternative to the PRM in some cases where the data is over-dispersed. But, multicollinearity between explanatory variables negatively affects traditional estimation methods, such as MLE. Therefore, to avoid this problem, several shrinkage estimators are proposed in the BRM. In this study, a new improved Liu-type estimator is proposed as an alternative to the other proposed biased estimators for the BRM to model count data with over-dispersion. Furthermore, the Monte Carlo simulation studies are executed to compare the performances of the proposed biased estimators. Finally, the obtained results are illustrated in real data.

A flexible quasi-likelihood model for microbiome abundance count data.

In this article, we present a flexible model for microbiome count data. We consider a quasi-likelihood framework, in which we do not make any assumptions on the distribution of the microbiome count except that its variance is an unknown but smooth function of the mean. By comparing our model to the negative binomial generalized linear model (GLM) and Poisson GLM in simulation studies, we show that our flexible quasi-likelihood method yields valid inferential results. Using a real microbiome study, we demonstrate the utility of our method by examining the relationship between adenomas and microbiota. We also provide an R package "fql" for the application of our method.

Counting the Unseen: Estimation of Susceptibility Proportions in Zero-Inflated Models Using a Conditional Likelihood Approach

Zero-inflated count data models are widely used in various fields such as ecology, epidemiology, and transportation, where count data with a large proportion of zeros is prevalent. Despite their widespread use, their theoretical properties have not been extensively studied. This study aims to investigate the impact of ignoring heterogeneity in event count intensity and susceptibility probability on zero-inflated count data analysis within the zero-inflated Poisson framework. To address this issue, we propose a novel conditional likelihood approach that uses positive count data only to estimate event count intensity parameters and develop a consistent estimator for estimating the average susceptibility probability. Our approach is compared with the maximum likelihood approach, and we demonstrate our findings through a comprehensive simulation study and real data analysis. The results can also be extended to zero-inflated binomial and geometric models with similar conclusions. These findings contribute to the understanding of the theoretical properties of zero-inflated count data models and provide a practical approach to handling heterogeneity in such models.

Predicting cyanobacteria abundance with Bayesian zero-inflated models

Abstract Cyanobacterial blooms are a persistent concern to water management and treatment, with blooms potentially causing the release of toxins and degrading water quality. However, previous models have not considered the zero inflation of cyanobacteria count data. Typically, a relatively large proportion of measured count data are zeros or non-detects of cyanobacteria, representing either no cyanobacteria was present or the cell number was too low to be detected. Commonly used Poisson and negative binomial models for count data underestimate the probability of zero data, making these models less reliable. This study proposes a Bayesian approach to fit the cyanobacteria abundance data with mixture models that handle zero-inflated data. Predictor variables considered included weather and water quality measures that can easily be obtained day-to-day. The optimal model (zero-inflated negative binomial) was used to predict cyanobacteria alert levels on a separate test set. The ability to predict narrow alert levels was limited, however, 76% accuracy was achieved in predicting cyanobacteria counts above or below 1,000 cells/mL. Parameter estimates were highly variable and demonstrated that complex and uncertain factors influence cyanobacteria count predictions. The modelling approach can be applied to a wide range of environmental problems where zero-inflated data is common.

Extended Laplace approximation for self-exciting spatio-temporal models of count data

Self-exciting models are statistical models of count data where the probability of an event occurring is influenced by the history of the process. In particular, self-exciting spatio-temporal models allow for spatial dependence as well as temporal self-excitation. For large spatial or temporal regions, however, the model leads to an intractable likelihood. An increasingly common method for dealing with large spatio-temporal models is by using Laplace approximations (LA). This method is convenient as it can easily be applied and is quickly implemented. However, as we will demonstrate in this manuscript, when applied to self-exciting Poisson spatial–temporal models, Laplace Approximations result in a significant bias in estimating some parameters. Due to this bias, we propose using up to sixth-order corrections to the LA for fitting these models. We will demonstrate how to do this in a Bayesian setting for self-exciting spatio-temporal models. We will further show there is a limited parameter space where the extended LA method still has bias. In these uncommon instances we will demonstrate how a more computationally intensive fully Bayesian approach using the Stan software program is possible in those rare instances. The performance of the extended LA method is illustrated with both simulation and real-world data.

Intensity of adaptations to heat stress in poultry farms: A behavioural analysis of farmers in Ondo state, Nigeria

The detrimental consequences of heat stress due to high ambient temperatures, particularly in the poultry industry, have led to the invention of several adaptation strategies. However, there is still limited information on the intensity of adaptations and the likely behavioural factors that influence farmers' decisions. Thus, understanding the practical adaptation behaviours of poultry farmers would improve our knowledge of the fundamental mechanisms for developing effective interventions. To fill this void, using a count data model, the study empirically examines the farmers' behavioural factors and the intensity of heat stress adaptation strategies’ adoption among poultry farmers in Ondo State, Nigeria. The data were drawn from a survey of 150 poultry farmers using a multistage sampling procedure. The empirical results show that the majority of the farmers perceived an increase in temperature, frequently experienced heat stress, and believed that heat stress is induced by climate change. An average of six adaptation strategies were simultaneously adopted to mitigate heat stress in the area. The results of the count regression model reveal that farm-level factors such as permanent water sources, the quantity of feed, and bird stock density exert a significant effect on the intensity of adaptations. Climate-related factors such as access to climate information, training participation, perceived increases in temperature, attitudes toward climate change, and motives for adoption have a significant behavioural effect on the intensity of adaptations. Likewise, variables such as poultry farming experience, educational status, and access to credit are accounted for as socioeconomic behavioural factors that influence the intensity of adopting heat stress adaptation strategies in the area. This concludes that behavioural factors are crucial in addressing heat stress adaptations and assisting in improving environmental management, which would form a key variable in the policy interventions.

Dynamic Modeling of Spike Count Data With Conway-Maxwell Poisson Variability.

In many areas of the brain, neural spiking activity covaries with features of the external world, such as sensory stimuli or an animal's movement. Experimental findings suggest that the variability of neural activity changes over time and may provide information about the external world beyond the information provided by the average neural activity. To flexibly track time-varying neural response properties, we developed a dynamic model with Conway-Maxwell Poisson (CMP) observations. The CMP distribution can flexibly describe firing patterns that are both under- and overdispersed relative to the Poisson distribution. Here we track parameters of the CMP distribution as they vary over time. Using simulations, we show that a normal approximation can accurately track dynamics in state vectors for both the centering and shape parameters (λ and ν). We then fit our model to neural data from neurons in primary visual cortex, "place cells" in the hippocampus, and a speed-tuned neuron in the anterior pretectal nucleus. We find that this method outperforms previous dynamic models based on the Poisson distribution. The dynamic CMP model provides a flexible framework for tracking time-varying non-Poisson count data and may also have applications beyond neuroscience.

A new exponentially weighted moving average control chart to monitor count data with applications in healthcare and manufacturing

Attribute control charts are widely used to monitor count data. Many distributions are proposed to model and monitor count data. This article has developed an exponentially weighted moving average (EWMA) control chart under Generalized Conway–Maxwell–Poisson (GCOMP) distribution and named as the GCOMP-EWMA chart. The GCOMP distribution is an extension of the Conway–Maxwell–Poisson (COMP) distribution and is a longer-tailed model than the COMP distribution. The GCOMP distribution can also model the shorter tail behaviour in count data. Considering the tail behaviour, the in-control and out-of-control performance of the GCOMP-EWMA chart have been evaluated for over- and under-dispersed count data. Without using the zero-inflation property, the GCOMP-EWMA chart performs efficiently in monitoring zero-inflated count data compared to existing zero-inflated models-based control charts. Finally, illustrative examples demonstrate the practical applications of the GCOMP-EWMA charts in different fields.

MODELING COUNT DATA WITH OVER-DISPERSION USING GENERALIZED POISSON REGRESSION: A CASE STUDY OF LOW BIRTH WEIGHT IN INDONESIA

Poisson regression is commonly used in modeling count data in various research fields. An essential assumption must be met when using Poisson regression, which is that the count data of the response has the mean and variance must be equal, namely equi-dispersion. This assumption is often unmet because many data for the response that the variance is greater than the mean, called over-dispersion. If the Poisson regression model contains the over-dispersion, then will be produced an invalid model can under-estimate standard errors and misleading inference for regression parameters. Therefore, an approach is needed to overcome the over-dispersion problem in Poisson regression. The generalized Poisson regression can handle the over-dispersion in Poisson regression. This study aims to obtain the generalized Poisson regression model and the factors affecting the low birth weight in Indonesia in 2021. The result shows that the factors affecting the low birth weight in Indonesia based on the generalized Poisson regression model were: poverty rate, percentage of households with access to appropriate sanitation, percentage of pregnant women at risk of chronic energy deficiency receiving additional food, percentage of pregnant women who received blood-boosting tablets, and percentage of antenatal care.

Does quality affect choice of family physician? Evidence from patients changing general practice without changing address

We examine whether quality affects the choice of practice by patients who are most likely to be well informed about quality: those who leave their practice and join another local practice without changing their address (non-movers). Using 2006/7–2010/11 data on 6766 English practices we estimate fixed effects panel count data models of the number of non-movers leaving a practice and of the number joining. Fewer non-movers leave a practice after increases in clinical quality, the proportion of patients satisfied with access, doctors per patient, and the proportion of doctors qualified in the UK. More join after increases in patient satisfaction with access and doctors per patient. A 10% increase in opening hours satisfaction is associated with a 5.75% reduction in non-movers leaving and a 2.9% increase in non-movers joining. Our results imply that improving information on quality will increase practice incentives to raise quality when competing for patients.

An integer GARCH model for a Poisson process with time-varying zero-inflation.

A serially dependent Poisson process with time-varying zero-inflation is proposed. Such formulations have the potential to model count data time series arising from phenomena such as infectious diseases that ebb and flow over time. The model assumes that the intensity of the Poisson process evolves according to a generalized autoregressive conditional heteroscedastic (GARCH) formulation and allows the zero-inflation parameter to vary over time and be governed by a deterministic function or by an exogenous variable. Both the expectation maximization (EM) and the maximum likelihood estimation (MLE) approaches are presented as possible estimation methods. A simulation study shows that both parameter estimation methods provide good estimates. Applications to two real-life data sets on infant deaths due to influenza show that the proposed integer-valued GARCH (INGARCH) model provides a better fit in general than existing zero-inflated INGARCH models. We also extended a non-linear INGARCH model to include zero-inflation and an exogenous input. This extended model performed as well as our proposed model with respect to some criteria, but not with respect to all.

Effects of regulations on the Airbnb market in Geneva

This study examines the impact of regulations on the supply and performance of Airbnb rentals in Geneva by focusing on the role of substitution effects between fully rented accommodations and individual rooms. A difference-in-differences approach is used in combination with logit and count data models with fixed effects for properties. The data consists of monthly Airbnb listings in the 10 largest Swiss cities for the period 2017–2018, with around 220,000 observations on 16,600 properties (60 per cent of which were being let as entire properties). The estimates show that the performance of Airbnb accommodations decreases significantly after the introduction of regulations in terms of bookings, days reserved, occupancy, and revenues. The performance of single rooms let within private properties, meanwhile, benefited from the new regulation in some cases, suggesting that there may be a substitution effect between the two groups. The magnitude of the impact of regulation is considerable, with monthly revenues of fully let Airbnb accommodations decreasing by an average of 15 per cent.

Geographical indications as an untapped opportunity for inner areas. An analysis of geographical indications from Southern Italy

Remote areas have been progressively obtained greater attention within rural development policies. Actually, a tool to foster the economic development of remote areas is valorising those high-quality agri-food products that are characterised by unique features through the use of Geographical Indications. In particular, socioeconomic characteristics and weaknesses might limit GI implementation, especially in remote areas. This work addresses this topic, by considering as a case study Southern Italian regions and their remote areas, as defined by the 2014 Italian National Strategy for Inner Areas. The work considers data on GIs at municipality (i.e., LAU2) level, adopting an empirical strategy based on the hurdle model for count data. Results suggest that geography plays a key role: actually, municipalities in the inner areas show a lower number of GIs compared to non-inner municipalities. Moreover, also social capital seems to play a role, stressing its importance when dealing with the registration of a new GI.

How do road infrastructure investments affect Powered Two-Wheelers crash risk?

The drivers of Powered Two-Wheelers (PTWs) pertain to the collective of so-called vulnerable road users. Crashes have scarcely decreased for these roadway users in recent years, whereas among other users, e.g. cars users, they have declined considerably. Meanwhile, the use of PTWs has risen sharply worldwide. This situation adds a further concern to transportation policies and makes evident the need to explore factors involved in PTW crashes. Yet there is a lack of studies specifically about road safety for PTWs. The present study therefore aspires to advance in the knowledge of the factors affecting PTW crashes on interurban roadways, by means of analyzing the effects of some variables not considered previously in this type of studies —mainly economic resources invested in roads—while also accounting specifically for the exposure to risk of PTWs (veh-km), along with relevant variables related to road traffic, the roadway infrastructure, and socioeconomic, meteorological and legislative factors. To this end, and bearing in mind the latest advancements of incorporating unobserved heterogeneity in count data models, different configurations of random parameters negative binomial models for data panels are presented. The realm of study is the network of national roads in Spain, distributed over 43 provinces, and the time period between 2007 and 2015. The results show significant associations for 11 of the variables considered: annual and accumulated investment in construction, expense on maintenance, proportion of motorways, light and heavy vehicle traffic, per capita GDP, age, unemployment rate, price of gasoline, and modification of the demerit point system (DPS). With respect to transport policy implications, the findings provided in this study may serve to monitor the effects of economic resources allocated to road construction and maintenance —along with other measures, such as gasoline prices and DPS—on PTWs safety.

On Poisson-Samade Distribution: Its Applications in Modelling Count Data

A new mixed Poisson model is proposed as a better alternative for modelling count data in the presence of overdispersion and/or heavy-tail. The mathematical properties of the model were derived. The maximum likelihood estimation method is employed to estimate the model’s parameters and its applications to the three real data sets discussed. The model is used to model sets of frequencies that have been used in different literature on the subject. The results of the new model were compared with Poisson, Negative Binomial and Generalized Poisson-Sujatha distributions (POD, NBD and GPSD, respectively). The parameter estimates expected frequencies and the goodness-of-fit statistics under each model are computed using R software. The results show that the proposed PSD fits better than POD, NBD and GPSD for all the data sets considered. Hence, PSD is a better alternative provided to model count data exhibiting overdispersion property.

Parallel dynamics in the yield of universal SARS-CoV-2 admission screening and population incidence

The majority of SARS-CoV-2 transmissions originates from either asymptomatic or presymptomatic individuals. To prevent unnoticed introduction of SARS-CoV-2, many hospitals have implemented universal admission screening during the COVID-19 pandemic. The present study aimed to investigate associations between results of an universal SARS-CoV-2 admission screening and public SARS-CoV-2 incidence. Over a study period of 44 weeks, all patients admitted to a large tertiary care hospital were tested for SARS-CoV-2 by polymerase chain reaction. SARS-CoV-2 positive patients were retrospectively categorized as symptomatic or asymptomatic at admission. Cantonal data were used to calculate weekly incidence rates per 100,000 inhabitants. We used regression models for count data to assess the association of the weekly cantonal incidence rate and the proportion of positive SARS-CoV-2 tests in the canton with (a) the proportion of SARS-CoV-2 positive individuals and (b) the proportion of asymptomatic SARS-CoV-2 infected individuals identified in universal admission screening, respectively. In a 44-week period, a total of 21,508 admission screenings were performed. SARS-CoV-2 PCR was positive in 643 (3.0%) individuals. In 97 (15.0%) individuals, the positive PCR reflected residual viral replication after recent COVID-19, 469 (72.9%) individuals had COVID-19 symptoms and 77 (12.0%) SARS-CoV-2 positive individuals were asymptomatic. Cantonal incidence correlated with the proportion of SARS-CoV-2 positive individuals [rate ratio (RR): 2.03 per 100 point increase of weekly incidence rate, 95%CI 1.92–2.14] and the proportion of asymptomatic SARS-CoV-2 positive individuals (RR: 2.40 per 100 point increase of weekly incidence rate, 95%CI 2.03–2.82). The highest correlation between dynamics in cantonal incidence and results of admission screening was observed at a lag time of one week. Similarly, the proportion of positive SARS-CoV-2 tests in the canton of Zurich correlated with the proportion of SARS-CoV-2 positive individuals (RR: 2.86 per log increase in the proportion of positive SARS-CoV-2 tests in the canton, 95%CI 2.56–3.19) and the proportion of asymptomatic SARS-CoV-2 positive individuals (RR: 6.50 per log increase in the proportion of positive SARS-CoV-2 tests in the canton, 95%CI 3.93–10.75) in admission screening. Around 0.36% of admission screenings were positive in asymptomatic patients. Admission screening results paralleled changes in population incidence with a brief lag.

INTERCEPT ESTIMATION IN NONLINEAR SELECTION MODELS

We propose various semiparametric estimators for nonlinear selection models, where slope and intercept can be separately identified. When the selection equation satisfies a monotonic index restriction, we suggest a local polynomial estimator, using only observations for which the marginal cumulative distribution function of the instrument index is close to one. Data-driven procedures such as cross-validation may be used to select the bandwidth for this estimator. We then consider the case in which the monotonic index restriction does not hold and/or the set of observations with a propensity score close to one is thin so that convergence occurs at a rate that is arbitrarily close to the cubic rate. We explore the finite sample behavior in a Monte Carlo study and illustrate the use of our estimator using a model for count data with multiplicative unobserved heterogeneity.

Internationalization under attack: the external threat of short sellers

PurposeThe purpose of this paper is to examine the role of short sellers in foreign direct investment (FDI) decisions. Drawing on threat rigidity theory, the authors argue that short sellers pose a threat to chief executive officers (CEOs) by exerting downward pressure to target firms’ stock prices. That threat will evoke rigid managerial responses that hinder new FDI activities. The authors also posit that CEOs will be less reactive to short sellers’ threats when they are generalist CEOs who have extensive general work experience or when they serve as the board chair.Design/methodology/approachThe authors collect data from S&P 1,500 firms, and the final sample consists of 717 firms and 6,930 firm-year observations from 1998 to 2016. The authors use an Arellano and Bond generalized method of moments static linear probability panel data model and an instrumental panel count data model to test the hypotheses.FindingsThe findings support the hypotheses and suggest that CEOs who are under more pressure from short sellers engage in fewer new FDI activities. The negative impact of short sellers on FDI decisions is less salient when CEOs have general work experience or are the chairperson of the board.Originality/valueThis study contributes to the international business research by stressing the need to consider the role of short sellers in firm internationalization decisions.

Location attributes explaining the entry of firms in creative industries: evidence from France

This paper focuses on creative industries and the role played by the existing spatial distribution and agglomeration economies of these activities in relation to their entry decisions. We rely on employment and firm-level data in the creative industries (provided by INSEE) and compare the location of new establishments in the creative and non-creative industries between 2009 and 2013 in French departments (NUTS 3 regions). We use count data models and spatial econometrics to show that location determinants are rather similar in creative and non-creative industries and that specialisation in creative industries positively influences the entry of all other industries. The French case provides new insights to understand the geographical patterns of creative industries.

Normal-Compound Gamma priors with Count Data

Count data models have become very common in several disciplines in recent years. Since these types of models can often be studied incorrectly using OLS methods, several solutions have been proposed to address this problem. One of these methods the normal-scale mixture method with different types of priors of the scale parameter. The importance of this method is to solve the issue of the bias-variance tradeoff by adding a local scale parameter to reduce the variance at the origin and reduce the bias at the tails. In this paper, a compound-gamma prior is placed for the scale parameter and the relevant Gibbs sampler is solved for posterior inference. The comparison of the performance of the proposed model with some other existing methods using both very sparse and low sparsity simulated data shows that the proposed model performs very well.