Statistical modelling for falls count data

In recent years, there has been considerable interest in regression models based on zero-inflated distributions. These models are commonly encountered in many disciplines, such as medicine, public health, and environmental sciences, among others. The zero-inflated Poisson (ZIP) model has been typically considered for these types of problems. However, the ZIP model can fail if the non-zero counts are overdispersed in relation to the Poisson distribution, hence the zero-inflated negative binomial (ZINB) model may be more appropriate. In this paper, we present a Bayesian approach for fitting the ZINB regression model. This model considers that an observed zero may come from a point mass distribution at zero or from the negative binomial model. The likelihood function is utilized to compute not only some Bayesian model selection measures, but also to develop Bayesian case-deletion influence diagnostics based on q-divergence measures. The approach can be easily implemented using standard Bayesian software, such as WinBUGS. The performance of the proposed method is evaluated with a simulation study. Further, a real data set is analyzed, where we show that ZINB regression models seems to fit the data better than the Poisson counterpart.

Testing overdispersion in the zero-inflated Poisson model

Methodologic Challenges in the Analysis of Count Data in Radiology Health Services Research

More than 60% of accidents in Iran occur within 30 kilometers of cities entrance roads. Therefore the number of accidents per kilometer in these regions, in contrast to the other parts of roads is very considerable. The city of Tehran, as the capital of Iran, is the cross point of major arterials of passenger and freight transportation. Thus the evaluation of road safety, entering and exiting the city in the 30 kilometers buffer, can be considered to improve countrywide road safety. To investigate the effects of roadway characteristics and traffic conditions, including number of traffic violations, on accident frequency within 30 km of Tehran entrance roads, Poisson and Negative Binomial regression model were calibrated in this study. Although the goodness of fit index in Poisson model is much greater than the Negative Binomial model, the accident data dispersion in this study implies that Negative Binomial model is more appropriate to show the influences of effective variables. According to results of modeling, the variables including average daily volume, share of heavy vehicles, average daily speed violations and number of direct accesses and interchanges have effective influence on accident frequencies. Controlling access to roads and using effective actions to reduce the speed and number of speed violation can be accounted as effective policies to reduce accident frequencies within 30 km of Tehran entrance roads.

Single cell RNA-sequencing (scRNA-seq) technology has significantly advanced the understanding of transcriptomic signatures. Although various statistical models have been used to describe the distribution of gene expression across cells, a comprehensive assessment of the different models is missing. Moreover, the growing number of features associated with scRNA-seq datasets creates new challenges for analytical accuracy and computing speed. Here, we developed a Python-based package (TensorZINB) to solve the zero-inflated negative binomial (ZINB) model using the TensorFlow deep learning framework. We used a sequential initialization method to solve the numerical stability issues associated with hurdle and zero-inflated models. A recursive feature selection protocol was used to optimize feature selections for data processing and downstream differentially expressed gene (DEG) analysis. We proposed a class of hybrid models combining nested models to further improve the model's performance. Additionally, we developed a new method to convert a continuous distribution to its equivalent discrete form, so that statistical models can be fairly compared. Finally, we showed that the proposed TensorFlow algorithm (TensorZINB) was numerically stable and that its computing speed and performance were superior to those of existing ZINB solvers. Moreover, we implemented seven hurdle and zero-inflated statistical models in Python and systematically assessed their performance using a real scRNA-seq dataset. We demonstrated that the ZINB model achieved the lowest Akaike information criterion compared with other models tested. Taken together, TensorZINB was accurate, efficient and scalable for the implementation of ZINB and for large-scale scRNA-seq data analysis with DEG identification.

Zero-inflated count data are characterized by an excessive frequency of zeros that cannot be adequately analyzed by a single distribution, such as Poisson or negative binomial. This problem is pervasive in many practical applications, including document–keyword matrix derived from text corpora, where most keyword frequencies are zero. Conventional statistical approaches, such as the zero-inflated Poisson (ZIP) and zero-inflated negative binomial (ZINB) models, explicitly separate a structural zero component from a count component, but they typically assume independent observations and can be unstable when covariates are high-dimensional and sparse. To address these limitations, this paper proposes a graph-based zero-inflated learning framework that combines simple graph convolution (SGC) with zero-inflated count regression heads such as ZIP and ZINB. We first construct an observation graph by connecting similar samples, and then apply SGC to propagate and smooth features over the graph, producing convolutional representations that incorporate neighborhood information while remaining computationally lightweight. The resulting representations are used as covariates in ZIP and ZINB heads, which preserve probabilistic interpretability through maximum likelihood learning. Our experiments on simulated zero-inflated datasets with controlled zero ratios demonstrate that the proposed ZIP+SGC and ZINB+SGC consistently reduce prediction errors compared with their non-graph baselines, as measured by mean absolute error and root mean squared error. Overall, the proposed approach provides an efficient and interpretable way to integrate graph neural computation with zero-inflated modeling for sparse count prediction problems.

Modeling Vehicle-pedestrian Crashes With Excess Zero Along Malaysia Federal Roads

Developing statistics methods to distinguish significant factors associated with roadways is one of the most feasible accesses to understand the nature of traffic accidents. In this study, zero-inflated negative binomial (ZINB) model was developed to allow for overdispersion and excess zeros, as well as the factors of land use, design and environment to examine the effects. The statistical tests show that ZINB model is preferred to zero-inflated Poisson and negative binomial models due to its ability to describe crash counts associated with severe injuries and fatalities more effectively. The results show that fatalities are positively associated with segment length, surface width, land use variables and rainfall. For example, an increase of one inch rainfall will result in an increase of 0.02% in fatalities. Interestingly, distances to hospitals yield positive impact, which suggests that longer distances lead to higher fatalities, presumably due to time lost in transporting crash victims to hospitals.

ObjectivesThe number of depression symptoms can be considered as count data in order to get complete and accurate analyses findings in studies of depression. This study aims to compare the...

This paper presents the findings on modeling the demand for shared e-scooter services (SES); specifically, spatio-temporal variation of SES demand. A zero-inflated negative binomial (ZINB) model is developed using the count data of trip origins at the dissemination area level from Kelowna, Canada. The motivation for adopting the ZINB model is the presence of excess zeros in the count data. ZINB has two components: the zero-inflated component accounts for excess zeros, and the count component accounts for the over-dispersion characteristics of data resulting from excess zeros. In addition to the ZINB, several other count models including hurdle models are estimated. The goodness-of-fit measures suggest that the ZINB model outperforms other methods. The model results confirm the effects of temporal, weather, transportation infrastructure, land use, and neighborhood characteristics. For example, the count model results reveal that SES demand is more likely to be higher during summer, mid-day on weekends, afternoons of weekdays, and days without rainfall. Furthermore, higher e-scooter index, higher density of cycle tracks, heterogeneous land use, urban centers, lower elevation, and neighborhoods with higher density of hotels and younger population might induce higher demand. The zero component results of the model are consistent with the findings revealed by the count component. The model is validated using a hold-out sample, and the validation results confirm that the prediction performance of the model is reasonably satisfactory. The findings of this study provide important insights into when and where the demand is higher, which will assist in effective policy-making supporting e-scooter use.

Forest tree ingrowth is a highly variable and largely stochastic process. Consequently, predicting occurrence, frequency, and composition of ingrowth is a challenging task but of great importance in long-term forest growth and yield model projections. However, ingrowth data often require different statistical techniques other than traditional Gaussian regression, because these data are often bounded, skewed, and non-normal and commonly contain a large fraction of zeros. This study presents a set of regression models based on discrete Poisson and negative binomial probability distributions for ingrowth data collected from permanent sample plots in the Acadian Forest Region of North America. Models considered here include regular Poisson, zero-inflated Poisson (ZIP), zero-altered Poisson (ZAP; hurdle Poisson), regular negative binomial (NB), zero-inflated negative binomial (ZINB), and zero-altered negative binomial (ZANB; hurdle NB). Plot-level random effects were incorporated into each of these models. The ZINB model with random effects was found to provide the best fit statistics for modeling annualized occurrence and frequency of ingrowth. The key explanatory variables were stand basal area per hectare, percentage of hardwood basal area, number of trees per hectare, a measure of site quality, and the minimum measured diameter at breast height of each plot. A similar model was developed to predict species composition. All models showed logical behavior despite the high variability observed in the original data.

Zero-inflated data from field experiments can be problematic, as these data require the use of specific statistical models during the analysis process. This study utilized the zero-inflated negative binomial (ZINB) model with the log- and logistic-link functions to describe the incidence of plants with Huanglongbing (HLB, caused by Candidatus liberibacter spp.) in commercial citrus orchards in the Northwestern Parana State, Brazil. Each orchard was evaluated at different times. The ZINB model with random effects in both link functions provided the best fit, as the inclusion of these effects accounted for variations between orchards and the numbers of diseased plants. The results of this model show that older plants exhibit a lower probability of acquiring HLB. The application of insecticides on a calendar basis or during new foliage flushes resulted in a three times larger probability of developing HLB compared with applying insecticides only when the vector was detected.

Modelling of vertical integration in commercial poultry production of Ghana: A count data model analysis

Effect of the measurement period and spatial dependence on the accuracy of urban freight trip generation models

To determine the most appropriate regression models to use when assessing risk factors for severe hypoglycaemia and to investigate the impact of model misspecification and its clinical implications. A total of 1229 children with Type 1 diabetes (mean age 11.7 years sd 4.1), of which 605 (49.2%) were males, were studied. Prospective assessment of severe hypoglycaemia (an event leading to loss of consciousness or seizure) was made over the 9-year period, 1992-2001. Patients were seen every 3 months and episodes of hypoglycaemia along with clinical data were recorded. Over 70% of children never experienced a severe hypoglycaemic event. Data were analysed using the Poisson regression, negative binomial, zero-inflated Poisson (ZIP) and zero-inflated negative binomial (ZINB) models. The over-dispersion and likelihood ratio statistics were calculated and the analytical methods compared. The Poisson regression model did not fit the data well. The negative binomial and the zero inflated Poisson and negative binomial models fitted the data better than Poisson. The commonly used Poisson regression models to analyse hypoglycaemia epidemiology may lead to biased parameter estimates and incorrect determination of risk factors for hypoglycaemia. We recommend the use of the negative binomial or zero inflated models to examine any risk factors associated with severe hypoglycaemia. Careful consideration must be given to the interpretation of hypoglycaemia surveys and their analysis.