Generalized Poisson Models Research Articles

Predicting nature recovery for river restoration planning and ecological assessment: A case study from England, 1991–2042

AbstractThe Global Biodiversity Framework established ambitious goals for nature recovery which governments must now incorporate into national legislation. In England, legally binding targets require authorities to halt the decline in species abundance by 2030 and reverse the decline by 2042. Riverine invertebrates represent a substantial proportion of the species contributing towards the targets. Thus, understanding the response of these species to potential river restoration actions is key to target delivery. We model counts for 188 riverine invertebrate taxa using zero‐inflated generalized Poisson models, applying the models to both inform river restoration planning and set expected values for use in ecological assessment. We identify catchment‐specific restoration strategies that combine one or more actions involving the removal of channel modifications, reductions in nitrate concentrations and reductions in total dissolved phosphorus concentrations as the most likely to deliver species abundance targets across three joint climate–socioeconomic scenarios. By hindcasting species abundances under alternative target frameworks, we also demonstrate a new approach to setting expected values in ecological assessment, accounting for changes in water temperature and hydrology that confound historical reference models presently used by regulators. Our findings represent the first systematic attempt to prioritise major actions to deliver species abundance targets in England, providing valuable insights for policymakers, river restoration practitioners and authorities responsible for monitoring river ecosystems.

Abstract P213: Examining Sociodemographic Disparities in Physical Activity and Diabetes: Preliminary Findings From 2007-2020 National Health and Nutrition Examination Survey

Purpose: Physical activity (PA) plays a crucial role in preventing diabetes, but few studies have examined whether sociodemographic factors were associated to PA, and PA and sociodemographic factors were related to diabetes. We aimed to 1) examine associations between sociodemographic factors and PA, and 2) investigate whether PA and sociodemographic are related to the prevalence of diabetes. Methods: Data came from the 2007-2020 National Health and Nutrition Examination Survey (NHANES), a series of cross-sectional cohort studies (total sample=30,788, Female: 49.1%, mean age =49.6). Two binary outcomes included: 1) Meeting PA guidelines (≥500 MET minutes/week) and 2) diabetes (yes/no). Sociodemographic variables included age group (20-44 [referent], 45-64, 65-79), sex, race/ethnicity (White [referent], Black, Hispanic, and other adults), and poverty income ratio (low, middle, high-income [referent]). PA guideline was also considered as exposure for diabetes analysis. By accounting for the complex survey design, two weighted generalized Poisson models were used to conduct the analyses, adjusting for covariates. Results: Model 1 showed that participants aged 45-64 and 65-79 had 14% and 16% lower likelihood of meeting PA guidelines than those aged 20-44. Females had an 18 % lower likelihood of meeting PA guidelines than males. Furthermore, Black, Hispanic, and other racial/ethnic adults were 7%, 8%, and 12% less likely to meet the PA guidelines than White adults. Adults with low- and middle-income had 13% and 8% lower likelihood of meeting PA guidelines than those with high income. Model 2 showed that participants from 2017-2020 were 22% more likely to have diabetes (AOR = 1.22) than those from 2007-2008. Adults aged 45-64 and 65-79 years had a 4.35- and 7.36-times higher likelihood of having diabetes than those aged 20-44. Females had a 25% lower likelihood of having diabetes than males. Black, Hispanic, and other groups were 49%, 35%, and 73% more likely to have diabetes than White adults, respectively. Adults with low- and middle-income had a 52% and 32% higher likelihood of having diabetes than those with high income. Adults meeting PA guidelines had a 28% lower likelihood of having diabetes than those not meeting the PA guidelines. Conclusion: The study highlights persistent disparities in PA levels and diabetes across different sociodemographic groups within the U.S. population. Future interventions targeting diabetes should prioritize addressing these disparities among vulnerable populations who do not meet PA guidelines. Emphasis should be placed on promoting PA as an integral component of diabetes prevention.

Modeling Zero-inflated Count Data Using Generalized Poisson and Ordinal Logistic Regression Models in Medical Research.

In medical research, the study's design and statistical methods are pivotal, as they guide interpretation and conclusion. Selecting appropriate statistical models hinges on the distribution of the outcome measure. Count data, frequently used in medical research, often exhibit over-dispersion or zero inflation. Occasionally, count data are considered ordinal (with a maximum outcome value of 5), and this calls for the application of ordinal regression models. Various models exist for analyzing over-dispersed data such as negative binomial, generalized Poisson (GP), and ordinal regression model. This study aims to examine whether the GP model is a superior alternative to the ordinal logistic regression (OLR) model, specifically in the context of zero-inflated Poisson models using both simulated and real-time data. Simulated data were generated with varied estimates of regression coefficients, sample sizes, and various proportions of zeros. The GP and OLR models were compared using fit statistics. Additionally, comparisons were made using real-time datasets. The simulated results consistently revealed lower bias and mean squared error values in the GP model compared to the OLR model. The same trend was observed in real-time datasets, with the GP model consistently demonstrating lower standard errors. Except when the sample size was 1000 and the proportions of zeros were 30% and 40%, the Bayesian information criterion consistently favored the GP model over the OLR model. This study establishes that the proposed GP model offers a more advantageous alternative to the OLR model. Moreover, the GP model facilitates easier modeling and interpretation when compared to the OLR model.

Testing latent classes in gut microbiome data using generalized Poisson regression models.

Human microbiome research has gained increasing importance due to its critical roles in comprehending human health and disease. Within the realm of microbiome research, the data generated often involves operational taxonomic unit counts, which can frequently present challenges such as over-dispersion and zero-inflation. To address dispersion-related concerns, the generalized Poisson model offers a flexible solution, effectively handling data characterized by over-dispersion, equi-dispersion, and under-dispersion. Furthermore, the realm of zero-inflated generalized Poisson models provides a strategic avenue to simultaneously tackle both over-dispersion and zero-inflation. The phenomenon of zero-inflation frequently stems from the heterogeneous nature of study populations. It emerges when specific microbial taxa fail to thrive in the microbial community of certain subjects, consequently resulting in a consistent count of zeros for these individuals. This subset of subjects represents a latent class, where their zeros originate from the genuine absence of the microbial taxa. In this paper, we introduce a novel testing methodology designed to uncover such latent classes within generalized Poisson regression models. We establish a closed-form test statistic and deduce its asymptotic distribution based on estimating equations. To assess its efficacy, we conduct an extensive array of simulation studies, and further apply the test to detect latent classes in human gut microbiome data from the Bogalusa Heart Study.

Relationship Between Recreational Cannabis Use and Helicobacter pylori Infection.

Background: Cannabis plant extracts suppress gastric acid secretion and inflammation, and promote gastroduodenal ulcer healing, all of which are triggered by Helicobacter Pylori infection (HPI). Here, we evaluate the association between cannabis use and HPI among a representative community sample. Materials and Methods: We identified respondents who completed cannabis use questions and were tested for HPI (H. pylori IgG antibody seropositivity) from the National Health and Nutrition Examination Survey III dataset (n=4556). Cannabis usage was categorized as ever-use (ever, never), cumulative lifetime use (>10-times, 1-10-times, never), or recent use (>31-days-ago, within-31-days, never). We calculated the crude and adjusted risk (prevalence rate ratio, cPRR and aPRR) of having HPI with cannabis use using generalized Poisson models (SAS 9.4). The models were adjusted for demographics and risk factors for HPI. Results: The prevalence of HPI was lower among ever versus never cannabis users (18.6% vs. 33%, p<0.0001). Cannabis use was associated with a decreased risk of HPI (cPRR: 0.56 confidence interval [95% CI: 0.47-0.67]; p<0.0001), which persisted after adjusting for demographics (aPRR: 0.75 [95% CI: 0.63-0.90]; p=0.0016) and comorbidities (aPRR: 0.79 [95% CI: 0.66-0.95]; p=0.0145). Further, individuals with >10-times lifetime cannabis use had a decreased risk of HPI compared with those with 1-10-times lifetime use (aPRR: 0.70 [95% CI: 0.55-0.89]; p=0.0011) and never-users (aPRR: 0.65 [95% CI: 0.50-0.84]; p=0.0002). Conclusion: Recreational cannabis use is associated with diminished risk of HPI. These observations suggest the need for additional research assessing the effects of medical cannabis formulations on HPI.

Sex-difference in air pollution-related acute circulatory and respiratory mortality and hospitalization

BackgroundNumerous studies have estimated adverse effects of short-term exposure to ambient air pollution on public health. Few have focused on sex-differences, and results have been inconsistent. The purpose of this study was three-fold: to identify sex-differences in air pollution-related health outcomes; to examine sex-differences by cause and season; and to examine time trends in sex-differences. MethodsDaily data were collected on circulatory- and respiratory-related mortality (for 29 years) and cause-specific hospitalization (for 17 years) with hourly concentrations of ozone (O3), nitrogen dioxide (NO2), and fine particulate matter (PM2.5). For hospitalization, more specific causes were examined: ischemic heart disease (IHD), other heart disease (OHD), cerebrovascular disease (CEV), chronic lower respiratory diseases (CLRD), and Influenza/Pneumonia (InfPn). Generalized Poisson models were applied to 24 Canadian cities, and the city-specific estimates were combined for nationwide estimates for each sex using Bayesian hierarchical models. Finally, sex-differences were tested statistically based on their interval estimates, considering the correlation between sex-specific national estimates. ResultsSex-differences were more frequently observed for hospitalization than mortality, respiratory than circulatory health outcomes, and warm than cold season. For hospitalization, males were at higher risk (M > F) for warm season (OHD and InfPn from O3; IHD from NO2; and InfPn from PM2.5), but F > M for cold season (CEV from O3 and OHD from NO2). For mortality, we found F > M only for circulatory diseases from ozone during the warm season. Among the above-mentioned sex-differences, three cases showed consistent time trends over the years: while M > F for OHD from O3 and IHD from NO2, F > M for OHD from NO2. ConclusionsWe found that sex-differences in effect of ambient air pollution varied over health outcome, cause, season and time. In particular, the consistent trends (either F > M or M > F) across 17 years provide stronger evidence of sex-differences in hospitalizations, and warrant investigation in other populations.

Comparing of Car-Bym, Generalized Poisson, and Negative Binomial Models on Tuberculosis Data in Banyumas Districs

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 (&gt;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.

Discrimination between Some Over Dispersed Count Distributions

The Poisson inverse Gaussian and generalized Poisson distributions are widely used in modelling overdispersed count data which are commonly found in healthcare, insurance, engineering, econometric and ecology. The inverse trinomial distribution is a relatively new count distribution arising from a one-dimensional random walk model (Shimizu &amp; Yanagimoto, 1991). The Poisson inverse Gaussian distribution is a popular count model that has been proposed as an alternative to the negative binomial distribution. The inverse trinomial and generalized Poisson models possess a common characteristic of having a cubic variance function, while the Poisson inverse Gaussian has a quadratic variance function. The nature of the variance function seems to be an important property in modelling overdispersed count data. Hence it is of interest to be able to select among the three models in practical applications. This paper considers discrimination of three models based on the likelihood ratio statistic and computes via Monte Carlo simulation the probability of correct selection.

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.

Assessment of the Air Quality Health Index (AQHI) and four alternate AQHI-Plus amendments for wildfire seasons in British Columbia.

Wildfire smoke is an important source of air pollution associated with a range of cardiopulmonary health conditions. The Air Quality Health Index (AQHI) is the most widely used tool in Canada to communicate with the public about air pollution, but it may not adequately reflect health risks from wildfire smoke. The objective of this study was to evaluate the ability of the AQHI and four alternate AQHI-Plus amendments to predict adverse population health effects from wildfire smoke. The maximum 1-h values of the AQHI and the four amendments were calculated for each 48-h period of the wildfire seasons from 2010 to 2017 for 32 health units in British Columbia. Generalized Poisson models were used to estimate the association between these values and daily counts of five health outcomes: all-cause mortality; physician visits for all circulatory causes; visits for all respiratory causes, including asthma; asthma-specific visits; and dispensations of salbutamol sulfate (i.e., Ventolin®). Model fit was evaluated with the Akaike information criterion. The AQHI and the four amendments were all associated with all five health outcomes. The AQHI exhibited best fit to the all-cause mortality and circulatory physician visits during all wildfire seasons, while the 1-h PM2.5Only AQHI-Plus exhibited best fit to the asthma-related outcomes during all wildfire seasons. Individuals with common respiratory conditions such as asthma and chronic obstructive pulmonary disease are particularly susceptible to wildfire smoke. As such, the 1-h PM2.5Only AQHI-Plus amendment was recommended for communicating about potential health effects of air quality during wildfire seasons in BC.

Second primary cancers in non-Hodgkin lymphoma: Family history and survival.

Second primary cancers (SPCs) account for an increasing proportion of all cancer diagnoses and family history of cancer may be a risk factor for SPCs. Using the Swedish Family-Cancer Database on non-Hodgkin lymphoma (NHL), we assessed the influence of family history on risk of SPCs and of SPCs on survival. NHL patients were identified from the years 1958 to 2015 and generalized Poisson models were used to calculate relative risks (RRs) for SPCs and familial SPCs. Among 14,393 NHL patients, a total of 1,866 (13.0%) were diagnosed with SPC. Familial risk of nine particular cancers was associated with risks of these cancers as SPCs, with twofold to fivefold increase in RRs. At the end of a 25-year follow-up period, the survival probability for persons with SPC was only 20% of that for patients without SPC; the hazard ratio for SPC was 1.59 (95% CI: 1.46-1.72). Survival could be predicted by the prognostic groups based on first cancers and HRs increase systematically with worse prognosis yielding a trend of p = 4.6 × 10-5 . SPCs had deleterious consequences for survival in NHL patients. Family history was associated with increasing numbers of SPCs. Prevention of SPCs and their early detection is an important target in the overall strategy to improve survival in NHL patients. Counseling for avoidance of risk factors and targeted screening based on family history are feasible steps in risk reduction.

Financial Inclusion, Health-Seeking Behavior, and Health Outcomes Among Older Adults in Ghana.

This study examines the associations between financial inclusion, health-seeking behavior, and health-related outcomes in older persons in Ghana. Employing data from a 2016/2017 Aging, Health, Psychological Well-Being and Health-Seeking Behavior Study (N = 1,200; mean age = 66.2 years [standard deviation = 11.9], we estimated regression models of self-rated health (SRH), psychological distress (PD), and health-care use (HCU) on a variable representing compositional characteristics of financial inclusion. Multivariate logistic and generalized Poisson models showed that financial inclusion is positively associated with SRH (β = .104, standard error [SE] = .033, p < .001) but inversely related to both PD (β = .038, SE = .032, p < .005) and HCU (β = -.006, SE = .009, p < .05) independent of other factors. However, after adjusting for socioeconomic and health-related factors, the associations were tempered and the effect of SRH decreased by 0.094 and PD increased by 0.065 points but HCU became statistically insignificant (β = -.020, SE = .0114, p > .05). Financial services inclusion profoundly appears to buffer against and retard health-related challenges in later life. Social and health policies targeted at improving the health outcomes of older people should include and build on the growing recognition of the importance of inclusive financial services and strategies.

Changes in Accident & Emergency Visits and Return Visits in Relation to the Enforcement of Daylight Saving Time and Photoperiod.

Daylight saving time (DST) is a source of circadian disruption impinging on millions of people every year. Our aim was to assess modifications, if any, in the number, type, and outcome of Accident & Emergency (A&E) visits/return visits over the DST months. The study included 366,527 visits and 84,380 return visits to the A&E of Padova hospital (Northern Italy) over 3 periods between the years 2007 and 2016: period 1 (2 weeks prior to DST to 19 weeks after), period 2 (2 weeks prior to the return to "winter time" to 4 weeks after), and period 3 (5 consecutive non-DST weeks). For each A&E visit/return visit, information was obtained on triage severity code, main medical complaint, and outcome. Data were aggregated by day, cumulated over the years, and analyzed by generalized Poisson models. Generalized additive models for Poisson data were then used to include photoperiod as an additional covariate. An increase in A&E visits and return visits (mostly white codes, resulting in discharges) was observed a few weeks after the enforcement of DST and was significant over most weeks of period 1 (increase of ≈30 [2.8%] visits and ≈25 [10%] return visits per week per year). After the return to winter time, a decrease in absolute number of return visits was observed (mostly white codes, resulting in discharges), which was significant at weeks 3 and 4 of period 2 (decrease of ≅25 [10%] return visits per week per year). When photoperiod was taken into account, changes in A&E visits (and related white codes/discharges) were no longer significant, while changes in return visits (and related white codes/discharges) were still significant. In conclusion, changes in A&E visits/return visits were observed in relation to both DST and photoperiod, which are worthy of further study and could lead to modifications in A&E organization/staffing.

Zero-inflated models and estimation in zero-inflated Poisson distribution

ABSTRACTIn this paper, we briefly overview different zero-inflated probability distributions. We compare the performance of the estimates of Poisson, Generalized Poisson, ZIP, ZIGP and ZINB models through Mean square error (MSE), bias and Standard error (SE) when the samples are generated from ZIP distribution. We propose a new estimator referred to as probability estimator (PE) of inflation parameter of ZIP distribution based on moment estimator (ME) of the mean parameter and compare its performance with ME and maximum likelihood estimator (MLE) through a simulation study. We use the PE along with ME and MLE to fit ZIP distribution to various zero-inflated datasets and observe that the results do not differ significantly. We recommend using PE in place of MLE since it is easy to calculate and the simulation study in this paper demonstrates that the PE performs as good as MLE irrespective of the sample size.

Semiparametric models for multilevel overdispersed count data with extra zeros.

This study proposes semiparametric models for analysis of hierarchical count data containing excess zeros and overdispersion simultaneously. The methods discussed in this paper handle nonlinear covariate effects through flexible semiparametric multilevel regression techniques. This is performed by providing a comprehensive comparison of semiparametric multilevel zero-inflated negative binomial and semiparametric multilevel zero-inflated generalized Poisson models under the real and simulated data. An EM algorithm based on Newton-Raphson equations for maximum penalized likelihood estimation approach is developed. The performance of the proposed models is assessed by using a Monte Carlo simulation study. We also illustrated the methods by the analysis of decayed, missing, and filled teeth of children aged 5-14 years old.

Modeling crash frequency and severity using multinomial-generalized Poisson model with error components

Since the factors contributing to crash frequency and severity usually differ, an integrated model under the multinomial generalized Poisson (MGP) architecture is proposed to analyze simultaneously crash frequency and severity—making estimation results increasingly efficient and useful. Considering the substitution pattern among severity levels and the shared error structure, four models are proposed and compared—the MGP model with or without error components (EMGP and MGP models, respectively) and two nested generalized Poisson models (NGP model). A case study based on accident data for Taiwan's No. 1 Freeway is conducted. The results show that the EMGP model has the best goodness-of-fit and prediction accuracy indices. Additionally, estimation results show that factors contributing to crash frequency and severity differ markedly. Safety improvement strategies are proposed accordingly.

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.

Testing Approaches for Overdispersion in Poisson Regression versus the Generalized Poisson Model

Overdispersion is a common phenomenon in Poisson modeling, and the negative binomial (NB) model is frequently used to account for overdispersion. Testing approaches (Wald test, likelihood ratio test (LRT), and score test) for overdispersion in the Poisson regression versus the NB model are available. Because the generalized Poisson (GP) model is similar to the NB model, we consider the former as an alternate model for overdispersed count data. The score test has an advantage over the LRT and the Wald test in that the score test only requires that the parameter of interest be estimated under the null hypothesis. This paper proposes a score test for overdispersion based on the GP model and compares the power of the test with the LRT and Wald tests. A simulation study indicates the score test based on asymptotic standard Normal distribution is more appropriate in practical application for higher empirical power, however, it underestimates the nominal significance level, especially in small sample situations, and examples illustrate the results of comparing the candidate tests between the Poisson and GP models. A bootstrap test is also proposed to adjust the underestimation of nominal level in the score statistic when the sample size is small. The simulation study indicates the bootstrap test has significance level closer to nominal size and has uniformly greater power than the score test based on asymptotic standard Normal distribution. From a practical perspective, we suggest that, if the score test gives even a weak indication that the Poisson model is inappropriate, say at the 0.10 significance level, we advise the more accurate bootstrap procedure as a better test for comparing whether the GP model is more appropriate than Poisson model. Finally, the Vuong test is illustrated to choose between GP and NB2 models for the same dataset.

Zero-inflated generalized Poisson models with regression effects on the mean, dispersion and zero-inflation level applied to patent outsourcing rates

This paper focuses on an extension of zero-inflated generalized Poisson (ZIGP) regression models for count data. We discuss generalized Poisson (GP) models where dispersion is modelled by an additional model parameter. Moreover, zero-inflated models, in which overdispersion is assumed to be caused by an excessive number of zeros, are discussed. In addition to ZIGP models considered by several authors, we now allow for regression on the overdispersion and zero-inflation parameters. Consequently, we propose tools for an exploratory data analysis on the dispersion and zero-inflation level. An application dealing with outsourcing of patent filing processes will be used to compare these nonnested models. The model parameters are fitted by maximum likelihood using our R package ‘ZIGP’ available on the Comprehensive RArchive Network (CRAN). Asymptotic normality of the Maximum Likelihood (ML) estimates in this non-exponential setting is proven. Standard errors are estimated using the asymptotic normality of the estimates. Appropriate exploratory data analysis tools are developed. Also, a model comparison using Akaike Information Criterion (AIC) statistics and Vuong tests is carried out. For the given data, our extended ZIGP regression model will prove to be superior over GP and zero-inflated Poisson (ZIP) models, and even over ZIGP models, with constant overall dispersion and zero-inflation parameters demonstrating the usefulness of our proposed extensions.

Poisson mixture models for regression analysisof stand-level mortality

Periodic stand-level mortality data from permanent plots tend to be highly variable, skewed, and frequently contain many zero observations. Such data have commonly been modeled using nonlinear mortality functions fitted by least squares, and more recently by a two stage approach incorporating a logistic regression step. This study describes a set of nonlinear regression models that structure stochastic variation about a mortality function according to basic probability distributions appropriate for non-negative count data, including the Poisson, negative binomial (NB), and generalized Poisson (GP). Also considered are zero-inflated and hurdle modifications of these basic models. The models are developed and fit to mortality data from a loblolly pine (Pinus taeda L.) spacing trial with a conspicuous mode at 0. The sample data exhibit more variability than can be accommodated by a Poisson or modified Poisson model; the NB and GP models incorporate the extra-Poisson dispersion and offer an improved fit. A hurdle NB model best describes this sample, but, like the zero-inflated models and two-stage approach, modifies the interpretation of the mean structure and raises the question of overfitting. Considering both data-model agreement and the biological relevance of these models' components, the analysis suggests that the NB model offers a more compelling and credible inferential basis for fitting stand-level mortality functions.