A marginalized zero-inflated Poisson regression model with overall exposure effects.

Background: Under-five mortality rate, often known by its acronym U5MR, indicates the probability of dying between birth and five years of age, expressed per 1,000 live births. Globally, 16,000 children under-five still die every day. Especially in Sub-Saharan Africa every 1 child in 12, dying before his or her fifth birthday. This study aims to identify the determinants of under-five mortality among women in child bearing age group of Tach-Armachiho district using count regression models. Methods: For achieving the objective, a two-stage random sampling technique (simple random sampling and systematic random sampling techniques in the first and second stages respectively) was used to select women respondents. The sample survey conducted in Tach-Armachiho district considered a total of 3815 households of women aged 15 to 49 years out of which the information was collected from 446 selected women through interviewer administrated questionnaire. Results: The descriptive statistics result showed that in the district 16.6% of mothers have faced the problem of at least one under-five death. In this study, Poisson regression, negative binomial, zero-inflated Poisson and zero-inflated negative binomial regression models were applied for data analysis. Each of these count models were compared by different statistical tests. So that, zero-inflated poisson regression model was found to be the best fit for the collected data. Results of the zero-inflated Poisson regression model showed that education of husband, source of water, mother occupation, kebele of mother, prenatal care, place of delivery, place of residence, wealth of house hold, average birth interval and average breast feeding were found to be statistically significant determinants of under-five mortality. Conclusions: In this study, it was found that the factors like average birth interval and average breast feeding were found to be statistically significant factors in both groups (not always zero category and always zero category) with under-five child deathwhereas education of husband, source of water, place of delivery, mother occupation and wealth index of the household have significant effect on under-five mortality under not always zero group. Place of residence, kebele of mother and prenatal care have a significant effect on under-five mortality in TachArmachiho district on inflated group

In this paper we address the problem of building user models that can predict the rate at which individuals consume items from a finite set, including items they have consumed in the past and items that are new. This combination of repeat and new item consumption is common in applications such as listening to music, visiting web sites, and purchasing products. We use zero-inflated Poisson (ZIP) regression models as the basis for our modeling approach, leading to a general framework for modeling user-item consumption rates over time. We show that these models are more flexible in capturing user behavior than alternatives such as well-known latent factor models based on matrix factorization. We compare the performance of ZIP regression and latent factor models on three different data sets involving music, restaurant reviews, and social media. The ZIP regression models are systematically more accurate across all three data sets and across different prediction metrics.

SummaryIn psychosocial and behavioral studies count outcomes recording the frequencies of the occurrence of some health or behavior outcomes (such as the number of unprotected sexual behaviors during a period of time) often contain a preponderance of zeroes because of the presence of ‘structural zeroes’ that occur when some subjects are not at risk for the behavior of interest. Unlike random zeroes (responses that can be greater than zero, but are zero due to sampling variability), structural zeroes are usually very different, both statistically and clinically. False interpretations of results and study findings may result if differences in the two types of zeroes are ignored. However, in practice, the status of the structural zeroes is often not observed and this latent nature complicates the data analysis. In this article, we focus on one model, the zero-inflated Poisson (ZIP) regression model that is commonly used to address zero-inflated data. We first give a brief overview of the issues of structural zeroes and the ZIP model. We then given an illustration of ZIP with data from a study on HIV-risk sexual behaviors among adolescent girls. Sample codes in SAS and Stata are also included to help perform and explain ZIP analyses.

Testing overdispersion in the zero-inflated Poisson model

ObjectiveTo propose a more realistic model for disease cluster detection, through a modification of the spatial scan statistic to account simultaneously for inflated zeros and overdispersion.IntroductionSpatial Scan Statistics [1] usually assume Poisson or Binomial distributed data, which is not adequate in many disease surveillance scenarios. For example, small areas distant from hospitals may exhibit a smaller number of cases than expected in those simple models. Also, underreporting may occur in underdeveloped regions, due to inefficient data collection or the difficulty to access remote sites. Those factors generate excess zero case counts or overdispersion, inducing a violation of the statistical model and also increasing the type I error (false alarms). Overdispersion occurs when data variance is greater than the predicted by the used model. To accommodate it, an extra parameter must be included; in the Poisson model, one makes the variance equal to the mean.MethodsTools like the Generalized Poisson (GP) and the Double Poisson [2] may be a better option for this kind of problem, modeling separately the mean and variance, which could be easily adjusted by covariates. When excess zeros occur, the Zero Inflated Poisson (ZIP) model is used, although ZIP’s estimated parameters may be severely biased if nonzero counts are too dispersed, compared to the Poisson distribution. In this case the Inflated Zero models for the Generalized Poisson (ZIGP), Double Poisson (ZIDP) and Negative Binomial (ZINB) could be good alternatives to the joint modeling of excess zeros and overdispersion. By one hand, Zero Inflated Poisson (ZIP) models were proposed using the spatial scan statistic to deal with the excess zeros [3]. By the other hand, another spatial scan statistic was based on a Poisson-Gamma mixture model for overdispersion [4]. In this work we present a model which includes inflated zeros and overdispersion simultaneously, based on the ZIDP model. Let the parameter p indicate the zero inflation. As the the remaining parameters of the observed cases map and the parameter p are not independent, the likelihood maximization process is not straightforward; it becomes even more complicated when we include covariates in the analysis. To solve this problem we introduce a vector of latent variables in order to factorize the likelihood, and obtain a facilitator for the maximization process using the E-M (Expectation-Maximization) algorithm. We derive the formulas to maximize iteratively the likelihood, and implement a computer program using the E-M algorithm to estimate the parameters under null and alternative hypothesis. The p-value is obtained via the Fast Double Bootstrap Test [5].ResultsNumerical simulations are conducted to assess the effectiveness of the method. We present results for Hanseniasis surveillance in the Brazilian Amazon in 2010 using this technique. We obtain the most likely spatial clusters for the Poisson, ZIP, Poisson-Gamma mixture and ZIDP models and compare the results.ConclusionsThe Zero Inflated Double Poisson Spatial Scan Statistic for disease cluster detection incorporates the flexibility of previous models, accounting for inflated zeros and overdispersion simultaneously.The Hanseniasis study case map, due to excess of zero cases counts in many municipalities of the Brazilian Amazon and the presence of overdispersion, was a good benchmark to test the ZIDP model. The results obtained are easier to understand compared to each of the previous spatial scan statistic models, the Zero Inflated Poisson (ZIP) model and the Poisson-Gamma mixture model for overdispersion, taken separetely. The E-M algorithm and the Fast Double Bootstrap test are computationally efficient for this type of problem.

The two most popular models inwell-known count regression models are Poisson and negative binomial regression models. Poisson regression is a generalized linear model form of regression analysis used to model count data and contingency tables. Poisson regression assumes the response variable Y has a Poisson distribution, and assumes the logarithm of its expected value can be modeled by a linear combination of unknown parameters. Negative binomial regression is similar to regular multiple regression except that the dependent (Y) variables an observed count that follows the negative binomial distribution. This research studies some factors affecting divorce using Poisson and negative binomial regression models. The factors are unemployment rate, inflation and Gini coefficient. The data were taken from the website of the Statistics Center for the years 2002 to 2023.Under the Poisson regression model, each factor has been reported to have an effect on the divorce rate. The two factors of inflation and unemployment had a direct effect and income inequality factors had an inverse effect on the divorce rate. But, under the negative binomial regression model, only inflation has an effect on the number of divorces. It is worth noting that according to the AIC values, the negative binomial regression model has a better fit than the Poisson regression model because its AIC value is lower.

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.

This paper makes a theoretical contribution by presenting a detailed derivation of a zero-inflated Poisson (ZIP) model, and then deriving the parameters of the ZIP model using a fishing data set. This model has several practical applications, and is largely performed to model count data that have an excess number of zero counts. In the scope of the paper, we introduce the complete formulae, the likelihood and log-likelihood functions and the estimating equation of the ZIP model. We then investigate the theory of large sample properties of this model under some regularity conditions. A simulation study and a fishing data set are studied for the ZIP model. The results in the actual application in this work are meaningful, useful and crucial in reality. The results also provide reliable evidence for obtaining the largest number of fish while fishing. This is the contribution of this research in terms of applications. Finally, the important applications of this model in practice, some conclusions, and future work is also presented for consideration.

Most of the existing methodologies for evaluating heterogeneity in zero-inflated Poisson (ZIP) models are often assuming that the Poisson mean is a function of nuisance parameters. However, these nuisance parameters can be misspecified when performing these methodologies, the validity and the power of the test may be affected. In this article, we primarily focus on investigating the impact of misspecification on the performance of score test for homogeneity in ZIP models. Through an intensive simulation study, we find that: 1) under misspecification, the limiting distribution of the score test statistic under the null no longer follows a distribution. A parametric bootstrap methodology is suggested to use to find the true null limiting distribution of the score test statistic; 2) the power of the test decreases as the number of covariates in the Poisson mean increases. The test with a constant Poisson mean has the highest power, even compared to the test with a well-specified mean. At last, simulation results are applied to the Wuhan Inpatient Care Insurance data which contain excess zeros.

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.

Data on the demand for medical care is usually measured by a number of different counts. These count data are most often correlated and subject to high proportions of zeros. However, excess zeros and the dependence between these data can jointly affect several utilization measures.In this paper, the zero-inflated bivariate Poisson regression model (ZIBP) was used to analyze health-care utilization data. First, the asymptotic properties of the maximum likelihood estimator (MLE) of this model were investigated theoretically. Then, a simulation study is conducted to evaluate the behaviour of the estimator in finite samples. Finally, an application of the ZIBP model to health care demand data is provided by way of illustration.

Data on the demand for medical care is usually measured by a number of different counts. These count data are most often correlated and subject to high proportions of zeros. However, excess zeros and the dependence between these data can jointly affect several utilization measures.In this paper, the zero-inflated bivariate Poisson regression model (ZIBP) was used to analyze health-care utilization data. First, the asymptotic properties of the maximum likelihood estimator (MLE) of this model were investigated theoretically.Then, a simulation study is conducted to evaluate the behaviour of the estimator in finite samples. Finally, an application of the ZIBP model to health care demand data is provided by way of illustration.

Little is known about the introduced European woodwasp, Sirex noctilio F. (Hymenoptera: Siricidae), and its hymenopteran parasitoid complex in North America. To assess within-tree and landscape-level densities and distributions of these insects, and develop a more cost effective approach for sampling and monitoring S. noctilio, 18 infested pines (12 P. resinosa Aiton and six P. sylvestris L.) were felled from six stands within three regions in central New York and cut into 0.5-m bolts. Bolts were carefully split to recover all siricids (S. noctilio and native siricids) and parasitoids. In total, 2,558 siricids were recovered; 1,972 siricid larvae and 586 teneral adult S. noctilio. Parasitism of siricids, a majority of which were S. noctilio based on larval rearing results, was 16.4% with Ibalia leucospoides ensiger Norton causing 10.7% of the documented mortality. Numbers of siricids and parasitoids declined 33-86% from the northern to the southern sampling regions, peak insect densities occurred in sections of the bole 15-19 cm in diameter and numbers of insects were generally higher in P. sylvestris than P. resinosa according to the highest ranked zero-inflated poisson and probit regression models. Bark thickness was not correlated with siricid or parasitoid species densities. We also describe sampling plans where as few as two 0.5-m samples from infested trees provided reliable within-tree insect densities.

Weather Variability and the Incidence of Cryptosporidiosis: Comparison of Time Series Poisson Regression and SARIMA Models

Bayesian signal detection methods, including the multiitem gamma Poisson shrinker (MGPS), assume a Poisson distribution for the number of reports. However, the database of the adverse event reporting system often has a large number of zero-count cells. A zero-inflated Poisson (ZIP) distribution can be more appropriate in this situation than a Poisson distribution. Few studies have considered ZIP-based models for Bayesian signal detection. In addition, most studies on Bayesian signal detection methods include simulation studies conducted assuming a gamma distribution for the prior. Herein, we extend the MGPS method using the ZIP model and apply various prior distributions. We evaluated the extended methods through an extensive simulation using more varied settings for the model and prior than existing methods. We varied the total number of reports, the number of true signals, the relative reporting rate, and the probability of observing a true zero. The results show that as the probability of observing a zero count increased, methods based on the ZIP model outperformed the Poisson model in most cases. We also found that using the mixture log-normal prior resulted in more conservative detection than other priors when the relative reporting rate is high. Conversely, more signals were found when using the mixture truncated normal distributions. We applied the Bayesian signal detection methods to data from the Korea Adverse Event Reporting System from 2012 to 2016.