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Time series of proportions are often encountered in applications such as ecology, environmental science and public health. Strategies for such data include linear regression after logistic transformation. Though easy to fit, the transformation approach renders covariate effects uninterpretable on the scale on which they were observed owing to Jensen's inequality. An alternative to the transformation approach has been to directly model the response via the beta distribution. In this paper, we extend zero-inflated beta regression models for independent proportions to time series data that is bounded over the unit interval and that may take on zero values. Estimation is within the partial-likelihood framework and is computationally feasible to implement. We outline the asymptotic theory of our maximum partial likelihood estimators under mild regularity conditions and investigate their bias and variability using simulation studies. The utility of our method is illustrated using two real data examples. [ABSTRACT FROM AUTHOR]

Distribution selection plays a key role in parametric statistics. Choosing one from a set of candidate distributions that best fits the sample data is a recurring task in a large number of statistical analysis. The choice of a misspecified and/or poor fitted distribution can lead to unreliable results and conclusions. Although distribution selection has been widely studied regarding goodness of fit procedures, less attention has been given on how the sampling design impacts the chance of choosing the most suitable distribution. In this work we address the performance of ranked set sampling (RSS), extreme ranked set sampling (ERSS), and mixture ranked set sampling (MRSS) in distribution selection. In particular, we focus on count data, an important and very usual class of random variables. A comprehensive simulation study was carried out, accounting for five distributions: Poisson, negative binomial, geometric, zero-inflated Poisson, and zero-inflated negative binomial. Results show that RSS and extensions performed better than simple random sampling (SRS) under perfect ranking. When ranking errors are present, better efficiency depends on how accurate is the ranking criterion, and the different RSS-based designs also differ in terms of their robustness. Findings are reinforced by additional simulation based on two real data sets. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

High throughput sequencing data collected to study the microbiome provide information in the form of relative abundances and should be treated as compositions. Although many approaches including scaling and rarefaction have been proposed for converting raw count data into microbial compositions, most of these methods simply return zero values for zero counts. However, zeros can distort downstream analyses, and they can also pose problems for composition-aware methods. This problem is exacerbated with microbiome abundance data because they are sparse with excessive zeros. In addition to data sparsity, microbial composition estimation depends on other data characteristics such as high dimensionality, over-dispersion, and complex co-occurrence relationships. To address these challenges, we introduce a zero-inflated probabilistic PCA (ZIPPCA) model that accounts for the compositional nature of microbiome data, and propose an empirical Bayes approach to estimate microbial compositions. An efficient iterative algorithm, called classification variational approximation, is developed for carrying out maximum likelihood estimation. Moreover, we study the consistency and asymptotic normality of variational approximation estimator from the perspective of profile M-estimation. Extensive simulations and an application to a dataset from the Human Microbiome Project are presented to compare the performance of the proposed method with that of the existing methods. The method is implemented in R and available at . for this article are available online. [ABSTRACT FROM AUTHOR]

An integer-valued ARCH process with a conditional zero-inflated binomial distribution is introduced. Stationarity, ergodicity and the autocovariance structure are studied as well as the estimation of parameters by conditional maximum likelihood. Numerical studies and an application to the number of hours in a day in which the prices of electricity for Portugal and Spain are different illustrate the performance of this model when compared with others. [ABSTRACT FROM AUTHOR]

We consider two classes of exponential dispersion models of discrete probability distributions which are defined by specifying their variance functions in their mean value parameterization. These classes were considered in our earlier paper as models of overdispersed zero-inflated distributions. In this paper we analyze the application of these classes to fit count data having overdispersed and zero-inflated statistics. For this reason, we first elaborate on the computational aspects of the probability distributions, before we consider the data fitting with our models. We execute an extensive comparison with other statistical models that are recently proposed, on both real data sets, and simulated data sets. Our findings are that our framework is a flexible tool that gives excellent results in a wide range of cases. Moreover, specifically when the data characteristics show also large skewness and kurtosis our models perform best. [ABSTRACT FROM AUTHOR]

In microbiome studies, it is of interest to use a sample from a population of microbes, such as the gut microbiota community, to estimate the population proportion of these taxa. However, due to biases introduced in sampling and preprocessing steps, these observed taxa abundances may not reflect true taxa abundance patterns in the ecosystem. Repeated measures, including longitudinal study designs, may be potential solutions to mitigate the discrepancy between observed abundances and true underlying abundances. Yet, widely observed zero-inflation and over-dispersion issues can distort downstream statistical analyses aiming to associate taxa abundances with covariates of interest. To this end, we propose a Zero-Inflated Poisson Gamma (ZIPG) model framework to address these aforementioned challenges. From a perspective of measurement errors, we accommodate the discrepancy between observations and truths by decomposing the mean parameter in Poisson regression into a true abundance level and a multiplicative measurement of sampling variability from the microbial ecosystem. Then, we provide a flexible ZIPG model framework by connecting both the mean abundance and the variability of abundances to different covariates, and build valid statistical inference procedures for both parameter estimation and hypothesis testing. Through comprehensive simulation studies and real data applications, the proposed ZIPG method provides significant insights into distinguished differential variability and mean abundance. for this article are available online. [ABSTRACT FROM AUTHOR]

Unobserved heterogeneity causing overdispersion and the excessive number of zeros take a prominent place in the methodological development on count modeling. An insight into the mechanisms that induce heterogeneity is required for better understanding of the phenomenon of overdispersion. When the heterogeneity is sourced by the stochastic component of the model, the use of a heterogenous Poisson distribution for this part encounters as an elegant solution. Hierarchical design of the study is also responsible for the heterogeneity as the unobservable effects at various levels also contribute to the overdispersion. Zero-inflation, heterogeneity and multilevel nature in the count data present special challenges in their own respect, however the presence of all in one study adds more challenges to the modeling strategies. This study therefore is designed to merge the attractive features of the separate strand of the solutions in order to face such a comprehensive challenge. This study differs from the previous attempts by the choice of two recently developed heterogeneous distributions, namely Poisson–Lindley (PL) and Poisson–Ailamujia (PA) for the truncated part. Using generalized linear mixed modeling settings, predictive performances of the multilevel PL and PA models and their hurdle counterparts were assessed within a comprehensive simulation study in terms of bias, precision and accuracy measures. Multilevel models were applied to two separate real world examples for the assessment of practical implications of the new models proposed in this study. [ABSTRACT FROM AUTHOR]

This paper aims to discuss the Bayesian estimation approach for the zero-inflated cure class of models, which extends the standard cure model by accommodating zero-inflated data in the survival analysis context. A comprehensive simulation study is carried out to assess the performance of the estimation procedure. A new estimation methodology is illustrated using a real dataset related to women diagnosed with invasive cervical cancer in Brazil. [ABSTRACT FROM AUTHOR]

An essential measure of hip fracture (HF) rehabilitation, the amount of physical therapy (PT) used per patient, has been severely understudied. This study (1) evaluates post-acute PT use after HF in Estonia, (2) presents causal variation modelling for examining inter- and intra-regional disparities, and (3) analyses its temporal trends. This retrospective cohort study used validated population-wide health data, including patients aged ≥50 years, with an index HF diagnosed between January 2009 and September 2017. Patients' 6-month PT use was analysed and reported separately for acute and post-acute phases. While most of the included 11,461 patients received acute rehabilitation, only 40% of them received post-acute PT by a median of 6 h. Analyses based on measures of central tendency revealed 2.5 to 2.6-fold inter-regional differences in HF post-acute rehabilitation. Variation modelling additionally detected intra-regional disparities, showing imbalances in the fairness of allocating local rehabilitation resources between a county's patients. This study demonstrates the advantages of causal variation modelling for identifying inter- and intra-regional disparities in rehabilitation. The analyses revealed persisting large multi-level disparities and accompanying overall inaccessibility of PT in HF rehabilitation in Estonia, showing an urgent need for system-wide improvements. This study demonstrates the advantages of causal variation modelling for identifying inter- and intra-regional disparities in rehabilitation, using an essential outcome measure – used physical therapy hours. The study revealed large multi-level disparities and overall inaccessibility of physical therapy in hip fracture rehabilitation in Estonia, showing an urgent need for system-wide improvements. This study expands our knowledge on unstudied topics – hip fracture post-acute care and long-term physical therapy use. This regional analysis provides the first evidence-based regional-level basis for improving the rehabilitation system in Estonia. [ABSTRACT FROM AUTHOR]

In obstetrics and gynecology, knowledge about how women's features are associated with childbirth is important. This leads to establishing guidelines and can help managers to describe the dynamics of pregnant women's hospital stays. Then, time is a variable of great importance and can be described by survival models. An issue that should be considered in the modeling is the inclusion of women for whom the duration of labor cannot be observed due to fetal death, generating a proportion of times equal to zero. Additionally, another proportion of women's time may be censored due to some intervention. The aim of this paper was to present the Log-Normal zero-inflated cure regression model and to evaluate likelihood-based parameter estimation by a simulation study. In general, the inference procedures showed a better performance for larger samples and low proportions of zero inflation and cure. To exemplify how this model can be an important tool for investigating the course of the childbirth process, we considered the Better Outcomes in Labor Difficulty project dataset and showed that parity and educational level are associated with the main outcomes. We acknowledge the World Health Organization for granting us permission to use the dataset. [ABSTRACT FROM AUTHOR]

Multivariate claim data are common in insurance applications, for example, claims of each policyholder from different types of insurance coverages. Understanding the dependencies among such multivariate risks is critical to the solvency and profitability of insurers. Effectively modeling insurance claim data is challenging due to their special complexities. At the policyholder level, claim outcomes usually follow a two-part mixed distribution: a probability mass at zero corresponding to no claim and an otherwise positive claim from a skewed and long-tailed distribution. To simultaneously accommodate the complex features of the marginal distributions while flexibly quantifying the dependencies among multivariate claims, copula models are commonly used. Although a substantial body of literature focusing on copulas with continuous outcomes has emerged, some key steps do not carry over to mixed data. In particular, existing nonparametric copula estimators are not consistent for mixed data, and thus copula specification and diagnostics for mixed outcomes have been a problem. However, insurance is a closely regulated industry in which model validation is particularly important, and it is essential to develop a baseline nonparametric copula estimator to identify the underlying dependence structure. In this article, we fill in this gap by developing a nonparametric copula estimator for mixed data. We show the uniform convergence of the proposed nonparametric copula estimator. Through simulation studies, we demonstrate that the proportion of zeros plays a key role in the finite sample performance of the proposed estimator. Using the claim data from the Wisconsin Local Government Property Insurance Fund, we illustrate that our nonparametric copula estimator can assist analysts in identifying important features of the underlying dependence structure, revealing how different claims or risks are related to one another. [ABSTRACT FROM AUTHOR]

Hundreds of autism risk genes have been reported recently, mainly based on genetic studies where these risk genes have more de novo mutations in autism subjects than healthy controls. However, as a complex disease, autism is likely associated with more risk genes and many of them may not be identifiable through de novo mutations. We hypothesize that more autism risk genes can be identified through their connections with known autism risk genes in personalized gene–gene interaction graphs. We estimate such personalized graphs using single-cell RNA sequencing (scRNA-seq) while appropriately modeling the cell dependence and possible zero-inflation in the scRNA-seq data. The sample size, which is the number of cells per individual, ranges from 891 to 1241 in our case study using scRNA-seq data in autism subjects and controls. We consider 1500 genes in our analysis. Since the number of genes is larger or comparable to the sample size, we perform penalized estimation. We score each gene's relevance by applying a simple graph kernel smoothing method to each personalized graph. The molecular functions of the top-scored genes are related to autism diseases. For example, a candidate gene RYR2 that encodes protein ryanodine receptor 2 is involved in neurotransmission, a process that is impaired in ASD patients. While our method provides a systemic and unbiased approach to prioritize autism risk genes, the relevance of these genes needs to be further validated in functional studies. for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement. [ABSTRACT FROM AUTHOR]

The coevolution between human and bacteria colonizing the human body has profound implications for heath and development, with a growing body of evidence linking the altered microbiome composition with a wide array of disease states. Yet dimension reduction and visualization analysis of microbiome data are still in their infancy and many challenges exist. In this article, we introduce a general framework, zero-inflated probabilistic principal component analysis (ZIPPCA), for dimension reduction and data ordination of multivariate abundance data, and propose an efficient variational approximation method for estimation, inference, and prediction. Extensive simulations show that the proposed method outperforms algorithm-based methods and compares favorably with existing model-based methods. We further apply our method to a gut microbiome dataset for visualization analysis of community composition across age and geography. The method is implemented in R and available at . [ABSTRACT FROM AUTHOR]

Basic negative binomial models can only capture over-dispersed count responses, because the variance of the distribution is always greater than the mean value. So, they are not the best selection when the data are under-dispersed or have less dispersion than the negative binomial. Over the last years, a variety of new distributions that can account a wide range of dispersion in count data, have been introduced. One of these novel distributions is Conway–Maxwell type negative binomial distribution. In biomedical studies, it is common to demonstrate excess zeros and a pattern of dispersion in count data. Also, the observations may be correlated in clusters or longitudinally. Here, we propose a multilevel zero-inflated Conway–Maxwell type negative binomial model. Statistical inference is employed via an expectation-maximization algorithm for the parameter estimation. The model performance is illustrated by simulation studies and with a real data set. [ABSTRACT FROM AUTHOR]

Count time series data with excess zeros are observed in several applied disciplines. When these zero-inflated counts are sequentially recorded, they might result in serial dependence. Ignoring the zero-inflation and the serial dependence might produce inaccurate results. In this paper, Markov zero-inflated count time series models based on a joint distribution on consecutive observations are proposed. The joint distribution function of the consecutive observations is constructed through copula functions. First- and second-order Markov chains are considered with the univariate margins of zero-inflated Poisson (ZIP), zero-inflated negative binomial (ZINB), or zero-inflated Conway–Maxwell–Poisson (ZICMP) distributions. Under the Markov models, bivariate copula functions such as the bivariate Gaussian, Frank, and Gumbel are chosen to construct a bivariate distribution of two consecutive observations. Moreover, the trivariate Gaussian and max-infinitely divisible copula functions are considered to build the joint distribution of three consecutive observations. Likelihood-based inference is performed and asymptotic properties are studied. To evaluate the estimation method and the asymptotic results, simulated examples are studied. The proposed class of models are applied to sandstorm counts example. The results suggest that the proposed models have some advantages over some of the models in the literature for modeling zero-inflated count time series data. [ABSTRACT FROM AUTHOR]

Psychiatric syndromes in dementia are often derived from the Neuropsychiatric Inventory (NPI) using principal component analysis (PCA). The validity of this statistical approach can be questioned, since the excessive proportion of zeros and skewness of NPI items may distort the estimated relations between the items. We propose a novel version of PCA, ZIBP-PCA, where a zero-inflated bivariate Poisson (ZIBP) distribution models the pairwise covariance between the NPI items. We compared the performance of the method to classical PCA under zero-inflation using simulations, and in two dementia-cohorts (N = 830, N = 1349). Simulations showed that component loadings from PCA were biased due to zero-inflation, while the loadings of ZIBP-PCA remained unaffected. ZIBP-PCA obtained a simpler component structure of "psychosis," "mood" and "agitation" in both dementia-cohorts, compared to PCA. The principal components from ZIBP-PCA had component loadings as follows: First, the component interpreted as "psychosis" was loaded by the items delusions and hallucinations. Second, the "mood" component was loaded by depression and anxiety. Finally, the "agitation" component was loaded by irritability and aggression. In conclusion, PCA is not equipped to handle zero-inflation. Using the NPI, PCA fails to identify components with a valid interpretation, while ZIBP-PCA estimates simple and interpretable components to characterize the psychopathology of dementia. [ABSTRACT FROM AUTHOR]

Residual analysis is a useful tool for checking lack of fit and for providing insight into model improvement. However, literature on residual analysis and the goodness of fit for hidden Markov models (HMMs) is limited. As HMMs with complex structures are increasingly used to accommodate different types of data, there is a need for further tools to check the validity of models applied to real world data. We review model checking methods for HMMs and develop new methods motivated by a particular case study involving a two-dimensional HMM developed for time series with many null events. We propose new residual analysis and stochastic reconstruction methods, which are adapted from model checking techniques for point process models. We apply the new methods to the case study model and discuss their adequacy. We find that there is not one "best" test for diagnostics but that our new methods have some advantages over previously developed tools. The importance of multiple tests for complex HMMs is highlighted and we use the results of our model checking to provide suggestions for possible improvements to the case study model. for this article are available online. [ABSTRACT FROM AUTHOR]

For count responses, there are situations in biomedical and sociological applications in which extra zeroes occur. Modeling correlated (e.g. repeated measures and clustered) zero-inflated count data includes special challenges because the correlation between measurements for a subject or a cluster needs to be taken into account. Moreover, zero-inflated count data are often faced with over/under dispersion problem. In this paper, we propose a random effect model for repeated measurements or clustered data with over/under dispersed response called random effect zero-inflated exponentiated-exponential geometric regression model. The proposed method was illustrated through real examples. The performance of the model and asymptotical properties of the estimations were investigated using simulation studies. [ABSTRACT FROM AUTHOR]

We develop a constrained extremely zero inflated joint (CEZIJ) modeling framework for simultaneously analyzing player activity, engagement, and dropouts (churns) in app-based mobile freemium games. Our proposed framework addresses the complex interdependencies between a player's decision to use a freemium product, the extent of her direct and indirect engagement with the product and her decision to permanently drop its usage. CEZIJ extends the existing class of joint models for longitudinal and survival data in several ways. It not only accommodates extremely zero-inflated responses in a joint model setting but also incorporates domain-specific, convex structural constraints on the model parameters. Longitudinal data from app-based mobile games usually exhibit a large set of potential predictors and choosing the relevant set of predictors is highly desirable for various purposes including improved predictability. To achieve this goal, CEZIJ conducts simultaneous, coordinated selection of fixed and random effects in high-dimensional penalized generalized linear mixed models. For analyzing such large-scale datasets, variable selection and estimation are conducted via a distributed computing based split-and-conquer approach that massively increases scalability and provides better predictive performance over competing predictive methods. Our results reveal codependencies between varied player characteristics that promote player activity and engagement. Furthermore, the predicted churn probabilities exhibit idiosyncratic clusters of player profiles over time based on which marketers and game managers can segment the playing population for improved monetization of app-based freemium games. for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement. [ABSTRACT FROM AUTHOR]

The zero-inflated regression models such as zero-inflated Poisson (ZIP), zero-inflated negative binomial (ZINB) or zero-inflated generalized Poisson (ZIGP) regression models can model the count data with excess zeros. The ZINB model can handle over-dispersed and the ZIGP model can handle the over or under-dispersed count data with excess zeros as well. Moreover, the count data may be correlated because of data collection procedure or special study design. The clustered sampling approach is one of the examples in which the correlation among subjects could be defined. In such situations, a marginal model using generalized estimating equation (GEE) approach can incorporate these correlations and lead up to the relationships at the population level. In this study, the GEE-based zero-inflated generalized Poisson regression model was proposed to fit over and under-dispersed clustered count data with excess zeros. [ABSTRACT FROM AUTHOR]

Purpose: The goal was to compare the micronucleus (MN) and dicentric plus ring chromosomes (D + R) assays for dose assessment in cases of partial body irradiations (PBI). Materials and methods: We constructed calibration curves for each assay at doses ranging from 0 to 5 Gy of X-rays at dose rate of 0.275 Gy/min. To simulate partial-body exposures, blood samples from two donors were irradiated with 0.5, 1, 2 and 4 Gy and the ratios of irradiated to unirradiated blood were 25, 50, and 100%. Different tests were used to confirm if all samples were overdispersed or zero-inflated and for partial-body dose assessment we used the Qdr, Dolphin and Bayesian model. Results: In our samples for D + R calibration curve, practically all doses agreed with Poisson assumption, but MN exhibited overdispersed and zero-inflated cellular distributions. The exact Poisson tests and zero-inflated tests demonstrate that virtually all samples of D + R from PBI simulation fit the Poisson distribution and were not zero-inflated, but the MN samples were also overdispersed and zero-inflated. In the partial-body estimation, when Qdr and Dolphin methods were used the D + R results were better than MN, but the doses estimation defined by the Bayesian methodology were more accurate than the classical methods. Conclusions: Dicentric chromosomes continue to prove to be the best biological marker for dose assessment. However exposure scenarios of partial-body estimation, overdispersion and zero-inflation may not occur, it being a critical point not only for dose assessment, but also to confirm partial-body exposure. MN could be used as alternative assay for partial-body dose estimation, but in case of an accident without any information, the MN assay could not define whether the accident was a whole-body irradiation (WBI) or a PBI. [ABSTRACT FROM AUTHOR]

In this paper, we propose the use of the Data Cloning (DC) approach to estimate parameter-driven zero-inflated Poisson and Negative Binomial models for time series of counts. The data cloning algorithm obtains the familiar maximum likelihood estimators and their standard errors via a fully Bayesian estimation. This provides some computational ease as well as inferential tools such as confidence intervals and diagnostic methods which, otherwise, are not readily available for parameter-driven models. To illustrate the performance of the proposed method, we use Monte Carlo Simulations and real data on asthma-related emergency department visits in the Canadian province of Ontario. [ABSTRACT FROM AUTHOR]

Commonly used methods of evaluating the impact of marketing communications during political elections struggle to account for respondents' exposures to these communications due to the problems associated with recall bias. In addition, they completely fail to account for the impact of mediated or earned communications, such as newspaper articles or television news, that are typically not within the control of the advertising party, nor are they effectively able to monitor consumers' perceptual responses over time. This study based on a new data collection technique using cell-phone text messaging (called real-time experience tracking or RET) offers the potential to address these weaknesses. We propose an RET-based model of the impact of communications and apply it to a unique choice situation: voting behavior during the 2010 UK general election, which was dominated by three political parties. We develop a Bayesian zero-inflated dynamic multinomial choice model that enables the joint modeling of: the interplay and dynamics associated with the individual voter's choice intentions over time, actual vote, and the heterogeneity in the exposure to marketing communications over time. Results reveal the differential impact over time of paid and earned media, demonstrate a synergy between the two, and show the particular importance of exposure valence and not just frequency, contrary to the predominant practitioner emphasis on share-of-voice metrics. Results also suggest that while earned media have a reducing impact on voting intentions as the final choice approaches, their valence continues to influence the final vote: a difference between drivers of intentions and behavior that implies that exposure valence remains critically important close to the final brand choice. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

The generalized Poisson (GP) regression model has been used to model count data that exhibit over-dispersion or under-dispersion. The zero-inflated GP (ZIGP) regression model can additionally handle count data characterized by many zeros. However, the parameters of ZIGP model cannot easily be used for inference on overall exposure effects. In order to address this problem, a marginalized ZIGP is proposed to directly model the population marginal mean count. The parameters of the marginalized zero-inflated GP model are estimated by the method of maximum likelihood. The regression model is illustrated by three real-life data sets. [ABSTRACT FROM AUTHOR]

A regression model, based on the exponentiated-exponential geometric distribution, is defined and studied. The regression model can be applied to count data with under-dispersion or over-dispersion. Some forms of its modifications to truncated or inflated data are mentioned. Some tests to discriminate between the regression model and its competitors are discussed. Real numerical data sets are used to illustrate the applications of the regression model. [ABSTRACT FROM PUBLISHER]

This paper presents a new family of distributions for count data, the so called zero-modified power series (ZMPS), which is an extension of the power series (PS) distribution family, whose support starts at zero. This extension consists in modifying the probability of observing zero of each PS distribution, enabling the new zero-modified distribution to appropriately accommodate data which have any amount of zero observations (for instance, zero-inflated or zero-deflated data). The Hurdle distribution version of the ZMPS distribution is presented. PS distributions included in the proposed ZMPS family are the Poisson, Generalized Poisson, Geometric, Binomial, Negative Binomial and Generalized Negative Binomial distributions. The paper also describes the properties and particularities of the new distribution family for count data. The distribution parameters are estimated via maximum likelihood method and the use of the new family is illustrated in three real data sets. We emphasize that the new distribution family can accommodate sets of count data without any previous knowledge on the characteristic of zero-inflation or zero-deflation present in the data. [ABSTRACT FROM PUBLISHER]

Count data often display excessive number of zero outcomes than are expected in the Poisson regression model. The zero-inflated Poisson regression model has been suggested to handle zero-inflated data, whereas the zero-inflated negative binomial (ZINB) regression model has been fitted for zero-inflated data with additional overdispersion. For bivariate and zero-inflated cases, several regression models such as the bivariate zero-inflated Poisson (BZIP) and bivariate zero-inflated negative binomial (BZINB) have been considered. This paper introduces several forms of nested BZINB regression model which can be fitted to bivariate and zero-inflated count data. The mean–variance approach is used for comparing the BZIP and our forms of BZINB regression model in this study. A similar approach was also used by past researchers for defining several negative binomial and zero-inflated negative binomial regression models based on the appearance of linear and quadratic terms of the variance function. The nested BZINB regression models proposed in this study have several advantages; the likelihood ratio tests can be performed for choosing the best model, the models have flexible forms of marginal mean–variance relationship, the models can be fitted to bivariate zero-inflated count data with positive or negative correlations, and the models allow additional overdispersion of the two dependent variables. [ABSTRACT FROM PUBLISHER]

In low-resource settings, prevalence mapping relies on empirical prevalence data from a finite, often spatially sparse, set of surveys of communities within the region of interest, possibly supplemented by remotely sensed images that can act as proxies for environmental risk factors. A standard geostatistical model for data of this kind is a generalized linear mixed model with binomial error distribution, logistic link, and a combination of explanatory variables and a Gaussian spatial stochastic process in the linear predictor. In this article, we first review statistical methods and software associated with this standard model, then consider several methodological extensions whose development has been motivated by the requirements of specific applications. These include: methods for combining randomized survey data with data from nonrandomized, and therefore potentially biased, surveys; spatio-temporal extensions; and spatially structured zero-inflation. Throughout, we illustrate the methods with disease mapping applications that have arisen through our involvement with a range of African public health programs. [ABSTRACT FROM AUTHOR]

In this article, an integer-valued self-exciting threshold model with a finite range based on the binomial INARCH(1) model is proposed. Important stochastic properties are derived, and approaches for parameter estimation are discussed. A real-data example about the regional spread of public drunkenness in Pittsburgh demonstrates the applicability of the new model in comparison to existing models. Feasible modifications of the model are presented, which are designed to handle special features such as zero-inflation. [ABSTRACT FROM PUBLISHER]

The Poisson gravity model along with pseudo maximum likelihood (ML) methods has become a popular way to model international trade flows. This approach has several econometric advantages that we outline in the paper. We argue that estimating the parameters by ML would only be justified statistically if the trade flows were independent. Such an assumption, however, is generally not valid, and a failure to account for spatial dependence may lead to biased parameter estimates and misleading inferences. To overcome this estimation problem we suggest eigenvector spatial filtering variants of the Poisson gravity model (without and with zero-inflation) along with pseudo ML estimation. [ABSTRACT FROM AUTHOR]

In this article, the zero-one inflated binomial mixed regression is proposed to model proportional data with large frequencies of both zeros and binomial denominators. Score tests for assessing both extra zeros and extra binomial denominators in proportional data are developed. The empirical levels and empirical powers of the score test statistics are evaluated using a simulation study. Finally, the application of the proposed model is illustrated on the whitefly data. [ABSTRACT FROM AUTHOR]

Many applications in public health, medical and biomedical or other studies demand modelling of two or more longitudinal outcomes jointly to get better insight into their joint evolution. In this regard, a joint model for a longitudinal continuous and a count sequence, the latter possibly overdispersed and zero-inflated (ZI), will be specified that assembles aspects coming from each one of them into one single model. Further, a subject-specific random effect is included to account for the correlation in the continuous outcome. For the count outcome, clustering and overdispersion are accommodated through two distinct sets of random effects in a generalized linear model as proposed by Molenberghs et al. [A family of generalized linear models for repeated measures with normal and conjugate random effects. Stat Sci. 2010;25:325–347]; one is normally distributed, the other conjugate to the outcome distribution. The association among the two sequences is captured by correlating the normal random effects describing the continuous and count outcome sequences, respectively. An excessive number of zero counts is often accounted for by using a so-called ZI or hurdle model. ZI models combine either a Poisson or negative-binomial model with an atom at zero as a mixture, while the hurdle model separately handles the zero observations and the positive counts. This paper proposes a general joint modelling framework in which all these features can appear together. We illustrate the proposed method with a case study and examine it further with simulations. [ABSTRACT FROM AUTHOR]

We describe a mixed-effect hurdle model for zero-inflated longitudinal count data, where a baseline variable is included in the model specification. Association between the count data process and the endogenous baseline variable is modeled through a latent structure, assumed to be dependent across equations. We show how model parameters can be estimated in a finite mixture context, allowing for overdispersion, multivariate association and endogeneity of the baseline variable. The model behavior is investigated through a large-scale simulation experiment. An empirical example on health care utilization data is provided. [ABSTRACT FROM PUBLISHER]

Overdispersion due to a large proportion of zero observations in data sets is a common occurrence in many applications of many fields of research; we consider such scenarios in count panel (longitudinal) data. A well-known and widely implemented technique for handling such data is that of random effects modeling, which addresses the serial correlation inherent in panel data, as well as overdispersion. To deal with the excess zeros, a zero-inflated Poisson distribution has come to be canonical, which relaxes the equal mean-variance specification of a traditional Poisson model and allows for the larger variance characteristic of overdispersed data. A natural proposal then to approach count panel data with overdispersion due to excess zeros is to combine these two methodologies, deriving a likelihood from the resulting conditional probability. In performing simulation studies, we find that this approach in fact poses problems of identifiability. In this article, we construct and explain in full detail why a model obtained from the marriage of two classical and well-established techniques is unidentifiable and provide results of simulation studies demonstrating this effect. A discussion on alternative methodologies to resolve the problem is provided in the conclusion. [ABSTRACT FROM PUBLISHER]

The generalized Poisson (GP) regression is an increasingly popular approach for modeling overdispersed as well as underdispersed count data. Several parameterizations have been performed for the GP regression, and the two well known models, the GP-1 and the GP-2, have been applied. The GP-P regression, which has been recently proposed, has the advantage of nesting the GP-1 and the GP-2 parametrically, besides allowing the statistical tests of the GP-1 and the GP-2 against a more general alternative. In several cases, count data often have excessive number of zero outcomes than are expected in the Poisson. This zero-inflation phenomenon is a specific cause of overdispersion, and the zero-inflated Poisson (ZIP) regression model has been proposed. However, if the data continue to suggest additional overdispersion, the zero-inflated negative binomial (ZINB-1 and ZINB-2) and the zero-inflated generalized Poisson (ZIGP-1 and ZIGP-2) regression models have been considered as alternatives. This article proposes a functional form of the ZIGP which mixes a distribution degenerate at zero with a GP-P distribution. The suggested model has the advantage of nesting the ZIP and the two well known ZIGP (ZIGP-1 and ZIGP-2) regression models, besides allowing the statistical tests of the ZIGP-1 and the ZIGP-2 against a more general alternative. The ZIP and the functional form of the ZIGP regression models are fitted, compared and tested on two sets of count data; the Malaysian insurance claim data and the German healthcare data. [ABSTRACT FROM AUTHOR]

In several cases, count data often have excessive number of zero outcomes. This zero-inflated phenomenon is a specific cause of overdispersion, and zero-inflated Poisson regression model (ZIP) has been proposed for accommodating zero-inflated data. However, if the data continue to suggest additional overdispersion, zero-inflated negative binomial (ZINB) and zero-inflated generalized Poisson (ZIGP) regression models have been considered as alternatives. This study proposes the score test for testing ZIP regression model against ZIGP alternatives and proves that it is equal to the score test for testing ZIP regression model against ZINB alternatives. The advantage of using the score test over other alternative tests such as likelihood ratio and Wald is that the score test can be used to determine whether a more complex model is appropriate without fitting the more complex model. Applications of the proposed score test on several datasets are also illustrated. [ABSTRACT FROM PUBLISHER]

Count data with extra zeros are common in many biomedical applications and the zero-inflated generalized power series (ZIGPS) distribution may be appropriate, in which the baseline discrete distribution is a generalized power series distribution, which is a natural extension of power series distribution. In this article, a Monte Carlo EM (MCEM) algorithm is proposed to obtain maximum likelihood estimates and standard errors for ZIGPS distribution with missing responses. A Monte Carlo approximation method combining the Gibbs sampler and M-H algorithm is used to implement E-step, whereas the M-step is completed via the method of conditional maximization. As classical model selection procedure such as Akaike's information criterion (AIC) becomes problematic for our considered ZIGPS distribution with incomplete data, some variations on AIC are presented under two different missingness mechanisms, namely, missing at random (MAR) and missing not at random (MNAR), respectively. The most attractive point is that our methods cannot only be used to select distributions and variables, but also can be used to find out whether there exists zero-inflation or not, which is conducted via score test or Bayesian test in previous literature. Finally, a simulation study and a real example are used to illustrate the proposed methodology. [ABSTRACT FROM AUTHOR]

Introduction: The Rutgers Alcohol Problem Index (RAPI) is a scale designed to identify alcohol-related problems experienced by adolescents and young adults. RAPI scores tend to be skewed due in part to a substantial proportion of zero scores. In this study, we compared different statistical models for analyzing the RAPI as an outcome measure using data collected as part of an alcohol intervention program for college freshmen. Predictors included intervention group indicators. Model fit, predictive ability and practicality of implementation were compared among competing models and recommendations are made. Results: Of 558 students who completed the baseline survey (68%% response rate), 76%% completed a 3-month follow-up survey. Mean RAPI scores were 4.7 (SD == 6.0) at baseline and 4.6 (SD == 5.5) at 3 months. Significance of intervention group differences at 3 months adjusting for baseline RAPI were heavily dependent upon the type of statistical model employed. A zero-inflated (ZI) negative binomial model provided the best model fit. Conclusions: This study demonstrated that inferences and conclusions about intervention efficacy were method-dependent in analysis of RAPI scores. There was empirical evidence of improved inference when methods accounting for zero-inflation and skewness were employed. [ABSTRACT FROM AUTHOR]

Zero-inflated Poisson mixed regression models are popular approaches to analyze clustered count data with excess zeros. Prior to application of these models, it is essential to examine the necessity of the adjustment for zero outcomes. The existing literature, however, has focused only on score tests for testing the suitability of zero-inflated models for correlated count data. In view of the observed bias and non-optimal size of score tests, it deserves further investigation of other alternative ways for the test. This article aims to explore the use of the null Wald and likelihood ratio tests for zero-inflation in correlated count data. Our simulation study shows that both the null Wald and likelihood ratio tests outperform the score test of Xiang et al. (2006) in terms of statistical power, regardless of the computational convenience of the score test. A bootstrap null Wald statistic is also proposed, which results in improved performance in terms of the size and power of the test. [ABSTRACT FROM AUTHOR]

The negative binomial (NB)-mixed regression in many situations is more appropriate for analysing the correlated and over-dispersed count data. In this paper, a score test for assessing extra zeros against the NB-mixed regression in the correlated count data with excess zeros is developed. The sampling distribution and power of the score test statistic is evaluated using a simulation study. The results show that under a wide range of conditions, the score statistic performs satisfactorily. Finally, the use of the score test is illustrated on DMFT index data of children aged 12 years old. [ABSTRACT FROM AUTHOR]

Homogeneity of dispersion parameters and zero-inflation parameters is a standard assumption in zero-inflated generalized Poisson regression (ZIGPR) models. However, this assumption may be not appropriate in some situations. This work develops a score test for varying dispersion and/or zero-inflation parameter in the ZIGPR models, and corresponding test statistics are obtained. Two numerical examples are given to illustrate our methodology, and the properties of score test statistics are investigated through Monte Carlo simulations. [ABSTRACT FROM AUTHOR]

This note extends the score test statistics for overdispersion in Poisson and binomial regression models (Dean, 1992) to the zero-inflated models. Some general results are obtained, and examples illustrate the application of the extended results. [ABSTRACT FROM AUTHOR]

In this study, estimation of the parameters of the zero-inflated count regression models and computations of posterior model probabilities of the log-linear models defined for each zero-inflated count regression models are investigated from the Bayesian point of view. In addition, determinations of the most suitable log-linear and regression models are investigated. It is known that zero-inflated count regression models cover zero-inflated Poisson, zero-inflated negative binomial, and zero-inflated generalized Poisson regression models. The classical approach has some problematic points but the Bayesian approach does not have similar flaws. This work points out the reasons for using the Bayesian approach. It also lists advantages and disadvantages of the classical and Bayesian approaches. As an application, a zoological data set, including structural and sampling zeros, is used in the presence of extra zeros. In this work, it is observed that fitting a zero-inflated negative binomial regression model creates no problems at all, even though it is known that fitting a zero-inflated negative binomial regression model is the most problematic procedure in the classical approach. Additionally, it is found that the best fitting model is the log-linear model under the negative binomial regression model, which does not include three-way interactions of factors. [ABSTRACT FROM AUTHOR]

The negative binomial (NB) model and the generalized Poisson (GP) model are common alternatives to Poisson models when overdispersion is present in the data. Having accounted for initial overdispersion, we may require further investigation as to whether there is evidence for zero-inflation in the data. Two score statistics are derived from the GP model for testing zero-inflation. These statistics, unlike Wald-type test statistics, do not require that we fit the more complex zero-inflated overdispersed models to evaluate zero-inflation. A simulation study illustrates that the developed score statistics reasonably follow a χ2 distribution and maintain the nominal level. Extensive simulation results also indicate the power behavior is different for including a continuous variable than a binary variable in the zero-inflation (ZI) part of the model. These differences are the basis from which suggestions are provided for real data analysis. Two practical examples are presented in this article. Results from these examples along with practical experience lead us to suggest performing the developed score test before fitting a zero-inflated NB model to the data. [ABSTRACT FROM AUTHOR]

Count data series with extra zeros relative to a Poisson distribution are common in many biomedical applications. A score test is presented to assess whether the zero-inflation problem is significant to warrant the analysis by the more complex zero-inflated Poisson autoregression model. The score test is implemented as a computer program in the Splus platform. For illustration, the test procedure is applied to a workplace injury series where many zero counts are observed due to the heterogeneity in injury risk and the dynamic population involved. [ABSTRACT FROM AUTHOR]

In recent years, zero-inflated count data models, such as zero-inflated Poisson (ZIP) models, are widely used as the count data with extra zeros are very common in many practical problems. In order to model the correlated count data which are either clustered or repeated and to assess the effects of continuous covariates or of time scales in a flexible way, a class of semiparametric mixed-effects models for zero-inflated count data is considered. In this article, we propose a fully Bayesian inference for such models based on a data augmentation scheme that reflects both random effects of covariates and mixture of zero-inflated distribution. A computational efficient MCMC method which combines the Gibbs sampler and M-H algorithm is implemented to obtain the estimate of the model parameters. Finally, a simulation study and a real example are used to illustrate the proposed methodologies. [ABSTRACT FROM AUTHOR]

When overdispersion is present in count data, a negative binomial (NB) model is commonly used in place of the standard Poisson model. However, the model is sometimes not adequate because of the occurrence of excess zeros and a zero-inflated negative binomial (ZNB) model may be more appropriate. This article proposes a general score test statistic for comparing a ZNB regression model to the NB model and the test is extended to a composite score test. Simulation results indicate that the test performs reasonably well and has a sampling distribution under the null hypothesis (NB model) approximated by the usual χ2 distribution. Use of the test is illustrated on a set of apple shoot propagation data. The composite score test is found to indicate suitable models. [ABSTRACT FROM AUTHOR]

Count data with excess zeros often occurs in areas such as public health, epidemiology, psychology, sociology, engineering, and agriculture. Zero-inflated Poisson (ZIP) regression and zero-inflated negative binomial (ZINB) regression are useful for modeling such data, but because of hierarchical study design or the data collection procedure, zero-inflation and correlation may occur simultaneously. To overcome these challenges ZIP or ZINB may still be used. In this paper, multilevel ZINB regression is used to overcome these problems. The method of parameter estimation is an expectation-maximization algorithm in conjunction with the penalized likelihood and restricted maximum likelihood estimates for variance components. Alternative modeling strategies, namely the ZIP distribution are also considered. An application of the proposed model is shown on decayed, missing, and filled teeth of children aged 12 years old. [ABSTRACT FROM AUTHOR]

The Hinde-Demétrio (HD) family of distributions, which are discrete exponential dispersion models with an additional real index parameter p, have been recently characterized from the unit variance function μ + μp. For p equals to 2, 3,..., the corresponding distributions are concentrated on non negative integers, overdispersed and zero-inflated with respect to a Poisson distribution having the same mean. The negative binomial (p = 2) and strict arcsine (p = 3) distributions are HD families; the limit case (p → ∞) is associated to a suitable Poisson distribution. Apart from these count distributions, none of the HD distributions has explicit probability mass functions pk. This article shows that the ratios rk = k pk/pk-1, k = 1,..., p - 1, are equal and different from rp. This new property allows, for a given count data set, to determine the integer p by some tests. The extreme situation of p = 2 is of general interest for count data. Some examples are used for illustrations and discussions. [ABSTRACT FROM AUTHOR]