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Joint species distribution models (JSDMs) have gained considerable traction among ecologists over the past decade, due to their capacity to answer a wide range of questions at both the species‐ and the community‐level. The family of generalised linear latent variable models in particular has proven popular for building JSDMs, being able to handle many response types including presence‐absence data, biomass, overdispersed and/or zero‐inflated counts.We extend latent variable models to handle percent cover response variables, with vegetation, sessile invertebrate and macroalgal cover data representing the prime examples of such data arising in community ecology.Sparsity is a commonly encountered challenge with percent cover data. Responses are typically recorded as percentages covered per plot, though some species may be completely absent or present, that is, have 0% or 100% cover, respectively, rendering the use of beta distribution inadequate.We propose two JSDMs suitable for percent cover data, namely a hurdle beta model and an ordered beta model. We compare the two proposed approaches to a beta distribution for shifted responses, transformed presence‐absence data and an ordinal model for percent cover classes. Results demonstrate the hurdle beta JSDM was generally the most accurate at retrieving the latent variables and predicting ecological percent cover data. [ABSTRACT FROM AUTHOR]

Generalized linear mixed models (GLMMs) have great potential to deal with count data in single-case experimental designs (SCEDs). However, applied researchers have faced challenges in making various statistical decisions when using such advanced statistical techniques in their own research. This study focused on a critical issue by investigating the selection of an appropriate distribution to handle different types of count data in SCEDs due to overdispersion and/or zero-inflation. To achieve this, I proposed two model selection frameworks, one based on calculating information criteria (AIC and BIC) and another based on utilizing a multistage-model selection procedure. Four data scenarios were simulated including Poisson, negative binominal (NB), zero-inflated Poisson (ZIP), and zero-inflated negative binomial (ZINB). The same set of models (i.e., Poisson, NB, ZIP, and ZINB) were fitted for each scenario. In the simulation, I evaluated 10 model selection strategies within the two frameworks by assessing the model selection bias and its consequences on the accuracy of the treatment effect estimates and inferential statistics. Based on the simulation results and previous work, I provide recommendations regarding which model selection methods should be adopted in different scenarios. The implications, limitations, and future research directions are also discussed. [ABSTRACT FROM AUTHOR]

Abstract Joint species distribution models (JSDMs) have gained considerable traction among ecologists over the past decade, due to their capacity to answer a wide range of questions at both the species‐ and the community‐level. The family of generalised linear latent variable models in particular has proven popular for building JSDMs, being able to handle many response types including presence‐absence data, biomass, overdispersed and/or zero‐inflated counts. We extend latent variable models to handle percent cover response variables, with vegetation, sessile invertebrate and macroalgal cover data representing the prime examples of such data arising in community ecology. Sparsity is a commonly encountered challenge with percent cover data. Responses are typically recorded as percentages covered per plot, though some species may be completely absent or present, that is, have 0% or 100% cover, respectively, rendering the use of beta distribution inadequate. We propose two JSDMs suitable for percent cover data, namely a hurdle beta model and an ordered beta model. We compare the two proposed approaches to a beta distribution for shifted responses, transformed presence‐absence data and an ordinal model for percent cover classes. Results demonstrate the hurdle beta JSDM was generally the most accurate at retrieving the latent variables and predicting ecological percent cover data.

The ”2019 novel coronavirus” known as “ the 2019-nCoV” or simply “COVID-19” has been declared by the World Health organization (WHO), in first quarter of 2020, as a world pandemic and a public health emergency of international concern. Alas, many details related to the COVID-19 have remained unsolved completely. The success of government strategies in fighting the COVID-19 relays mainly on the results from epidemiological or statistical studies. Statistical models play a major role in providing reliable results based on appropriate analyses. Traditional (one-part) models, mixture models and mixed-effects models for counts are used to investigate effects of the WHO-regions and Cumulated COVID-19 cases on the outcome variable COVID-19 new deaths tolls. Overall result reveals there is a strong association between number of new deaths COVID-19 with predictors including the WHO regions and cumulated cases. Besides, models that account for the overdispersion feature have smallest AICs and have reasonable regression model fits.

Semicontinuous data frequently occur in longitudinal studies. The popular two‐part modelling approach deals with longitudinal semicontinuous data by analyzing the occurrence of positive values and the intensity of positive values separately; however, this separation may break down the natural sequence of semicontinuous data within a subject and destroy its serial dependence structure. In this article, we introduce a Tweedie compound Poisson mixed model to study the occurrence of positive values and the quantity of the semicontinuous response simultaneously. In our approach, covariate effects on the semicontinuous response are assessed directly. The correlation within a subject and the unobserved heterogeneity are incorporated with serially correlated nonparametric random effects. Our model unifies subject‐specific and population‐averaged interpretations. We illustrate the approach with applications to a Brief Symptom Inventory study and an infants' fluoride intake study. [ABSTRACT FROM AUTHOR]

Non-negative ordered survey data often exhibit an unusually high frequency of zeros in the first interval. Zero-inflated interval regression models handle the excess of zeros by combining a split probit model and an ordered probit model. In the presence of data violating distributional assumptions, standard inference based on the maximum likelihood method gives biased estimates with large standard errors. In this paper, we consider robust inference based on the exponential tilting methodology for the zero-inflated interval regression model. The application considers data on cyber security to study the relationship between investments in cyber defences and losses from cyber breaches. Robust estimates obtained via tilting clearly show an effect of the investments in reducing the loss amount. [ABSTRACT FROM AUTHOR]

In this paper, performance of hurdle models in rare events data is improved by modifying their binary component. The rare-event weighted logistic regression model is adopted in place of logistic regression to deal with class imbalance due to rare events. Poisson Hurdle Rare Event Weighted Logistic Regression (REWLR) and Negative Binomial Hurdle (NBH) REWLR are developed as two-part models which use the REWLR model to estimate the probability of a positive count and a Poisson or NB zero-truncated count model to estimate non-zero counts. This research aimed to develop and assess the performance of the Poisson and Negative Binomial (NB) Hurdle Rare Event Weighted Logistic Regression (REWLR) models, applied to simulated data with various degrees of zero inflation and to Nairobi county's maternal mortality data. The study data on maternal mortality were pulled from JPHES. The data contain the number of maternal deaths, which is the outcome variable, and other obstetric and demographic factors recorded in MNCH facilities in Nairobi between October 2021 and January 2022. The models were also fit and evaluated based on simulated data with varying degrees of zero inflation. The obtained results are numerically validated and then discussed from both the mathematical and the maternal mortality perspective. Numerical simulations are also presented to give a more complete representation of the model dynamics. Results obtained suggest that NB Hurdle REWLR is the best performing model for zero inflated count data due to rare events.

We consider INAR(1) processes modulated by an unobserved strongly dependent 0 - 1 process. The observed process exhibits zero inflation and long memory. A simple method is proposed for estimating the INAR-parameters without modelling the unobserved modulating process. Asymptotic results for the estimators are derived, and a zero-inflation test is introduced. Asymptotic rejection regions and asymptotic power under long-memory alternatives are derived. A small simulation study illustrates the asymptotic results. [ABSTRACT FROM AUTHOR]

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]

When overdispersion and zero-inflated feature are both concerned, Zero-inflated negative binomial (ZINB) model tends to be more appropriate than the popular Zero-inflated Poisson (ZIP) model most used. Moreover, when some variables that model the mean response and the probability of zero-excess have missing data, ignoring the missing or using inappropriate methods is likely to produce questionable estimates. To remedy this problem, we propose a non-parametric and parametric inverse probability weighting (IPW) estimators to estimate parameters of the ZINB models. In particular, the generalized additive models (GAMs), the indicator or kernel smoothing functions are considered for the non-parametric approaches. Meanwhile, logistic model is used to estimate selection probability in parametric method. The performance of our proposed methods are investigated by conducting several simulation studies and exploring a real example analysis. We aim to develop and compare several IPW estimators in order to recommend the most accurate approaches. Numerical illustrations support that the semiparametric IPW methods which were based on the kernel smoothing or indicator function weights tend to produce the best results, because they tend to outperform the GAMs and parametric IPW estimates in terms of efficiency. Hence we recommend that the first approach to be used in the analysis for the ZINB model should be the semiparametric IPW based on the kernel smoothing or indicator function weights. The GAM and parametric weighting estimators are also quite good, as long as their related estimated weights are correct. • This study proposes the parameter estimations on Zero-inflated Negative Binomial (ZINB) model with missing data. • The inverse probability weighting (IPW) method is considered in this work. • We propose the three different approaches include: parametric, non-parametric and generalized additive models. • We compared the proposed approaches with the easiest method of this topic which is the complete case (CC) method. • Many numerical simulations and a real data sets includes the infected blood cells (IBC) was conducted in this study. [ABSTRACT FROM AUTHOR]

A challenging, yet fundamental part of initiating effective control measures against an invasive pest species is developing reliable means of monitoring the pest's seasonal abundance. Halyomorpha halys, a polyphagous insect pest native to East Asia, has become a major economic threat to agricultural systems following unintentional introductions to North America, South America, and Europe. Research involving the seasonal phenology and monitoring attractant preferences of H. halys from its native range remain scarce. An 11-year collection of H. halys monitoring trap data from black light, incandescent light, and methyl (E, E, Z)-2, 4, 6-decatrienoate (MDT) lured traps from three locations in Kyoto, Japan was analyzed to fill gaps in knowledge relating to the native seasonal abundance and effectiveness of diferent trapping techniques for the pest. Due to a high amount of zero trap counts, a zero-inflated approach was taken to analyze the dataset. Overall, H. halys followed a bell-shaped population trend in Kyoto, with abundance peaking in the mid-summer. The attractant preference of H. halys varied slightly with the season, with black light traps producing to highest mean trap counts. The MDT lure traps generated the lowest mean trap counts, but displayed potential use in the reliable detection of early season H. halys. This work is expected to provide greater insight on H. halys in its native range and ultimately help refine existing management programs in invaded regions. [ABSTRACT FROM AUTHOR]

Count outcomes are frequently encountered in single-case experimental designs (SCEDs). Generalized linear mixed models (GLMMs) have shown promise in handling overdispersed count data. However, the presence of excessive zeros in the baseline phase of SCEDs introduces a more complex issue known as zero-inflation, often overlooked by researchers. This study aimed to deal with zero-inflated and overdispersed count data within a multiple-baseline design (MBD) in single-case studies. It examined the performance of various GLMMs (Poisson, negative binomial [NB], zero-inflated Poisson [ZIP], and zero-inflated negative binomial [ZINB] models) in estimating treatment effects and generating inferential statistics. Additionally, a real example was used to demonstrate the analysis of zero-inflated and overdispersed count data. The simulation results indicated that the ZINB model provided accurate estimates for treatment effects, while the other three models yielded biased estimates. The inferential statistics obtained from the ZINB model were reliable when the baseline rate was low. However, when the data were overdispersed but not zero-inflated, both the ZINB and ZIP models exhibited poor performance in accurately estimating treatment effects. These findings contribute to our understanding of using GLMMs to handle zero-inflated and overdispersed count data in SCEDs. The implications, limitations, and future research directions are also discussed. [ABSTRACT FROM AUTHOR]

This article provides an overview of count data and count models, explores zero inflation, introduces likelihood ratio tests, and explains how the Vuong test can be used as a model selection criterion for assessing overdispersion. The motivation of this work was to create a Vuong test implementation from scratch using the Python programming language. This implementation supports our objective of enhancing the accessibility and applicability of the Vuong test in real-world scenarios, providing a valuable contribution to the academic community, since Python did not have an implementation of this statistical test. [ABSTRACT FROM AUTHOR]

Many researchers employed Poisson distribution-based control charts to monitor count data. Nevertheless, these charts can handle count data that deviate from the Poisson assumption of equal mean and variance. This paper suggests a new control chart (CC) that uses the generalized Conway–Maxwell–Poisson (GCOMP) distribution, which can deal with count data that have different levels of dispersion and zero-inflation (ZI). The proposed chart is designed considering the total number of counts. The main advantage of this study is that it pays attention to the tails of the count data when monitoring the process. The performance is measured by the average run length using L control limits at different sample sizes and parametric settings. The findings demonstrate that, for count data with varying tail behaviors, the proposed chart performs better compared to existing CCs. ZI count data can also be monitored with the proposed chart. The proposed chart can be applied in a variety of fields, as verified by the examples provided in this paper. [ABSTRACT FROM AUTHOR]

Semicontinuous outcomes commonly arise in a wide variety of fields, such as insurance claims, healthcare expenditures, rainfall amounts, and alcohol consumption. Regression models, including Tobit, Tweedie, and two-part models, are widely employed to understand the relationship between semicontinuous outcomes and covariates. Given the potential detrimental consequences of model misspecification, after fitting a regression model, it is of prime importance to check the adequacy of the model. However, due to the point mass at zero, standard diagnostic tools for regression models (eg, deviance and Pearson residuals) are not informative for semicontinuous data. To bridge this gap, we propose a new type of residuals for semicontinuous outcomes that is applicable to general regression models. Under the correctly specified model, the proposed residuals converge to being uniformly distributed, and when the model is misspecified, they significantly depart from this pattern. In addition to in-sample validation, the proposed methodology can also be employed to evaluate predictive distributions. We demonstrate the effectiveness of the proposed tool using health expenditure data from the US Medical Expenditure Panel Survey. [ABSTRACT FROM AUTHOR]

Over-dispersed models are commonly utilized when the variation is more than what the model actually predicts. Since one of the reasons for over-dispersion is the large number of zeros, we employ zero-inflated models instead of more traditional ones to handle this observed occurrence. We present a zero-inflated version of a discrete distribution that was developed in 2021 in our research. Significant statistical characteristics of the suggested model have been identified, such as moments, the over-dispersion feature, generating functions, and related measures, among others. We have carried the parametric estimation using the maximum likelihood estimate. Maximum likelihood estimates are checked for usefulness in a simulation exercise. We evaluated the applicability of our developed model using three real-world data sets. [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]

While modeling political participation as a latent variable, researchers usually choose whether to conceptualize and model participation as a latent continuous or latent categorical variable. When participation is modeled as a continuous variable, factor analytic and item-response theory models are used. When modeled as a categorical variable, latent class analysis is employed. However, both conceptualizations and modeling approaches rest upon very strong assumptions. In the continuous case, all subjects are assumed to come from the same homogenous population; in the categorical case, we assume that no quantitative heterogeneity exists within the latent classes. In this work, I argue that these assumptions are implausible and propose to model participation using zero-inflated measurement and regression models that assume the existence of two latent classes-politically disengaged and politically active-with the latter class being quantitatively heterogenous (people in that class are thought to participate to a varying degree). The results show that the models accounting for the latent class of politically disengaged have much better out-of-sample predictive accuracy. Moreover, modeling the zero-inflation changes estimates of measurement and regression models, and offers new research opportunities because with zero-inflated models we can explicitly tackle the question of what impacts the probability of ending up in the latent class of politically disengaged. [ABSTRACT FROM AUTHOR]

The presence of a large number of zero counts is quite common in studies involving count data. This causes overdispersion. Therefore, different types of models have been proposed as alternatives and a very frequent practice is to use the negative binomial model. In 2018, Bonat (2018) considered a new type of model, based on the Poisson-Tweedie dispersion models, which can automatically adapt to different degrees of overdispersion in count data. This article presents a simulation study in order to compare the estimates derived from the Poisson-Tweedie model for a wide range of overdispersed data with estimates derived from the negative binomial model. In both models, the relative percent bias of the estimated coefficients was very small. Nevertheless, the Poisson-Tweedie model showed a better performance with smaller values for the mean squared errors, particularly in scenarios with more dispersion. Hence, it would be possible to suggest the data analyst in which situations it would be enough to work with the popular negative binomial model or when it would be best to use the Poisson-Tweedie family. Additionally, the comparison between the fit of the negative binomial model and that of the Poisson-Tweedie family is illustrated by analysing the number of pediatric consultations of a group of children who receive health care in a public health center in Rosario, Argentina. Although the results obtained in both models were similar, the estimates in the Poisson-Tweedie model were more accurate. [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]

The Dirichlet‐multinomial (DM) distribution plays a fundamental role in modern statistical methodology development and application. Recently, the DM distribution and its variants have been used extensively to model multivariate count data generated by high‐throughput sequencing technology in omics research due to its ability to accommodate the compositional structure of the data as well as overdispersion. A major limitation of the DM distribution is that it is unable to handle excess zeros typically found in practice which may bias inference. To fill this gap, we propose a novel Bayesian zero‐inflated DM model for multivariate compositional count data with excess zeros. We then extend our approach to regression settings and embed sparsity‐inducing priors to perform variable selection for high‐dimensional covariate spaces. Throughout, modeling decisions are made to boost scalability without sacrificing interpretability or imposing limiting assumptions. Extensive simulations and an application to a human gut microbiome dataset are presented to compare the performance of the proposed method to existing approaches. We provide an accompanying R package with a user‐friendly vignette to apply our method to other datasets. [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]

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

Over-dispersed models are often used whenever the variation is more than what in point of fact is anticipated by a model. One of the reasons behind experiencing over-dispersion is an excessive number of zeros, hence when modeling this observed fact, we use zero-inflated models rather than more traditional ones. As a part of our research, we have suggested a zero-inflated variant of Poisson-Akash distribution that was introduced in 2015. We have calculated crucial statistical characteristics of the suggested model which are not confined to generating functions, over-dispersion property, moments and associated measures. The parametric estimation has been carried out using the maximum likelihood estimation. Two different simulation exercises have been carried out, one to test the performance of maximum likelihood estimates and the other for testing the compatibility of our devised model when data has been simulated from different zero-inflated models. For the purpose of testing the compatibility of our proposed model, we have used four real life data sets and considered different performance measures like Goodness-of-fit, Akaike's information criterion, Bayesian information criterion, Dispersion index etc. The fitting results have been compared with some other models of interest. Moreover, we have tested the significance of the zero-inflation parameter using Likelihood ratio test, Score test and the Wald test itself. [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]

The mediation analysis methodology of the cause-and-effect relationship through mediators has been increasingly popular over the past decades. The human microbiome can contribute to the pathogenesis of many complex diseases by mediating disease-leading causal pathways. However, standard mediation analysis is not adequate for microbiome data due to the excessive number of zero values and the over-dispersion in the sequencing reads, which arise for both biological and sampling reasons. To address these unique challenges brought by the zero-inflated mediator, we developed a novel mediation analysis algorithm under the potential-outcome framework to fill this gap. The proposed semiparametric model estimates the mediation effect of the microbiome by decomposing indirect effects into two components according to the zero-inflated distributions. The bootstrap algorithm is utilized to calculate the empirical confidence intervals of the causal effects. We conducted extensive simulation studies to investigate the performance of the proposed weighting-based approach and some model-based alternatives, and our proposed model showed robust performance. The proposed algorithm was implemented in a real human microbiome study of identifying whether some taxa mediate the relationship between LACTIN-V treatment and immune response. [ABSTRACT FROM AUTHOR]

The infants' gut microbiome is dynamic in nature. Literature has shown high inter-individual variability of gut microbial composition in the early years of infancy compared to adulthood. Although next-generation sequencing technologies are rapidly evolving, several statistical analysis aspects need to be addressed to capture the variability and dynamic nature of the infants' gut microbiome. In this study, we proposed a Bayesian Marginal Zero-inflated Negative Binomial (BAMZINB) model, addressing complexities associated with zero-inflation and multivariate structure of the infants' gut microbiome data. Here, we simulated 32 scenarios to compare the performance of BAMZINB with glmFit and BhGLM as the two other widely similar methods in the literature in handling zero-inflation, over-dispersion, and multivariate structure of the infants' gut microbiome. Then, we showed the performance of the BAMZINB approach on a real dataset using SKOT cohort (I and II) studies. Our simulation results showed that the BAMZINB model performed as well as those two methods in estimating the average abundance difference and had a better fit for almost all scenarios when the signal and sample size were large. Applying BAMZINB on SKOT cohorts showed remarkable changes in the average absolute abundance of specific bacteria from 9 to 18 months for infants of healthy and obese mothers. In conclusion, we recommend using the BAMZINB approach for infants' gut microbiome data taking zero-inflation and over-dispersion properties into account in multivariate analysis when comparing the average abundance difference.

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]

With the aim of providing better estimation for count data with overdispersion and/or excess zeros, we develop a novel estimation method— optimal weighting based on cross-validation —for the zero-inflated negative binomial model, where the Poisson, negative binomial, and zero-inflated Poisson models are all included as its special cases. To facilitate the selection of the optimal weight vector, a K -fold cross-validation technique is adopted. Unlike the jackknife model averaging discussed in Hansen and Racine (2012), the proposed method deletes one group of observations rather than only one observation to enhance the computational efficiency. Furthermore, we also theoretically prove the asymptotic optimality of the newly developed optimal weighting based on cross-validation method. Simulation studies and three empirical applications indicate the superiority of the presented optimal weighting based on cross-validation method when compared with the three commonly used information-based model selection methods and their model averaging counterparts. [ABSTRACT FROM AUTHOR]

In this paper, performance of hurdle models in rare events data is improved by modifying their binary component. The rare-event weighted logistic regression model is adopted in place of logistic regression to deal with class imbalance due to rare events. Poisson Hurdle Rare Event Weighted Logistic Regression (REWLR) and Negative Binomial Hurdle (NBH) REWLR are developed as two-part models which use the REWLR model to estimate the probability of a positive count and a Poisson or NB zero-truncated count model to estimate non-zero counts. This research aimed to develop and assess the performance of the Poisson and Negative Binomial (NB) Hurdle Rare Event Weighted Logistic Regression (REWLR) models, applied to simulated data with various degrees of zero inflation and to Nairobi county’s maternal mortality data. The study data on maternal mortality were pulled from JPHES. The data contain the number of maternal deaths, which is the outcome variable, and other obstetric and demographic factors recorded in MNCH facilities in Nairobi between October 2021 and January 2022. The models were also fit and evaluated based on simulated data with varying degrees of zero inflation. The obtained results are numerically validated and then discussed from both the mathematical and the maternal mortality perspective. Numerical simulations are also presented to give a more complete representation of the model dynamics. Results obtained suggest that NB Hurdle REWLR is the best performing model for zero inflated count data due to rare events.

We describe a new pathway for multivariate analysis of data consisting of counts of species abundances that includes two key components: copulas, to provide a flexible joint model of individual species, and dissimilarity-based methods, to integrate information across species and provide a holistic view of the community. Individual species are characterized using suitable (marginal) statistical distributions, with the mean, the degree of over-dispersion, and/or zero-inflation being allowed to vary among a priori groups of sampling units. Associations among species are then modeled using copulas, which allow any pair of disparate types of variables to be coupled through their cumulative distribution function, while maintaining entirely the separate individual marginal distributions appropriate for each species. A Gaussian copula smoothly captures changes in an index of association that excludes joint absences in the space of the original species variables. A permutation-based filter with exact family-wise error can optionally be used a priori to reduce the dimensionality of the copula estimation problem. We describe in detail a Monte Carlo expectation maximization algorithm for efficient estimation of the copula correlation matrix with discrete marginal distributions (counts). The resulting fully parameterized copula models can be used to simulate realistic ecological community data under fully specified null or alternative hypotheses. Distributions of community centroids derived from simulated data can then be visualized in ordinations of ecologically meaningful dissimilarity spaces. Multinomial mixtures of data drawn from copula models also yield smooth power curves in dissimilarity-based settings. Our proposed analysis pathway provides new opportunities to combine model-based approaches with dissimilarity-based methods to enhance understanding of ecological systems. We demonstrate implementation of the pathway through an ecological example, where associations among fish species were found to increase after the establishment of a marine reserve.

Integration of multi-omics data is a challenging but necessary step to advance our understanding of the biology underlying human health and disease processes. To date, investigations seeking to integrate multi-omics (e.g., microbiome and metabolome) employ simple correlation-based network analyses; however, these methods are not always well-suited for microbiome analyses because they do not accommodate the excess zeros typically present in these data. In this paper, we introduce a bivariate zero-inflated negative binomial (BZINB) model-based network and module analysis method that addresses this limitation and improves microbiome–metabolome correlation-based model fitting by accommodating excess zeros. We use real and simulated data based on a multi-omics study of childhood oral health (ZOE 2.0; investigating early childhood dental caries, ECC) and find that the accuracy of the BZINB model-based correlation method is superior compared to Spearman's rank and Pearson correlations in terms of approximating the underlying relationships between microbial taxa and metabolites. The new method, BZINB-iMMPath, facilitates the construction of metabolite–species and species–species correlation networks using BZINB and identifies modules of (i.e., correlated) species by combining BZINB and similarity-based clustering. Perturbations in correlation networks and modules can be efficiently tested between groups (i.e., healthy and diseased study participants). Upon application of the new method in the ZOE 2.0 study microbiome–metabolome data, we identify that several biologically-relevant correlations of ECC-associated microbial taxa with carbohydrate metabolites differ between healthy and dental caries-affected participants. In sum, we find that the BZINB model is a useful alternative to Spearman or Pearson correlations for estimating the underlying correlation of zero-inflated bivariate count data and thus is suitable for integrative analyses of multi-omics data such as those encountered in microbiome and metabolome studies. [ABSTRACT FROM AUTHOR]

This article introduces a new version of first-order binomial autoregressive (BAR(1)) process with zero-and-one inflated binomial marginals using the idea of hidden Markov models, which contains the BAR(1) and other existing processes as special cases. Stochastic properties of the new model are investigated and model parameters are estimated by the probability-based, quasi-maximum likelihood, maximum likelihood and Bayesian methods. A binomial one-inflation index is constructed and further utilized to develop a method to test whether zero and/or one inflation with respect to a BAR(1) model. We also give the asymptotic distribution of the corresponding test statistics under the null hypothesis. Applications to rainy-days and assaults-on-officers counts are conducted, which shows that the proposed model can accurately capture zero-inflation, one-inflation and overdispersion characteristics of the data. The predictive distributions are employed to identify the occurrence of anomalies and then establish early warning system of risk. [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]

Single-cell RNA-sequencing (scRNAseq) data contain a high level of noise, especially in the form of zero-inflation, that is, the presence of an excessively large number of zeros. This is largely due to dropout events and amplification biases that occur in the preparation stage of single-cell experiments. Recent scRNAseq experiments have been augmented with unique molecular identifiers (UMI) and External RNA Control Consortium (ERCC) molecules which can be used to account for zero-inflation. However, most of the current methods on graphical models are developed under the assumption of the multivariate Gaussian distribution or its variants, and thus they are not able to adequately account for an excessively large number of zeros in scRNAseq data. In this article, we propose a single-cell latent graphical model (scLGM)—a Bayesian hierarchical model for estimating the conditional dependency network among genes using scRNAseq data. Taking advantage of UMI and ERCC data, scLGM explicitly models the two sources of zero-inflation. Our simulation study and real data analysis demonstrate that the proposed approach outperforms several existing methods. [ABSTRACT FROM AUTHOR]

Species' responses to broad‐scale environmental or spatial gradients are typically unimodal. Current models of species' responses along gradients tend to be overly simplistic (e.g., linear, quadratic or Gaussian GLMs), or are suitably flexible (e.g., splines, GAMs) but lack direct ecologically interpretable parameters. We describe a parametric framework for species‐environment non‐linear modelling ('senlm'). The framework has two components: (i) a non‐linear parametric mathematical function to model the mean species response along a gradient that allows asymmetry, flattening/peakedness or bimodality; and (ii) a statistical error distribution tailored for ecological data types, allowing intrinsic mean–variance relationships and zero‐inflation. We demonstrate the utility of this model framework, highlighting the flexibility of a range of possible mean functions and a broad range of potential error distributions, in analyses of fish species' abundances along a depth gradient, and how they change over time and at different latitudes. [ABSTRACT FROM AUTHOR]

To improve the estimation of healthcare expenditures by introducing a novel method that is well-suited to situations where data exhibit strong skewness and zero-inflation. Simulations, and two real-world datasets: the 2016–2017 Medical Expenditure Panel Survey; the Back Pain Outcomes using Longitudinal Data. Super learner is an ensemble machine learning approach that can combine several algorithms to improve estimation. We propose a two-stage super learner that is well suited for healthcare expenditure data by separately estimating the probability of any healthcare expenditure and the mean amount of healthcare expenditure conditional on having healthcare expenditures. These estimates can then be combined to yield a single estimate of expenditures for each observation. The analytical strategy can flexibly incorporate a range of individual estimation approaches for each stage of estimation, including both regression-based approaches and machine learning algorithms such as random forests. We compare the performance of the two-stage super learner with a one-stage super learner, and with multiple individual algorithms for estimation of healthcare cost under a broad range of data settings in simulated and real data. The predictive performance was compared using Mean Squared Error and R2. Our results indicate that the two-stage super learner has better performance compared with a one-stage super learner and individual algorithms, for healthcare cost estimation under a wide variety of settings in simulations and in empirical analyses. The improvement of the two-stage super learner over the one-stage super learner was particularly evident in settings when zero-inflation is high. [ABSTRACT FROM AUTHOR]

Modeling bivariate (or multivariate) count data has received increased interest in recent years. The aim is to model the number of different but correlated counts taking into account covariate information. Bivariate Poisson regression models based on the shock model approach are widely used because of their simple form and interpretation. However, these models do not allow for overdispersion or negative correlation, and thus, other models have been proposed in the literature to avoid these limitations. The present paper proposes copula-based bivariate finite mixture of regression models. These models offer some advantages since they have all the benefits of a finite mixture, allowing for unobserved heterogeneity and clustering effects, while the copula-based derivation can produce more flexible structures, including negative correlations and regressors. In this paper, the new approach is defined, estimation through an EM algorithm is presented, and then different models are applied to a Spanish insurance claim count database. [ABSTRACT FROM AUTHOR]

A fundamental consideration in aquatic invasive species risk management is the distribution of invasive taxa relative to the risk assessment area. However, sampling the distribution of aquatic invasive species (AIS) is costly and time consuming, especially when they are rare or clustered. While random sampling removes bias in most estimates, it could lead to many zeroes in the response variable if the target species is not evenly distributed. We surveyed the distribution of Tubifex tubifex, the obligate secondary host of Myxobolus cerebralis, an invasive parasite that causes whirling disease in salmonids. We used intensive grid and random sampling in a lake and two river systems but collected many samples with zero T. tubifex. Zeroaltered models identified a single source of zero T. tubifex counts in each dataset and improved model validation compared to Poisson or negative binomial models. While T. tubifex counts were not predictable using the covariates we measured, the binomial processes identified zero odds of a T. tubifex occurrence at lake sites with water depths > 2 m and stream sites with channel slopes > 3%. These covariates could be used to stratify the landscape for future sampling, which would save survey time and resources and likely reduce uncertainty in parameter estimates. Model-based sample stratification could address some of the challenges with AIS surveys when species are at low abundance or are clustered. [ABSTRACT FROM AUTHOR]

Transmission of Ross River virus (RRV) is influenced by climatic, environmental, and socio-economic factors. Accurate and robust predictions based on these factors are necessary for disease prevention and control. However, the complicated transmission cycle and the characteristics of RRV notification data present challenges. Studies to compare model performance are lacking. In this study, we used RRV notification data and exposure data from 2001 to 2020 in Queensland, Australia, and compared ten models (including generalised linear models, zero-inflated models, and generalised additive models) to predict RRV incidence in different regions of Queensland. We aimed to compare model performance and to evaluate the effect of statistical overdispersion and zero-inflation of RRV surveillance data, and non-linearity of predictors on model fit. A variable selection strategy for screening important predictors was developed and was found to be efficient and able to generate consistent and reasonable numbers of predictors across regions and in all training sets. Negative binomial models generally exhibited better model fit than Poisson models, suggesting that over-dispersion in the data is the primary factor driving model fit compared to nonlinearity of predictors and excess zeros. All models predicted the peak periods well but were unable to fit and predict the magnitude of peaks, especially when there were high numbers of cases. Adding new variables including historical RRV cases and mosquito abundance may improve model performance. The standard negative binomial generalised linear model is stable, simple, and effective in prediction, and is thus considered the best choice among all models. [ABSTRACT FROM AUTHOR]

Abstract Background Zero-inflated models are generally aimed to addressing the problem that arises from having two different sources that generate the zero values observed in a distribution. In practice, this is due to the fact that the population studied actually consists of two subpopulations: one in which the value zero is by default (structural zero) and the other is circumstantial (sample zero). Methods This work proposes a new methodology to fit zero inflated Bernoulli data from a Bayesian approach, able to distinguish between two potential sources of zeros (structural and non-structural). Results The proposed methodology performance has been evaluated through a comprehensive simulation study, and it has been compiled as an R package freely available to the community. Its usage is illustrated by means of a real example from the field of occupational health as the phenomenon of sickness presenteeism, in which it is reasonable to think that some individuals will never be at risk of suffering it because they have not been sick in the period of study (structural zeros). Without separating structural and non-structural zeros one would be studying jointly the general health status and the presenteeism itself, and therefore obtaining potentially biased estimates as the phenomenon is being implicitly underestimated by diluting it into the general health status. Conclusions The proposed methodology is able to distinguish two different sources of zeros (structural and non-structural) from dichotomous data with or without covariates in a Bayesian framework, and has been made available to any interested researcher in the form of the bayesZIB R package ( https://cran.r-project.org/package=bayesZIB ).