Search

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]

A growing body of applied research on political violence employs split-population models to address problems of zero inflation in conflict event counts and related binary dependent variables. Nevertheless, conflict researchers typically use standard ordered probit models to study discrete ordered dependent variables characterized by excessive zeros (e.g., levels of conflict). This study familiarizes conflict scholars with a recently proposed split-population model—the zero-inflated ordered probit (ZiOP) model—that explicitly addresses the econometric challenges that researchers face when using a “zero-inflated” ordered dependent variable. We show that the ZiOP model provides more than an econometric fix: it provides substantively rich information about the heterogeneous pool of “peace” observations that exist in zero-inflated ordinal variables that measure violent conflict. We demonstrate the usefulness of the model through Monte Carlo experiments and replications of published work and also show that the substantive effects of covariates derived from the ZiOP model can reveal nonmonotonic relationships between these covariates and one’s conflict probabilities of interest. [ABSTRACT FROM PUBLISHER]

This paper presents catch per unit effort (CPUE) standardizations and model selection procedures for four billfish species (Family Istiophoridae) caught primarily as bycatch in the Hawaii-based pelagic longline fishery during 1995–2011: Blue marlin Makaira nigricans ; Striped marlin Kajikia audax ; Shortbill spearfish Tetrapturus angustirostris ; and Sailfish Istiophorus platypterus . The first three species were analyzed on a fishery-wide basis. For sailfish, the fishery data came exclusively from tuna-targeted longline sets in the deep-set sector of the Hawaii-based fishery. We used fishery observer data from the NOAA Fisheries Pacific Islands Regional Observer Program to fit the CPUE standardization models. In this context, our objective was to investigate the quality of model fit for five types of generalized linear models (GLMs: Poisson; negative binomial; zero-inflated Poisson; zero-inflated negative binomial; delta-Gamma). Each of these models represented a different hypothesis about the capture process for a bycatch species for which the catch data primarily consisted of zero catch observations. The five GLMs were fitted by forward entry variable selection, and the best fitting GLM for each species was selected on the basis of Akaike Information Criterion values and calculated Akaike weights. The best-fitting model selected for each species was a zero-inflated negative binomial GLM (ZINB). The ZINB model was comprised of a negative binomial counts model for expected zero catch sets and a positive catch per set distribution along with a binomial inflation model to account for excess zeros. For each species, the important explanatory variables for standardizing CPUE were fishing year, fishing (i.e., calendar) quarter, and fishing region. The best-fitting models indicated that standardized CPUE for striped and blue marlins decreased significantly during the study period. Because the ZINB model was selected as the best fitting model for all species, we suggest that longline CPUE for incidentally caught billfishes is best represented as a process characterized by zero inflation and overdispersion in the positive catches and expected zero catches. We therefore recommend that ZINB models be considered as an a priori model for CPUE standardizations of billfishes and other bycatch species in longline fisheries. [ABSTRACT FROM AUTHOR]

We present motivation and new commands for modeling heaped count data. These data may appear when subjects report counts that are rounded or favor multiples (digit preference) of a certain outcome, such as the number of cigarettes reported. The new commands for fitting count regression models (Poisson, generalized Poisson, negative binomial) are also accompanied by real-world examples comparing the heaped regression model with the usual regression model as well as the heaped zero-inflated model with the usual zero-inflated model. [ABSTRACT FROM AUTHOR]

The presence and abundance of standing dead trees (SDTs) in forests is typically characterized by an excess number of zeros and high variation. The variability inherent in SDT data naturally leads to the assessment of novel quantitative methods to represent SDT populations and their role in contributing to forest ecosystem structure. This analysis assessed the performance of count regression methods fit with Bayesian mixed-effects models that estimate SDTs (all dead trees with a diameter at breast height $${\ge }12.7\hbox { cm}$$ found on plots 0.07-ha in size) on over 17,000 forest inventory plots across the US Lake States (Michigan, Minnesota, and Wisconsin). Random effects models that used the independent variables basal area, mean annual temperature, and plot ownership (i.e., publicly- or privately-owned) as fixed effects and forest type as a random effect outperformed a method which used fixed-effects, alone. Standard and zero-inflated negative binomial models were effective in accounting for overdispersion present in the data (variance/mean ratio for SDT counts was 72.6), whereas Poisson count models were not. Random effects were calibrated on a new population of SDTs. Employing informative prior distributions from the developed model led to improved estimates of SDT abundance by reducing root mean square error by seven percent. This analysis highlights an approach that uses existing models for representing population averages while calibrating their local random effects with new data to arrive at improved estimates of SDTs across the region. [ABSTRACT FROM AUTHOR]

Quantitative microbiological risk assessment (QMRA) is influenced by the choice of the probability distribution used to describe pathogen concentrations, as this may eventually have a large effect on the distribution of doses at exposure. When fitting a probability distribution to microbial enumeration data, several factors may have an impact on the accuracy of that fit. Analysis of the best statistical fits of different distributions alone does not provide a clear indication of the impact in terms of risk estimates. Thus, in this study we focus on the impact of fitting microbial distributions on risk estimates, at two different concentration scenarios and at a range of prevalence levels. By using five different parametric distributions, we investigate whether different characteristics of a good fit are crucial for an accurate risk estimate. Among the factors studied are the importance of accounting for the Poisson randomness in counts, the difference between treating “true” zeroes as such or as censored below a limit of quantification (LOQ) and the importance of making the correct assumption about the underlying distribution of concentrations. By running a simulation experiment with zero-inflated Poisson-lognormal distributed data and an existing QMRA model from retail to consumer level, it was possible to assess the difference between expected risk and the risk estimated with using a lognormal, a zero-inflated lognormal, a Poisson-gamma, a zero-inflated Poisson-gamma and a zero-inflated Poisson-lognormal distribution. We show that the impact of the choice of different probability distributions to describe concentrations at retail on risk estimates is dependent both on concentration and prevalence levels. We also show that the use of an LOQ should be done consciously, especially when zero-inflation is not used. In general, zero-inflation does not necessarily improve the absolute risk estimation, but performance of zero-inflated distributions in QMRA tends to be more robust to changes in prevalence and concentration levels, and to the use of an LOQ to interpret zero values, compared to that of their non-zero-inflated counterparts. [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]

Count time series are frequently encountered in biomedical, epidemiological and public health applications. In principle, such series may exhibit three distinctive features: overdispersion, zero-inflation and temporal correlation. Developing a modelling framework that is sufficiently general to accommodate all three of these characteristics poses a challenge. To address this challenge, we propose a flexible class of dynamic models in the state-space framework. Certain models that have been previously introduced in the literature may be viewed as special cases of this model class. For parameter estimation, we devise a Monte Carlo Expectation-Maximization (MCEM) algorithm, where particle filtering and particle smoothing methods are employed to approximate the high-dimensional integrals in the E-step of the algorithm. To illustrate the proposed methodology, we consider an application based on the evaluation of a participatory ergonomics intervention, which is designed to reduce the incidence of workplace injuries among a group of hospital cleaners. The data consists of aggregated monthly counts of work-related injuries that were reported before and after the intervention. [ABSTRACT FROM PUBLISHER]

In a recent issue (vol. 43) of the Journal of Biogeography, Davies et al. (2015) presented novel analyses of the spatial distribution of tree species around termite mounds in a South African savanna. However, some of their conclusions are not supported by the data. My aim in this correspondence is to point out some limitations of their analyses, stimulate cautious interpretation of their results and suggest better methods for future use. [ABSTRACT FROM AUTHOR]

Temporal replicate counts are often aggregated to improve model fit by reducing zero-inflation and count variability, and in the case of migration counts collected hourly throughout a migration, allows one to ignore nonindependence. However, aggregation can represent a loss of potentially useful information on the hourly or seasonal distribution of counts, which might impact our ability to estimate reliable trends. We simulated 20-year hourly raptor migration count datasets with known rate of change to test the effect of aggregating hourly counts to daily or annual totals on our ability to recover known trend. We simulated data for three types of species, to test whether results varied with species abundance or migration strategy: a commonly detected species, e.g., Northern Harrier, Circus cyaneus; a rarely detected species, e.g., Peregrine Falcon, Falco peregrinus; and a species typically counted in large aggregations with overdispersed counts, e.g., Broad-winged Hawk, Buteo platypterus. We compared accuracy and precision of estimated trends across species and count types (hourly/daily/annual) using hierarchical models that assumed a Poisson, negative binomial (NB) or zero-inflated negative binomial (ZINB) count distribution. We found little benefit of modeling zero-inflation or of modeling the hourly distribution of migration counts. For the rare species, trends analyzed using daily totals and an NB or ZINB data distribution resulted in a higher probability of detecting an accurate and precise trend. In contrast, trends of the common and overdispersed species benefited from aggregation to annual totals, and for the overdispersed species in particular, trends estimating using annual totals were more precise, and resulted in lower probabilities of estimating a trend (1) in the wrong direction, or (2) with credible intervals that excluded the true trend, as compared with hourly and daily counts.

The scan statistic is widely used in spatial cluster detection applications of inhomogeneous Poisson processes. However, real data may present substantial departure from the underlying Poisson process. One of the possible departures has to do with zero excess. Some studies point out that when applied to data with excess zeros, the spatial scan statistic may produce biased inferences. In this work, we develop a closed-form scan statistic for cluster detection of spatial zero-inflated count data. We apply our methodology to simulated and real data. Our simulations revealed that the Scan-Poisson statistic steadily deteriorates as the number of zeros increases, producing biased inferences. On the other hand, our proposed Scan-ZIP and Scan-ZIP+EM statistics are, most of the time, either superior or comparable to the Scan-Poisson statistic. [ABSTRACT FROM AUTHOR]

Chromatin Immunoprecipitation followed by sequencing (ChIP-seq) is a valuable tool for epigenetic studies. Analysis of the data arising from ChIP-seq experiments often requires implicit or explicit statistical modeling of the read counts. The simple Poisson model is attractive, but does not provide a good fit to observed ChIP-seq data. Researchers therefore often either extend to a more general model (e.g., the Negative Binomial), and/or exclude regions of the genome that do not conform to the model. Since many modeling strategies employed for ChIP-seq data reduce to fitting a mixture of Poisson distributions, we explore the problem of inferring the optimal mixing distribution. We apply the Constrained Newton Method (CNM), which suggests the Negative Binomial - Negative Binomial (NB-NB) mixture model as a candidate for modeling ChIP-seq data. We illustrate fitting the NB-NB model with an accelerated EM algorithm on four data sets from three species. Zero-inflated models have been suggested as an approach to improve model fit for ChIP-seq data. We show that the NB-NB mixture model requires no zero-inflation and suggest that in some cases the need for zero inflation is driven by the model's inability to cope with both artifactual large read counts and the frequently observed very low read counts. We see that the CNM-based approach is a useful diagnostic for the assessment of model fit and inference in ChIP-seq data and beyond. Use of the suggested NB-NB mixture model will be of value not only when calling peaks or otherwise modeling ChIP-seq data, but also when simulating data or constructing blacklists de novo. [ABSTRACT FROM AUTHOR]

Count data are most commonly modeled using the Poisson model, or by one of its many extensions. Such extensions are needed for a variety of reasons: (1) a hierarchical structure in the data, e.g., due to clustering, the collection of repeated measurements of the outcome, etc.; (2) the occurrence of overdispersion (or underdispersion), meaning that the variability encountered in the data is not equal to the mean, as prescribed by the Poisson distribution; and (3) the occurrence of extra zeros beyond what a Poisson model allows. The first issue is often accommodated through the inclusion of random subject-specific effects. Though not always, one conventionally assumes such random effects to be normally distributed. Overdispersion is often dealt with through a model developed for this purpose, such as, for example, the negative-binomial model for count data. This can be conceived through a random Poisson parameter. Excess zeros are regularly accounted for using so-called zero-inflated models, which combine either a Poisson or negative-binomial model with an atom at zero. The novelty of this article is that it combines all these features. The work builds upon the modelling framework defined by Molenberghs et al. (2010) in which clustering and overdispersion are accommodated for through two separate sets of random effects in a generalized linear model. [ABSTRACT FROM PUBLISHER]

Zero-inflated (ZI) models, which may be derived as a mixture involving a degenerate distribution at value zero and a distribution such as negative binomial (ZINB), have proved useful in dental and other areas of research by accommodating ‘extra’ zeroes in the data. Used in conjunction with generalised linear models, they allow covariate-adjusted inference of an exposure effect on the mixing probability and on the mean for the non-degenerate distribution. However, these models do not directly provide covariate-adjusted inference for the overall exposure effect. Focusing on the ZINB and ZI beta binomial models, we propose an approach that uses model-predicted values for each person under each exposure state. This ‘average predicted value’ method allows covariate-adjusted estimation of flexible functions of exposure group means such as the difference or ratio. A second approach considers a log link for both components of the ZINB to allow a direct approach to estimation. We apply these new methods to a study of dental caries in very low birth weight adolescents. Simulation studies show good bias and robustness properties for both approaches under various scenarios. Robustness diminishes when there is exposure group imbalance for a covariate with a large effect. [ABSTRACT FROM PUBLISHER]

In this paper we consider spatial regression models for count data. We examine not only the Poisson distribution but also the generalized Poisson capable of modeling over-dispersion, the negative Binomial as well as the zero-inflated Poisson distribution which allows for excess zeros as possible response distribution. We add random spatial effects for modeling spatial dependency and develop and implement MCMC algorithms in $$R$$ for Bayesian estimation. The corresponding R library 'spatcounts' is available on CRAN. In an application the presented models are used to analyze the number of benefits received per patient in a German private health insurance company. Since the deviance information criterion is only appropriate for exponential family models, we use in addition the Vuong and Clarke test with a Schwarz correction to compare possibly non nested models. We illustrate how they can be used in a Bayesian context. [ABSTRACT FROM AUTHOR]

Abstract: Logistic regression models integrating disease presence/absence data are widely used to identify risk factors for a given disease. However, when data arise from imperfect surveillance systems, the interpretation of results is confusing since explanatory variables can be related either to the occurrence of the disease or to the efficiency of the surveillance system. As an alternative, we present spatial and non-spatial zero-inflated Poisson (ZIP) regressions for modelling the number of highly pathogenic avian influenza (HPAI) H5N1 outbreaks that were reported at subdistrict level in Thailand during the second epidemic wave (July 3rd 2004 to May 5th 2005). The spatial ZIP model fitted the data more effectively than its non-spatial version. This model clarified the role of the different variables: for example, results suggested that human population density was not associated with the disease occurrence but was rather associated with the number of reported outbreaks given disease occurrence. In addition, these models allowed estimating that 902 (95% CI 881–922) subdistricts suffered at least one HPAI H5N1 outbreak in Thailand although only 779 were reported to veterinary authorities, leading to a general surveillance sensitivity of 86.4% (95% CI 84.5–88.4). Finally, the outputs of the spatial ZIP model revealed the spatial distribution of the probability that a subdistrict could have been a false negative. The methodology presented here can easily be adapted to other animal health contexts. [Copyright &y& Elsevier]

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]

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., (© The Author 2021. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.)

Objective: 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., Data Sources: Simulations, and two real-world datasets: the 2016-2017 Medical Expenditure Panel Survey (MEPS); the Back Pain Outcomes using Longitudinal Data (BOLD)., Study Design: 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 R 2 ., Conclusions: 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., Competing Interests: Conflicts of interest/Competing interests The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

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., (© 2022 The Authors. Ecology Letters published by John Wiley & Sons Ltd.)

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 over-dispersion 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 non-linearity 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., Competing Interests: The authors declare there are no competing interests., (©2022 Qian et al.)

Background: Malaria transmission is highly heterogeneous and analysis of incidence data must account for this for correct statistical inference. Less widely appreciated is the occurrence of a large number of zero counts (children without a malaria episode) in malaria cohort studies. Zero-inflated regression methods provide one means of addressing this issue, and also allow risk factors providing complete and partial protection to be disentangled. Methods: Poisson, negative binomial (NB), zero-inflated Poisson (ZIP) and zero-inflated negative binomial (ZINB) regression models were fitted to data from two cohort studies of malaria in children in Ghana. Multivariate models were used to understand risk factors for elevated incidence of malaria and for remaining malaria-free, and to estimate the fraction of the population not at risk of malaria. Results: ZINB models, which account for both heterogeneity in individual risk and an unexposed sub-group within the population, provided the best fit to data in both cohorts. These approaches gave additional insight into the mechanism of factors influencing the incidence of malaria compared to simpler approaches, such as NB regression. For example, compared to urban areas, rural residence was found to both increase the incidence rate of malaria among exposed children, and increase the probability of being exposed. In Navrongo, 34% of urban residents were estimated to be at no risk, compared to 3% of rural residents. In Kintampo, 47% of urban residents and 13% of rural residents were estimated to be at no risk. Conclusion: These results illustrate the utility of zero-inflated regression methods for analysis of malaria cohort data that include a large number of zero counts. Specifically, these results suggest that interventions that reach mainly urban residents will have limited overall impact, since some urban residents are essentially at no risk, even in areas of high endemicity, such as in Ghana. [ABSTRACT FROM AUTHOR]

This paper develops a Bayesian spike and slab model for zero-inflated count models which are commonly used in health economics. We account for model uncertainty and allow for model averaging in situations with many potential regressors. The proposed techniques are applied to a German data set analyzing the demand for health care. An accompanying package for the free statistical software environment R is provided. [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]

Abstract: Despite the importance of aquatic symbionts in community organization, often little is known about the relative role of host and environmental characteristics on symbiont abundance. We investigated the importance of environmental and host physical characteristics on the abundance of the branchiobdellidan, Branchiobdella kozarovi, on a population of narrow-clawed crayfish, Astacus leptodactylus, in the Islamic Republic of Iran. Crayfish from four sites in the Aras Dam Reservoir were sampled on 12 occasions during 2009. Abundance of B. kozarovi was modeled against water temperature, crayfish length, mass, and sex after controlling for temporal and spatial effects. The most parsimonious model indicates that B. kozarovi abundance was primarily related to water temperature but also increased linearly with host body length. We found that omitting water temperature dramatically decreased model performance while omitting host physical characteristics decreased model performance marginally. We recommend that ecologists consider both environmental and host physical characteristics when monitoring aquatic symbionts such as branchiobdellidans, as both types of factors will provide insight into community dynamics and guide future management strategies. [Copyright &y& Elsevier]

The estimation of demographic parameters is a key component of evolutionary demography and conservation biology. Capture-mark-recapture methods have served as a fundamental tool for estimating demographic parameters. The accurate estimation of demographic parameters in capture-mark-recapture studies depends on accurate modeling of the observation process. Classic capture-mark-recapture models typically model the observation process as a Bernoulli or categorical trial with detection probability conditional on a marked individual's availability for detection (e.g., alive, or alive and present in a study area). Alternatives to this approach are underused, but may have great utility in capture-recapture studies. In this paper, we explore a simple concept: in the same way that counts contain more information about abundance than simple detection/non-detection data, the number of encounters of individuals during observation occasions contains more information about the observation process than detection/non-detection data for individuals during the same occasion . Rather than using Bernoulli or categorical distributions to estimate detection probability, we demonstrate the application of zero-inflated Poisson and gamma-Poisson distributions. The use of count distributions allows for inference on availability for encounter, as well as a wide variety of parameterizations for heterogeneity in the observation process. We demonstrate that this approach can accurately recover demographic and observation parameters in the presence of individual heterogeneity in detection probability and discuss some potential future extensions of this method., Competing Interests: The authors have no conflict of interest to declare., (© 2022 The Authors. Ecology and Evolution published by John Wiley & Sons Ltd.)

The performance of computational methods and software to identify differentially expressed features in single-cell RNA-sequencing (scRNA-seq) has been shown to be influenced by several factors, including the choice of the normalization method used and the choice of the experimental platform (or library preparation protocol) to profile gene expression in individual cells. Currently, it is up to the practitioner to choose the most appropriate differential expression (DE) method out of over 100 DE tools available to date, each relying on their own assumptions to model scRNA-seq expression features. To model the technological variability in cross-platform scRNA-seq data, here we propose to use Tweedie generalized linear models that can flexibly capture a large dynamic range of observed scRNA-seq expression profiles across experimental platforms induced by platform- and gene-specific statistical properties such as heavy tails, sparsity, and gene expression distributions. We also propose a zero-inflated Tweedie model that allows zero probability mass to exceed a traditional Tweedie distribution to model zero-inflated scRNA-seq data with excessive zero counts. Using both synthetic and published plate- and droplet-based scRNA-seq datasets, we perform a systematic benchmark evaluation of more than 10 representative DE methods and demonstrate that our method (Tweedieverse) outperforms the state-of-the-art DE approaches across experimental platforms in terms of statistical power and false discovery rate control. Our open-source software (R/Bioconductor package) is available at https://github.com/himelmallick/Tweedieverse., (© 2022 John Wiley & Sons Ltd. This article has been contributed to by U.S. Government employees and their work is in the public domain in the USA.)

Response data containing an excessive number of zeros are referred to as zero-inflated data. When differential item functioning (DIF) detection is of interest, zero-inflation can attenuate DIF effects in the total sample and lead to underdetection of DIF items. The current study presents a DIF detection procedure for response data with excess zeros due to the existence of unobserved heterogeneous subgroups. The suggested procedure utilizes the factor mixture modeling (FMM) with MIMIC (multiple-indicator multiple-cause) to address the compromised DIF detection power via the estimation of latent classes. A Monte Carlo simulation was conducted to evaluate the suggested procedure in comparison to the well-known likelihood ratio (LR) DIF test. Our simulation study results indicated the superiority of FMM over the LR DIF test in terms of detection power and illustrated the importance of accounting for latent heterogeneity in zero-inflated data. The empirical data analysis results further supported the use of FMM by flagging additional DIF items over and above the LR test., Competing Interests: Declaration of Conflicting Interests: The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article., (© The Author(s) 2021.)

Purpose: 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., Materials and Methods: 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., Results: 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., Conclusions: 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.Implications for rehabilitationThis 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.

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., Competing Interests: No potential conflict of interest was reported by the author(s)., (© 2022 Informa UK Limited, trading as Taylor & Francis Group.)

In many medical and social science studies, count responses with excess zeros are very common and often the primary outcome of interest. Such count responses are usually generated under some clustered correlation structures due to longitudinal observations of subjects. To model such longitudinal count data with excess zeros, the zero-inflated binomial (ZIB) models for bounded outcomes, and the zero-inflated negative binomial (ZINB) and zero-inflated poisson (ZIP) models for unbounded outcomes all are popular methods. To alleviate the effects of deviations from model assumptions, a semiparametric (or, distribution-free) weighted generalized estimating equations has been proposed to estimate model parameters when data are subject to missingness. In this article, we further explore important covariates for the response variable. Without assumptions on the data distribution, a model selection criterion based on the expected weighted quadratic loss is proposed to select an appropriate subset of covariates, especially when count responses have excess zeros and data are subject to nonmonotone missingness in both responses and covariates. To understand the selection effects of the percentages of excess zeros and missingness, we design various scenarios for covariate selection in the mean model via simulation studies and a real data example regarding the study of cardiovascular disease is also presented for illustration., (© 2022 John Wiley & Sons Ltd.)

The goal of mediation analysis is to identify and explicate the mechanism that underlies a relationship between a risk factor and an outcome via an intermediate variable (mediator). In this paper, we consider the estimation of mediation effects in zero-inflated (ZI) models intended to accommodate 'extra' zeros in count data. Focusing on the ZI negative binomial models, we provide a mediation formula approach to estimate the (overall) mediation effect in the standard two-stage mediation framework under a key sequential ignorability assumption. We also consider a novel decomposition of the overall mediation effect for the ZI context using a three-stage mediation model. Estimation of the components of the overall mediation effect requires an assumption involving the joint distribution of two counterfactuals. Simulation study results demonstrate low bias of mediation effect estimators and close-to-nominal coverage probability of confidence intervals. We also modify the mediation formula method by replacing 'exact' integration with a Monte Carlo integration method. The method is applied to a cohort study of dental caries in very low birth weight adolescents. For overall mediation effect estimation, sensitivity analysis was conducted to quantify the degree to which key assumption must be violated to reverse the original conclusion. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Copyright of Research Papers of the Wroclaw University of Economics / Prace Naukowe Uniwersytetu Ekonomicznego we Wroclawiu is the property of Uniwersytet Ekonomiczny we Wroclawiu and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

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]

Researchers are often interested in modeling longitudinal count data, where the response is a count of some quantity measured on multiple occasions on the same person. Random effects (RE) Poisson regression can be used to model longitudinal count data; however, if there is an excess number of zero counts relative to the Poisson distribution (zero-inflated data), other models may be more appropriate. In this article, RE Poisson, RE negative binomial (RE NB), RE Poisson hurdle (RE PH), RE negative binomial hurdle (RE NBH), RE zero-inflated Poisson (RE ZIP), and RE zero-inflated negative binomial (RE ZINB) models are discussed and compared to a RE logistic-lognormal model. These models are applied to zero-inflated longitudinal count data obtained from the Study of Health and Physical Activity in People with Spinal Cord Injury (SHAPE-SCI), which investigated predictors and outcomes of leisure-time physical activity in people with spinal cord injury. Alternatives to the RE Poisson and RE NB models, such as the RE PH, RE NBH, RE ZIP, and RE ZINB models, are appropriate for analyzing longitudinal count data that is zero-inflated. The choice of model should be based on fit, study design and purpose, and ease of interpretation. [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]

Abstract: The study of species abundance often relies on repeated abundance counts whose number is limited by logistic or financial constraints. The distribution of abundance counts is generally right-skewed (i.e. with many zeros and few high values) and needs to be modelled for statistical inference. We used an extensive dataset involving about 100,000 fish individuals of 12 freshwater fish species collected in electrofishing points (7m2) during 350 field surveys made in 25 stream sites, in order to compare the performance and the generality of four distribution models of counts (Poisson, negative binomial and their zero-inflated counterparts). The negative binomial distribution was the best model (Bayesian Information Criterion) for 58% of the samples (species–survey combinations) and was suitable for a variety of life histories, habitat, and sample characteristics. The performance of the models was closely related to samples’ statistics such as total abundance and variance. Finally, we illustrated the consequences of a distribution assumption by calculating confidence intervals around the mean abundance, either based on the most suitable distribution assumption or on an asymptotical, distribution-free (Student’s) method. Student’s method generally corresponded to narrower confidence intervals, especially when there were few (≤3) non-null counts in the samples. [Copyright &y& Elsevier]

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]