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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]

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]

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]

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]

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]

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]

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]

Thanks to advances in high-throughput sequencing technologies, the importance of microbiome to human health and disease has been increasingly recognized. Analyzing microbiome data from sequencing experiments is challenging due to their unique features such as compositional data, excessive zero observations, overdispersion, and complex relations among microbial taxa. Clustered microbiome data have become prevalent in recent years from designs such as longitudinal studies, family studies, and matched case–control studies. The within-cluster dependence compounds the challenge of the microbiome data analysis. Methods that properly accommodate intra-cluster correlation and features of the microbiome data are needed. We develop robust and powerful differential composition tests for clustered microbiome data. The methods do not rely on any distributional assumptions on the microbial compositions, which provides flexibility to model various correlation structures among taxa and among samples within a cluster. By leveraging the adjusted sandwich covariance estimate, the methods properly accommodate sample dependence within a cluster. The two-part version of the test can further improve power in the presence of excessive zero observations. Different types of confounding variables can be easily adjusted for in the methods. We perform extensive simulation studies under commonly adopted clustered data designs to evaluate the methods. We demonstrate that the methods properly control the type I error under all designs and are more powerful than existing methods in many scenarios. The usefulness of the proposed methods is further demonstrated with two real datasets from longitudinal microbiome studies on pregnant women and inflammatory bowel disease patients. The methods have been incorporated into the R package "miLineage" publicly available at https://tangzheng1.github.io/tanglab/software.html. [ABSTRACT FROM AUTHOR]

Quantile regression is a powerful tool for modeling non-Gaussian data, and also for modeling different quantiles of the probability distributions of the responses. We propose a Bayesian approach of estimating the quantiles of multivariate longitudinal data where the responses contain excess zeros. We consider a Tobit regression approach, where the latent responses are estimated using a linear mixed model. The longitudinal dependence and the correlations among different (latent) responses are modeled by the subject-specific vector of random effects. We consider a mixture representation of the Asymmetric Laplace Distribution (ALD), and develop an efficient MCMC algorithm for estimating the model parameters. The proposed approach is used for analyzing data from the health and retirement study (HRS) conducted by the University of Michigan, USA; where we jointly model (i) out-of-pocket medical expenditures, (ii) total financial assets, and (iii) total financial debt for the aged subjects, and estimate the effects of different covariates on these responses across different quantiles. Simulation studies are performed for assessing the operating characteristics of the proposed approach. [ABSTRACT FROM AUTHOR]

Students' performance is a crucial aspect for university programs effectiveness and organization. In this paper, we introduce and analyze a performance index for the first-year students of a private Italian university, namely the Libera Università Maria Ss. Assunta. We use administrative data on 532 undergraduate students enrolled in any of the eight available bachelor degrees in 2015. Our aim is to improve the general understanding of performance linking it with personal student's characteristics and with degree-specific aspects. A beta inflated latent class approach is employed to identify clusters of performance establishing a link with all available explanatory variables. The empirical analysis unveils that a good and balanced degree organization may improve students' performance. The student's ability plays a crucial role in discriminating between good and bad performances, and also strongly depends on individual-specific characteristics, such as the final mark obtained at high school. [ABSTRACT FROM AUTHOR]

The marginal distribution of count data processes rarely follows a simple Poisson model in practice. Instead, one commonly observes deviations such as overdispersion or zero inflation. To express the extend of such deviations from a Poisson model, one can compute an appropriately defined dispersion index or zero index. In this article, we develop several tests based on such indexes, including joint tests being based on an index combination. The asymptotic distribution of the resulting test statistics under the null hypothesis of a Poisson INAR(1) model is derived, and the finite-sample performance of the resulting tests is analyzed. Real data examples illustrate the application of these tests in practice. [ABSTRACT FROM AUTHOR]

In this paper, we construct a new mixture of geometric INAR(1) process for modeling over-dispersed count time series data, in particular data consisting of large number of zeros and ones. For some real data sets, the existing INAR(1) processes do not fit well, e.g., the geometric INAR(1) process overestimates the number of zero observations and underestimates the one observations, whereas Poisson INAR(1) process underestimates the zero observations and overestimates the one observations. Furthermore, for heavy tails, the PINAR(1) process performs poorly in the tail part. The existing zero-inflated Poisson INAR(1) and compound Poisson INAR(1) processes have the same kind of limitations. In order to remove this problem of under-fitting at one point and over-fitting at others points, we add some extra probability at one in the geometric INAR(1) process and build a new mixture of geometric INAR(1) process. Surprisingly, for some real data sets, it removes the problem of under and over-fitting over all the observations up to a significant extent. We then study the stationarity and ergodicity of the proposed process. Different methods of parameter estimation, namely the Yule-Walker and the quasi-maximum likelihood estimation procedures are discussed and illustrated using some simulation experiments. Furthermore, we discuss the future prediction along with some different forecasting accuracy measures. Two real data sets are analyzed to illustrate the effective use of the proposed model. [ABSTRACT FROM AUTHOR]

Count data with excess zeros are often encountered in many medical, biomedical and public health applications. In this paper, an extension of zero-inflated Poisson mixed regression models is presented for dealing with multilevel data set, referred as hierarchical mixture zero-inflated Poisson mixed regression models. A stochastic EM algorithm is developed for obtaining the ML estimates of interested parameters and a model comparison is also considered for comparing models with different latent classes through BIC criterion. An application to the analysis of count data from a Shanghai Adolescence Fitness Survey and a simulation study illustrate the usefulness and effectiveness of our methodologies. [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]

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]

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]

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]

Maydeu-Olivares and Joe (J. Am. Stat. Assoc. 100:1009–1020, ; Psychometrika 71:713–732, ) introduced classes of chi-square tests for (sparse) multidimensional multinomial data based on low-order marginal proportions. Our extension provides general conditions under which quadratic forms in linear functions of cell residuals are asymptotically chi-square. The new statistics need not be based on margins, and can be used for one-dimensional multinomials. We also provide theory that explains why limited information statistics have good power, regardless of sparseness. We show how quadratic-form statistics can be constructed that are more powerful than X and yet, have approximate chi-square null distribution in finite samples with large models. Examples with models for truncated count data and binary item response data are used to illustrate the theory. [ABSTRACT FROM AUTHOR]

In many ecological research studies, abundance data are skewed and contain more zeros than might be expected. Often, the aim is to model abundance in terms of covariates, and to estimate expected abundance for a given set of covariate values. An approach that has been advocated recently involves the use of a conditional model. This allows one to separately model presence and abundance given presence, which should lead to a more complete understanding as to how the covariates influence abundance. The focus of this article is on the calculation of confidence intervals for expected abundance given particular values of the covariates. The standard Wald confidence interval is symmetric, and therefore unlikely to be of much use for skewed data, where reliable confidence intervals for abundance will generally be asymmetric. The purpose of this article is to show how to calculate a profile likelihood confidence interval for expected abundance using a conditional model. [ABSTRACT FROM AUTHOR]

Count data with excess zeros encountered in many applications often exhibit extra variation. Therefore, zero-inflated Poisson (ZIP) model may fail to fit such data. In this paper, a zero-inflated double Poisson model (ZIDP), which is generalization of the ZIP model, is studied and the score tests for the significance of dispersion and zero-inflation in ZIDP model are developed. Meanwhile, this work also develops homogeneous tests for dispersion and/or zero-inflation parameter, and corresponding score test statistics are obtained. One numerical example is given to illustrate our methodology and the properties of score test statistics are investigated through Monte Carlo simulations. [ABSTRACT FROM AUTHOR]