Related papers: Zero & $N$-inflated overdispersed binomial models …
We provide novel probabilistic portrayals of two multivariate models designed to handle zero-inflation in count-compositional data. We develop a new unifying framework that represents both as finite mixture distributions. One of these…
Microorganisms play critical roles in human health and disease. It is well known that microbes live in diverse communities in which they interact synergistically or antagonistically. Thus for estimating microbial associations with clinical…
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…
Dimension reduction of high-dimensional microbiome data facilitates subsequent analysis such as regression and clustering. Most existing reduction methods cannot fully accommodate the special features of the data such as count-valued and…
Imputation of missing values is a strategy for handling non-responses in surveys or data loss in measurement processes, which may be more effective than ignoring them. When the variable represents a count, the literature dealing with this…
Background: Outcome measures that are count variables with excessive zeros are common in health behaviors research. There is a lack of empirical data about the relative performance of prevailing statistical models when outcomes are…
The analysis of count data is commonly done using Poisson models. Negative binomial models are a straightforward and readily motivated generalization for the case of overdispersed data, i.e., when the observed variance is greater than…
We propose a novel statistical inference methodology for multiway count data that is corrupted by false zeros that are indistinguishable from true zero counts. Our approach consists of zero-truncating the Poisson distribution to neglect all…
Microbiome `omics approaches can reveal intriguing relationships between the human microbiome and certain disease states. Along with the identification of specific bacteria taxa associated with diseases, recent scientific advancements…
The workhorse model for zero-truncated count data (y = 1, 2, ...) is the zero-truncated negative binomial (ZTNB) model. We find it should seldom be used. Instead, we recommend the one-inflated zero-truncated negative binomial (OIZTNB) model…
1. Species distribution models (SDM) are tools used to determine environmental features that influence the geographic distribution of species' abundance and have been used to analyze presence-only records. Analysis of presence-only records…
Detecting associations between microbial compositions and sample characteristics is one of the most important tasks in microbiome studies. Most of the existing methods apply univariate models to single microbial species separately, with…
Count data with high frequencies of zeros are found in many areas, specially in biology. Statistical models to analyze such data started to be developed in the 80s and are still a topic of active research. Such models usually assume a…
Zero-inflated count data arise in various fields, including health, biology, economics, and the social sciences. These data are often modelled using probabilistic distributions such as zero-inflated Poisson (ZIP), zero-inflated negative…
Claim frequency data in insurance records the number of claims on insurance policies during a finite period of time. Given that insurance companies operate with multiple lines of insurance business where the claim frequencies on different…
We introduce a class of two-parameter discrete dispersion models, obtained by combining convolution with a factorial tilting operation, similar to exponential dispersion models which combine convolution and exponential tilting. The…
Analyzing overdispersed, zero-inflated, longitudinal count data poses significant modeling and computational challenges, which standard count models (e.g., Poisson or negative binomial mixed effects models) fail to adequately address. We…
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…
We consider three new classes of exponential dispersion models of discrete probability distributions which are defined by specifying their variance functions in their mean value parameterization. In a previous paper (Bar-Lev and Ridder,…
Factor analysis for high-dimensional data is a canonical problem in statistics and has a wide range of applications. However, there is currently no factor model tailored to effectively analyze high-dimensional count responses with…