A common feature of ecological data sets is their tendency to contain many zero values. Statistical inference based on such data are likely to be inefficient or wrong unless careful thought is given to how these zeros arose and how best to model them. In this paper, we propose a framework for understanding how zero-inflated data sets originate and deciding how best to model them. We define and classify the different kinds of zeros that occur in ecological data and describe how they arise: either from 'true zero' or 'false zero' observations. After reviewing recent developments in modelling zero-inflated data sets, we use practical examples to demonstrate how failing to account for the source of zero inflation can reduce our ability to detect relationships in ecological data and at worst lead to incorrect inference. The adoption of methods that explicitly model the sources of zero observations will sharpen insights and improve the robustness of ecological analyses.

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Zero tolerance ecology: improving ecological inference by modelling the source of zero observations

Summary. Models based on the bivariate Poisson distribution are used for modelling sports data. Independent Poisson distributions are usually adopted to model the number of goals of two competing teams. We replace the independence assumption by considering a bivariate Poisson model and its extensions. The models proposed allow for correlation between the two scores, which is a plausible assumption in sports with two opposing teams competing against each other. The effect of introducing even slight correlation is discussed. Using just a bivariate Poisson distribution can improve model fit and prediction of the number of draws in football games. The model is extended by considering an inflation factor for diagonal terms in the bivariate joint distribution. This inflation improves in precision the estimation of draws and, at the same time, allows for overdispersed, relative to the simple Poisson distribution, marginal distributions. The properties of the models proposed as well as interpretation and estimation procedures are provided. An illustration of the models is presented by using data sets from football and water-polo.

https://www.jstor.org/stable/pdfplus/4128211.pdf

Analysis of sports data by using bivariate Poisson models

Background Topical fluoride therapy (TFT) in the form of varnish, gel, mouthrinse or toothpaste has been used extensively as a caries-preventive intervention for over three decades. Objectives To determine the effectiveness and safety of fluoride varnishes, gels, mouthrinses, and toothpastes in the prevention of dental caries in children and to examine factors potentially modifying their effect. Search strategy We searched the Cochrane Oral Health Group's Trials Register (May 2000), CENTRAL (The Cochrane Library Issue 2, 2000), MEDLINE (1966 to January 2000), plus several other databases. We handsearched journals, reference lists of articles and contacted selected authors and manufacturers. Selection criteria Randomized or quasi-randomized controlled trials with blind outcome assessment, comparing fluoride varnish, gel, mouthrinse, or toothpaste with placebo or no treatment in children up to 16 years during at least 1 year. The main outcome was caries increment measured by the change in decayed, missing and filled tooth surfaces (D(M)FS). Data collection and analysis Inclusion decisions, quality assessment and data extraction were duplicated in a random sample of one third of studies, and consensus achieved by discussion or a third party. Authors were contacted for missing data. The primary measure of effect was the prevented fraction (PF) that is the difference in mean caries increments between the treatment and control groups expressed as a percentage of the mean increment in the control group. Random effects meta-analyses were performed where data could be pooled. Potential sources of heterogeneity were examined in random effects metaregression analyses. Main results There were 144 studies included. For the 133 that contributed data for meta-analysis (involving 65,169 children) the D(M)FS pooled prevented fraction estimate was 26% (95% CI, 24% to 29%; p Reviewer's conclusions The benefits of topical fluorides have been firmly established on a sizeable body of evidence from randomized controlled trials. While the formal examination of sources of heterogeneity between studies has been important in the overall conclusions reached, these should be interpreted with caution. We were unable to reach definite conclusions about any adverse effects that might result from the use of topical fluorides, because data reported in the trials are scarce.

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Topical fluoride (toothpastes, mouthrinses, gels or varnishes) for preventing dental caries in children and adolescents

flexmix provides infrastructure for flexible fitting of finite mixture models in R using the expectation-maximization (EM) algorithm or one of its variants. The functionality of the package was enhanced. Now concomitant variable models as well as varying and constant parameters for the component specific generalized linear regression models can be fitted. The application of the package is demonstrated on several examples, the implementation described and examples given to illustrate how new drivers for the component specific models and the concomitant variable models can be defined.

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FlexMix Version 2: Finite Mixtures with Concomitant Variables and Varying and Constant Parameters

Comparing species abundance models

For frequency counts, the situation of extra zeros often arises in biomedical applications. This is demonstrated with count data from a dental epidemiological study in Belo Horizonte (the Belo Horizonte caries prevention study) which evaluated various programmes for reducing caries. Extra zeros, however, violate the variance–mean relationship of the Poisson error structure. This extra-Poisson variation can easily be explained by a special mixture model, the zero-inflated Poisson (ZIP) model. On the basis of the ZIP model, a graphical device is presented which not only summarizes the mixing distribution but also provides visual information about the overall mean. This device can be exploited to evaluate and compare various groups. Ways are discussed to include covariates and to develop an extension of the conventional Poisson regression. Finally, a method to evaluate intervention effects on the basis of the ZIP regression model is described and applied to the data of the Belo Horizonte caries prevention study.

U. Kirchner

Papers

The zero-inflated Poisson model and the decayed, missing and filled teeth index in dental epidemiology

Corrigendum: The zero‐inflated Poisson model and the decayed, missing and filled teeth index in dental epidemiology