Search

A tolerance band for a functional response provides a region that is expected to contain a given fraction of observations from the sampled population at each point in the domain. This band is a functional analogue of the tolerance interval for a univariate response. Although the problem of constructing functional tolerance bands has been considered for a Gaussian response, it has not been investigated for non‐Gaussian responses, which are common in biomedical applications. We describe a methodology for constructing tolerance bands for two non‐Gaussian members of the exponential family: binomial and Poisson. The approach is to first model the data using the framework of generalized functional principal components analysis. Then, a parameter is identified in which the marginal distribution of the response is stochastically monotone. We show that the tolerance limits can be readily obtained from confidence limits for this parameter, which in turn can be computed using large‐sample theory and bootstrapping. Our proposed methodology works for both dense and sparse functional data. We report the results of simulation studies designed to evaluate its performance and get recommendations for practical applications. We illustrate our proposed method using two actual biomedical studies, and also provide computer source code that implements our method. [ABSTRACT FROM AUTHOR]

The meta–analysis of two trials is valuable in many practical situations, such as studies of rare and/or orphan diseases focussed on a single intervention. In this context, additional concerns, like small sample size and/or heterogeneity in the results obtained, might make standard frequentist and Bayesian techniques inappropriate. In a meta–analysis, moreover, the presence of between–sample heterogeneity adds model uncertainty, which must be taken into consideration when drawing inferences. We suggest that the most appropriate way to measure this heterogeneity is by clustering the samples and then determining the posterior probability of the cluster models. The meta–inference is obtained as a mixture of all the meta–inferences for the cluster models, where the mixing distribution is the posterior model probability. We present a simple two–component form of Bayesian model averaging that is unaffected by characteristics such as small study size or zero–cell counts, and which is capable of incorporating uncertainties into the estimation process. Illustrative examples are given and analysed, using real sparse binomial data. [ABSTRACT FROM AUTHOR]

This paper presents a new model-based generalized functional clustering method for discrete longitudinal data, such as multivariate binomial and Poisson distributed data. For this purpose, we propose a multivariate functional principal component analysis (MFPCA)-based clustering procedure for a latent multivariate Gaussian process instead of the original functional data directly. The main contribution of this study is two-fold: modeling of discrete longitudinal data with the latent multivariate Gaussian process and developing of a clustering algorithm based on MFPCA coupled with the latent multivariate Gaussian process. Numerical experiments, including real data analysis and a simulation study, demonstrate the promising empirical properties of the proposed approach. [ABSTRACT FROM AUTHOR]

It is not uncommon for researchers to want to interrogate paired binomial data. For example, researchers may want to compare an organism's response (positive or negative) to two different stimuli. If they apply both stimuli to a sample of individuals, it would be natural to present the data in a 2 × 2 table. There would be two cells with concordant results (the frequency of individuals which responded positively or negatively to both stimuli) and two cells with discordant results (the frequency of individuals who responded positively to one stimulus, but negatively to the other). The key issue is whether the totals in the two discordant cells are sufficiently different to suggest that the stimuli trigger different reactions. In terms of the null hypothesis testing paradigm, this would translate as a P value which is the probability of seeing the observed difference in these two values or a more extreme difference if the two stimuli produced an identical reaction. The statistical test designed to provide this P value is the McNemar test. Here, we seek to promote greater and better use of the McNemar test. To achieve this, we fully describe a range of circumstances within biological research where it can be effectively applied, describe the different variants of the test that exist, explain how these variants can be accessed in R, and offer guidance on which of these variants to adopt. To support our arguments, we highlight key recent methodological advances and compare these with a novel survey of current usage of the test. Significance statement: When analysing paired binomial data, researchers appear to reflexively apply a chi-squared test, with the McNemar test being largely overlooked, despite it often being more appropriate. As these tests evaluate a different null hypothesis, selecting the appropriate test is essential for effective analysis. When using the McNemar test, there are four methods that can be applied. Recent advice has outlined clear guidelines on which method should be used. By conducting a survey, we provide support for these guidelines, but identify that the method chosen in publications is rarely specified or the most appropriate. Our study provides clear guidance on which method researchers should select and highlights examples of when this test should be used and how it can be implemented easily to improve future research. [ABSTRACT FROM AUTHOR]

Copyright of Erzincan University Journal of Science & Technology is the property of Erzincan Binali Yildirim Universitesi 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.)

Discrete data in the form of proportions with overdispersion and zero inflation can arise in toxicology and other similar fields. In regression analysis of such data, another problem that also may arise in practice is that some responses may be missing. In this paper, we develop estimation procedure for the parameters of a zero-inflated overdispersed binomial model in the presence of missing responses under three different missing data mechanisms. A weighted expectation maximization algorithm is used for the maximum likelihood estimation of the parameters involved. Extensive simulations are conducted to study the properties of the estimates in terms of average of estimates, relative bias, variance, mean squared error, and coverage probability of estimates. Simulations show much superior properties of the estimates obtained using the weighted expectation maximization algorithm. Some illustrative examples and a discussion are given. [ABSTRACT FROM AUTHOR]

Germination data are discrete and binomial. Although analysis of variance (ANOVA) has long been used for the statistical analysis of these data, generalized linear mixed models (GzLMMs) provide a more consistent theoretical framework. GzLMMs are suitable for final germination percentages (FGP) as well as longitudinal studies of germination time-courses. Germination indices (i.e., single-value parameters summarizing the results of a germination assay by combining the level and rapidity of germination) and other data with a Gaussian error distribution can be analyzed too. There are, however, different kinds of GzLMMs: Conditional (i.e., random effects are modeled as deviations from the general intercept with a specific covariance structure), marginal (i.e., random effects are modeled solely as a variance/covariance structure of the error terms), and quasi-marginal (some random effects are modeled as deviations from the intercept and some are modeled as a covariance structure of the error terms) models can be applied to the same data. It is shown that: (a) For germination data, conditional, marginal, and quasi-marginal GzLMMs tend to converge to a similar inference; (b) conditional models are the first choice for FGP; (c) marginal or quasi-marginal models are more suited for longitudinal studies, although conditional models lead to a congruent inference; (d) in general, common random factors are better dealt with as random intercepts, whereas serial correlation is easier to model in terms of the covariance structure of the error terms; (e) germination indices are not binomial and can be easier to analyze with a marginal model; (f) in boundary conditions (when some means approach 0% or 100%), conditional models with an integral approximation of true likelihood are more appropriate; in non-boundary conditions, (g) germination data can be fitted with default pseudo-likelihood estimation techniques, on the basis of the SAS-based code templates provided here; (h) GzLMMs are remarkably good for the analysis of germination data except if some means are 0% or 100%. In this case, alternative statistical approaches may be used, such as survival analysis or linear mixed models (LMMs) with transformed data, unless an ad hoc data adjustment in estimates of limit means is considered, either experimentally or computationally. This review is intended as a basic tutorial for the application of GzLMMs, and is, therefore, of interest primarily to researchers in the agricultural sciences.

A commonly occurring problem in reliability testing is how to combine pass/fail test data that is collected from disparate environments. We have worked with colleagues in aerospace engineering for a number of years where two types of test environments in use are ground tests and flight tests. Ground tests are less expensive and consequently more numerous. Flight tests are much less frequent, but directly reflect the actual usage environment. We discuss a relatively simple combining approach that realizes the benefit of a larger sample size by using ground test data, but at the same time accounts for the difference between the two environments. We compare our solution with what look like more sophisticated approaches to the problem in order to calibrate its limitations. Overall, we find that our proposed solution is robust to its inherent assumptions, which explains its usefulness in practice. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Investigating the relationship between vegetation cover and substrate typologies is important for habitat conservation. To study these relationships, common practice in modern ecological surveys is to collect information regarding vegetation cover and substrate typology over fine regular lattices, as derived from digital ground photos. Information on substrate typologies is often available as compositional measures, e.g., the area proportion occupied by a certain substrate. Two primary issues are of interest for ecologists: first, how much substrate typologies differ in terms of relative suitability for vegetation cover and, second, whether suitability varies over time. This paper develops a procedure for managing compositional covariates within a Bayesian hierarchical framework to effectively address the aforementioned issues. A spatio-temporal model is adopted to estimate the temporal pattern characterizing substrate relative suitability for vegetation cover and, at the same time, to account for spatio-temporal correlation. Relative suitability is modeled by time-varying regression coefficients, and spatial, temporal and spatio-temporal random effects are modeled using Gaussian Markov Random Field models. [ABSTRACT FROM AUTHOR]

The analysis of geographical and temporal variability of binomial data, using generalized additive mixed models, are considered. In this class of models, spatially correlated random effects and temporal components are adopted. The frequentist analysis of these complex models is computationally difficult. Recently developed method of data cloning has overcome the computational challenges of the analysis of mixed models from the frequentist approach. We use data cloning, which yields to maximum likelihood estimation, to propose frequentist analysis of spatiotemporal modeling of odds of disease. The advantages of the data cloning approach are that the prediction and prediction interval of the smoothing odds over space and time are easily obtained. We illustrate this approach using a real dataset of yearly asthma physician visits by children in the province of Manitoba, Canada, during 2000-2010. The performance of the proposed approach is also studied through a simulation study. [ABSTRACT FROM AUTHOR]

Highlights: [•] More lonely people disclosed private information such as Address than the connected. [•] Less lonely people did not disclose any private information compared to the connected. [•] Less lonely people disclosed their Views and their Wall than those connected people. [•] More lonely people did not disclose Views and their Wall compared to connected people. [•] No other significant associations between loneliness and other variables were found. [Copyright &y& Elsevier]

When modelling multivariate binomial data, it often occurs that it is necessary to take into consideration both clustering and overdispersion, the former arising from the dependence between data, and the latter due to the additional variability in the data not prescribed by the distribution. If interest lies in accommodating both phenomena at the same time, we can use separate sets of random effects that capture the within-cluster association and the extra variability. In particular, the random effects for overdispersion can be included in the model either additively or multiplicatively. For this purpose, we propose a series of Bayesian hierarchical models that deal simultaneously with both phenomena. The proposed models are applied to bivariate repeated prevalence data for hepatitis C virus (HCV) and human immunodeficiency virus (HIV) infection in injecting drug users in Italy from 1998 to 2007. [ABSTRACT FROM AUTHOR]

This article deals with binomial logit models where the parameters are estimated within a Bayesian framework. Such models arise, for instance, when repeated measurements are available for identical covariate patterns. To perform MCMC sampling, we rewrite the binomial logit model as an augmented model which involves some latent variables called random utilities. It is straightforward, but inefficient, to use the individual random utility model representation based on the binary observations reconstructed from each binomial observation. Alternatively, we present in this article a new method to aggregate the random utilities for each binomial observation. Based on this aggregated representation, we have implemented an independence Metropolis-Hastings sampler, an auxiliary mixture sampler, and a novel hybrid auxiliary mixture sampler. A comparative study on five binomial datasets shows that the new aggregation method leads to a superior sampler in terms of efficiency compared to previously published data augmentation samplers. [ABSTRACT FROM AUTHOR]

This article is motivated by the need of biological and environmental scientists to fit a popular nonlinear model to binary dose-response data. The four-parameter logistic model, also known as the Hill model, generalizes the usual logistic regression model to allow the lower and upper response asymptotes to be greater than zero and less than one, respectively. This article develops an EM algorithm, which is naturally suited for maximum likelihood estimation under the Hill model after conceptualizing the problem as a mixture of subpopulations in which some subjects respond regardless of dose, some fail to respond regardless of dose, and some respond with a probability that depends on dose. The EM algorithm leads to a pair of functionally independent two-parameter optimizations and is easy to program. Not only can this approach be computationally appealing compared to simultaneous optimization with respect to all four parameters, but it also facilitates estimating covariances, incorporating predictors, and imposing constraints. This article is motivated by, and the EM algorithm is illustrated with, data from a toxicology study of the dose effects of selenium on the death rates of flies. Other biological and environmental applications, as well as medical and agricultural applications, are also described briefly. Computer code for implementing the EM algorithm is available as supplemental material online. [ABSTRACT FROM AUTHOR]

Traps for monitoring of flying insect pests constitute a critical part of integrated pest management strategies. However, interpretation of trap captures is hampered by 1) factors associated with the performance of traps (i.e., lure, trap design, placement); 2) an often poorly defined relationship between trap captures and population density; and 3) interpretation approaches being highly specific to a certain insect species, trapping method, or trapping environment. The main purpose of this study was to identify a trap capture interpretation approach with little sensitivity to characteristics specific to a given data set, which would allow easier comparison of trapping data sets and make it easier to standardize sampling plans across insect pests and trapping environments. Based on fits of trapping data sets to standard distributions (normal, Poisson, and negative binomial), evaluations of the index of aggregation, k, and linear regression coefficients from Taylor's power law, we concluded that these characteristics varied considerably among data sets, which means that enumerative sampling plans may not be appropriate. Across 13 trapping data sets of six insect species, we showed a consistent nonlinear relationship between average trap captures and number of traps with zero captures and that the k can be stabilized by converting trapping data into binomial data. A trap interpretation approach based on number of zero captures is both easy to use, was found to be species-independent, and means that it may be possible to establish meaningful and reliable action thresholds based on trap captures of flying insects. Although developed using trapping data from food facilities, this approach may have application to trapping data from other environments as well. [ABSTRACT FROM AUTHOR]

In longitudinal data analysis one frequently encounters non-Gaussian data that are repeatedly collected for a sample of individuals over time. The repeated observations could be binomial, Poisson or of another discrete type or could be continuous. The timings of the repeated measurements are often sparse and irregular. We introduce a latent Gaussian process model for such data, establishing a connection to functional data analysis. The functional methods proposed are non-parametric and computationally straightforward as they do not involve a likelihood. We develop functional principal components analysis for this situation and demonstrate the prediction of individual trajectories from sparse observations. This method can handle missing data and leads to predictions of the functional principal component scores which serve as random effects in this model. These scores can then be used for further statistical analysis, such as inference, regression, discriminant analysis or clustering. We illustrate these non-parametric methods with longitudinal data on primary biliary cirrhosis and show in simulations that they are competitive in comparisons with generalized estimating equations and generalized linear mixed models. [ABSTRACT FROM AUTHOR]

The Cochran-Armitage test is the most frequently used test for trend among binomial proportions. This test can be performed based on the asymptotic normality of its test statistic or based on an exact null distribution. As an alternative, a recently introduced modification of the Baumgartner-Weiß-Schindler statistic, a novel nonparametric statistic, can be used. Simulation results indicate that the exact test based on this modification is preferable to the Cochran-Armitage test. This exact test is less conservative and more powerful than the exact Cochran-Armitage test. The power comparison to the asymptotic Cochran-Armitage test does not show a clear winner, but the difference in power is usually small. The exact test based on the modification is recommended here because, in contrast to the asymptotic Cochran-Armitage test, it guarantees a type I error rate less than or equal to the significance level. Moreover, an exact test is often more appropriate than an asymptotic test because randomization rather than random sampling is the norm, for example in biomedical research. The methods are illustrated with an example data set. [ABSTRACT FROM AUTHOR]

When a complaint of discrimination is made, an employer may respond by hiring more minorities. From a legal viewpoint, the practices in effect during the time period prior to the complaint are more relevant for determining liability than those of the postcharge period. In Gay v. Waiters, the trial judge observed that the data suggested that a change occurred after the charge was filed. Because the data had not been subject to a formal statistical analysis, the court was reluctant to base its decision on this observation. Gastwirth and Freidlin and Gastwirth proposed cumulative-sum-based procedures for the analysis of hiring data following the binomial model. In this article, the procedures are extended to data following the hypergeometric model and to analysis of stratified data. Several datasets that were submitted to the courts in the United States are analyzed by the proposed methods. Because the data are usually reported by year, the ordinary large-sample theory is not sufficiently accurate. Therefore, we obtain the p values of the statistics by simulation. For binomial data, recent improvements in the Bonferroni inequality are used to derive a new upper bound. [ABSTRACT FROM AUTHOR]

Consider the conditionally independent hierarchical model (CIHM) in which observations y1 are independently distributed from f(y, ∣ θ1), the parameters θ1 are independently distributed from distributions g(θ/λ), and the hyperpararneters A are distributed according to a distribution h(λ). The posterior distribution of all parameters of the CIHM can be efficiently simulated by Markov chain Monte Carlo (MCMC) algorithms. Although these simulation algorithms have facilitated the application of CIHMs, they generally have not addressed the problem of computing quantities useful in model selection. This article explores how MCMC simulation algorithms and other related computational algorithms can be used to compute Bayes factors that arc useful in criticizing a particular CIHM. In the case where the CIHM models a belief that the parameters are exchangeable or lie on a regression surface, the Bayes factor can measure the consistency of the data with the structural prior belief. Hayes factors can also be used to judge the suitability of particular assumptions in CIHMs, including the choice of link function, the nonexistence or existence of outliers, and the prior belief in exchangeability, The methods are illustrated in the situation in which a CIHM is used to model structural prior information about a set of binomial probabilities. [ABSTRACT FROM AUTHOR]

To analyze hiring data in equal employment cases, the available positions should be stratified in accordance with the qualifications needed for the jobs. It is then necessary to combine the results of each stratum to obtain an overall test of equal hiring rates. Furthermore, a summary measure, which compares the hiring rate of a minority applicant to that of a majority one, is then estimated. Indeed, the relative risk measure is used by the government in assessing an employment practice for possible discriminatory impact. Sometimes reliable data on the applicants is unavailable, but an accurate estimate of the minority fraction, pi[sub 1], of qualified persons in the appropriate labor market is obtainable from census or other external data. Usually the number of hires, t,, in each occupation is small relative to the number of applicants, which itself is a small fraction of the large external pool of qualified persons. Then the number of minority hires, x,, in each occupation can be regarded as a binomial variable with parameters (t[sub 1], pi[sub 1]). This binomial model has been used to analyze hires in a single occupation where there was no need for stratification. This article develops analogs of the Mantel-Haenszel (1959) and maximum likelihood estimators of a common odds ratio for several 2 x 2 tables for the binomial situation. In addition to presenting the large sample theory of these estimators, two tests to check the validity of the assumption of a common odds ratio are developed. The methods are used to analyze data from two cases, one in which the assumption of a common odds ratio was appropriate and one in which it was not. The sensitivity of the results to the assumed values of e, is also explored, and the assumptions implicit in the use of the binomial model for minority hires are... [ABSTRACT FROM AUTHOR]

Useful model checking tools can be constructed by measuring the distance between a prior distribution that concentrates most of its mass around a model of interest, and the resulting posterior distribution. In this paper we use this approach to construct a diagnostic measure for detecting lack of fit in discrete data, with special focus on binomial data. We begin by constructing a suitable probability model “around” the model of interest, via a Dirichlet Process elaboration. We derive the resulting diagnostic and show that, approximately, it is the sum of two terms: the first is the logarithm of the Bayes factor and the second is proportional to the Pearson chi-square statistics. We give details of a simulation algorithm for computing the diagnostic and illustrate its use in an application to biomedical data. [ABSTRACT FROM AUTHOR]

The analysis of discrete observations has always presented problems with a variety of methods of varying complexity but typically none simple. Unless, that is, one ignores the categorical nature of the data and does a usual analysis of variance. Surprisingly this often does quite well yielding "p values" quite similar to more appropriate methods, e.g. logistic regression for binomial data. If one is interested in estimates, however, these may be more interpretable using an appropriate nonlinear method. Currently there is readily available software for the analyses. A series of case studies will be presented. [ABSTRACT FROM AUTHOR]