A simulation study on the influence of ties on uniform scores test for circular data

Uniform scores test is a rank-based method that tests the homogeneity of k-populations in circular data problems. The influence of ties on the uniform scores test has been emphasized by several authors in several articles and books. Moreover, it is suggested that the uniform scores test should be used with caution if ties are present in the data. This paper investigates the influence of ties on the uniform scores test by computing the power of the test using average, randomization, permutation, minimum, and maximum methods to break ties. Monte Carlo simulation is performed to compute the power of the test under several scenarios such as having 5% or 10% of ties and tie group structures in the data. The simulation study shows no significant difference among the methods under the existence of ties but the test loses its power when there are many ties or complicated group structures. Thus, randomization or average methods are equally powerful to break ties when applying uniform scores test. Also, it can be concluded that k-sample uniform scores test can be used safely without sacrificing the power if there are only less than 5% of ties or at most two groups of a few ties.     

A Bayesian analysis of the change-point problem for directional data

In this paper, we discuss a simple fully Bayesian analysis of the change-point problem for the directional data in the parametric framework with von Mises or circular normal distribution as the underlying distribution. We first discuss the problem of detecting change in the mean direction of the circular normal distribution using a latent variable approach when the concentration parameter is unknown. Then, a simpler approach, beginning with proper priors for all the unknown parameters – the sampling importance resampling technique – is used to obtain the posterior marginal distribution of the change-point. The method is illustrated using the wind data [E.P. Weijers, A. Van Delden, H.F. Vugts and A.G.C.A. Meesters, The composite horizontal wind field within convective structures of the atmospheric surface layer, J. Atmos. Sci. 52 (1995. 3866–3878]. The method can be adapted for a variety of situations involving both angular and linear data and can be used with profit in the context of statistical process control in Phase I of control charting and also in Phase II in conjunction with control charts.     

A random‐effects model for clustered circular data

This article considers a circular regression model for clustered data, where both the cluster effects and the regression errors have von Mises distributions. It involves β, a vector of parameters for the fixed effects, and two concentration parameters for the error distribution. A measure of intra‐cluster circular correlation and a predictor for an unobserved cluster random effect are studied. Preliminary estimators for the vector β and the two concentration parameters are proposed, and their performance is compared with that of the maximum likelihood estimators in a simulation study. A numerical example investigating the factors impacting the orientation taken by a sand hopper when released is presented. The Canadian Journal of Statistics 47: 712–728; 2019 © 2019 Statistical Society of Canada     

A log-linear regression model for the odd Weibull distribution with censored data

We introduce the log-odd Weibull regression model based on the odd Weibull distribution (Cooray, 2006). We derive some mathematical properties of the log-transformed distribution. The new regression model represents a parametric family of models that includes as sub-models some widely known regression models that can be applied to censored survival data. We employ a frequentist analysis and a parametric bootstrap for the parameters of the proposed model. We derive the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes and present some ways to assess global influence. Further, for different parameter settings, sample sizes and censoring percentages, some simulations are performed. In addition, the empirical distribution of some modified residuals are given and compared with the standard normal distribution. These studies suggest that the residual analysis usually performed in normal linear regression models can be extended to a modified deviance residual in the proposed regression model applied to censored data. We define martingale and deviance residuals to check the model assumptions. The extended regression model is very useful for the analysis of real data.     

Correspondence analysis of repair data: a case study for electric cable shovels

In mining operation, effective maintenance scheduling is very important because of its effect on the performance of equipment and production costs. Classifying equipment on the basis of repair durations is considered one of the essential works to schedule maintenance activities effectively. In this study, repair data of electric cable shovels used in the Western Coal Company, Turkey, has been analyzed using correspondence analysis to classify shovels in terms of repair durations. Correspondence analysis, particularly helpful in analysing cross-tabular data in the form of numerical frequencies, has provided a graphical display that permitted more rapid interpretation and understanding of the repair data. The results indicated that there are five groups of shovels according to their repair duration. Especially, shovels numbered 2, 3, 7, 10 and 11 required a repair duration of<1 h and maintained relatively good service condition when compared with others. Thus, priority might be given to repair them in maintenance job scheduling even if there is another failed shovel waiting to be serviced. This type of information will help mine managers to increase the number of available shovels in operation.     

A case study in non-centering for data augmentation: Stochastic epidemics

In this paper, we introduce non-centered and partially non-centered MCMC algorithms for stochastic epidemic models. Centered algorithms previously considered in the literature perform adequately well for small data sets. However, due to the high dependence inherent in the models between the missing data and the parameters, the performance of the centered algorithms gets appreciably worse when larger data sets are considered. Therefore non-centered and partially non-centered algorithms are introduced and are shown to out perform the existing centered algorithms.     

Design considerations in clinical trials with cure rate survival data: A case study in oncology

For clinical trials with time‐to‐event as the primary endpoint, the clinical cutoff is often event‐driven and the log‐rank test is the most commonly used statistical method for evaluating treatment effect. However, this method relies on the proportional hazards assumption in that it has the maximal power in this circumstance. In certain disease areas or populations, some patients can be curable and never experience the events despite a long follow‐up. The event accumulation may dry out after a certain period of follow‐up and the treatment effect could be reflected as the combination of improvement of cure rate and the delay of events for those uncurable patients. Study power depends on both cure rate improvement and hazard reduction. In this paper, we illustrate these practical issues using simulation studies and explore sample size recommendations, alternative ways for clinical cutoffs, and efficient testing methods with the highest study power possible.     

Integrated nested Laplace approximation for the analysis of count data via the combined model: A simulation study

The combined model accounts for different forms of extra-variability and has traditionally been applied in the likelihood framework, or in the Bayesian setting via Markov chain Monte Carlo. In this article, integrated nested Laplace approximation is investigated as an alternative estimation method for the combined model for count data, and compared with the former estimation techniques. Longitudinal, spatial, and multi-hierarchical data scenarios are investigated in three case studies as well as a simulation study. As a conclusion, integrated nested Laplace approximation provides fast and precise estimation, while avoiding convergence problems often seen when using Markov chain Monte Carlo.     

The analysis of dependence for three ways contingency tables with ordinal variables: A case study of patient satisfaction data

For many questionnaires and surveys in the marketing, business, and health disciplines, items often involve ordinal scales (such as the Likert scale and rating scale) that are associated in sometimes complex ways. Techniques such as classical correspondence analysis provide a simple graphical means of describing the nature of the association. However, the procedure does not allow the researcher to specify how one item may be associated with another, nor does the analysis allow for the ordinal structure of the scales to be reflected. This article presents a graphical approach that can help the researcher to study in depth the complex association of the items and reflect the structure of the items. We will demonstrate the applicability of this approach using data collected from a study that involves identifying major factors that influence the level of patient satisfaction in a Neapolitan hospital.     

Comparison of methods for analyzing binary repeated measures data: A simulation-based study (comparison of methods for binary repeated measures)

In this study, some methods suggested for binary repeated measures, namely, Weighted Least Squares (WLS), Generalized Estimating Equations (GEE), and Generalized Linear Mixed Models (GLMM) are compared with respect to power, type 1 error, and properties of estimates. The results indicate that with adequate sample size, no missing data, the only covariate being time effect, and a relatively limited number of time points, the WLS method performs well. The GEE approach performs well only for large sample sizes. The GLMM method is satisfactory with respect to type I error, but its estimates have poorer properties than the other methods.     

Modeling low birth weights using threshold regression: results for U. S. birth data

Babies born live under 2,500 g or with a gestational age under 37 weeks are often inadequately developed and have elevated risks of infant mortality, congenital malformations, mental retardation, and other physical and neurological impairments. In this paper, we model birth weight as a first hitting time (FHT) of a birthing boundary in a Wiener process representing fetal development. We associate the parameters of the process and boundary with covariates describing maternal characteristics and the birthing environment using a relatively new regression methodology called threshold regression. Two FHT models for birth weight are developed. One is a mixture model and the other a competing risks model. These models are tested in a case demonstration using a 4%-systematic sample of the more than four million live births in the United States in 2002. An extensive data set for these births was provided by the National Center for Health Statistics. The focus of this paper is on the conceptual framework, models and methodology. A full empirical study is deferred to a later occasion.