MAXIMUM LIKELIHOOD ESTIMATION FOR A POISSON RATE PARAMETER WITH MISCLASSIFIED COUNTS

This paper proposes a Poisson‐based model that uses both error‐free data and error‐prone data subject to misclassification in the form of false‐negative and false‐positive counts. It derives maximum likelihood estimators (MLEs) for the Poisson rate parameter and the two misclassification parameters — the false‐negative parameter and the false‐positive parameter. It also derives expressions for the information matrix and the asymptotic variances of the MLE for the rate parameter, the MLE for the false‐positive parameter, and the MLE for the false‐negative parameter. Using these expressions the paper analyses the value of the fallible data. It studies characteristics of the new double‐sampling rate estimator via a simulation experiment and applies the new MLE estimators and confidence intervals to a real dataset.     

MORE INFORMATIVE TESTING FOR BIVARIATE SYMMETRY

In testing for bivariate symmetry against arbitrary alternatives the well‐known test developed by Bowker in 1948 is shown to be a score test, and to have useful components. These components are asymptotically independent and asymptotically have the standard normal distribution. Moreover they assess particular pairs of cells for symmetry. These components can also be used in a data analytic manner to complement a test for bivariate symmetry against ordered alternatives.     

Random Weighted Bootstrap Method for Recurrent Events with Informative Censoring

Using the data from the AIDS Link to Intravenous Experiences cohort study as an example, an informative censoring model was used to characterize the repeated hospitalization process of a group of patients. Under the informative censoring assumption, the estimators of the baseline rate function and the regression parameters were shown to be related to a latent variable. Hence, it becomes impractical to directly estimate the unknown quantities in the moments of the estimators for the bandwidth selection of a smoothing estimator and the construction of confidence intervals, which are respectively based on the asymptotic mean squared errors and the asymptotic distributions of the estimators. To overcome these difficulties, we develop a random weighted bootstrap procedure to select appropriate bandwidths and to construct approximated confidence intervals. One can see that our method is simple and faster to implement from a practical point of view, and is at least as accurate as other bootstrap methods. In this article, it is shown that the proposed method is useful through the performance of a Monte Carlo simulation. An application of our procedure is also illustrated by a recurrent event sample of intravenous drug users for inpatient cares over time.     

Bayesian model selection for join point regression with application to age-adjusted cancer rates

Summary.  The method of Bayesian model selection for join point regression models is developed. Given a set of K +1 join point models M ₀,  M ₁, …,  M _K with 0, 1, …,  K join points respec-tively, the posterior distributions of the parameters and competing models M _k are computed by Markov chain Monte Carlo simulations. The Bayes information criterion BIC is used to select the model M _k with the smallest value of BIC as the best model. Another approach based on the Bayes factor selects the model M _k with the largest posterior probability as the best model when the prior distribution of M _k is discrete uniform. Both methods are applied to analyse the observed US cancer incidence rates for some selected cancer sites. The graphs of the join point models fitted to the data are produced by using the methods proposed and compared with the method of Kim and co-workers that is based on a series of permutation tests. The analyses show that the Bayes factor is sensitive to the prior specification of the variance σ ², and that the model which is selected by BIC fits the data as well as the model that is selected by the permutation test and has the advantage of producing the posterior distribution for the join points. The Bayesian join point model and model selection method that are presented here will be integrated in the National Cancer Institute's join point software ( http://www.srab.cancer.gov/joinpoint/ ) and will be available to the public.     

Bayesian sample-size determination for one and two Poisson rate parameters with applications to quality control

We formulate Bayesian approaches to the problems of determining the required sample size for Bayesian interval estimators of a predetermined length for a single Poisson rate, for the difference between two Poisson rates, and for the ratio of two Poisson rates. We demonstrate the efficacy of our Bayesian-based sample-size determination method with two real-data quality-control examples and compare the results to frequentist sample-size determination methods.     

Estimation of non-parametric regression for dasometric measures

The aim of this paper is to describe a simulation procedure to compare parametric regression against a non-parametric regression method, for different functions and sets of information. The proposed methodology improves lack of fit at the edges of the regression curves, and an acceptable result is obtained for the no-parametric estimation in all studied cases. Larger differences appear at the edges of the estimation. The results are applied to the study of dasometric variables, which do not fulfil the normality hypothesis needed for parametric estimation. The kernel regression shows the relationship between the studied variables, which would not be detected with more rigid parametric models.     

The Next Generation of Collective Action Research

The articles presented in this volume describe part of a new generation of interest and vigor in the social psychological study of collective action. This new wave builds nicely on the foundation set by social identity, self-categorization, and relative deprivation theories but also introduces a number of important innovative perspectives and variables. In this commentary, I review some of these expansions and additions, raise a number of conceptual concerns that arise out of these new directions, and discuss more generally some novel and important directions that emerge from the work presented in the volume and in other recent work on collective action.     

Social Networks Derived from Affiliations and Friendships, Multi-informant and Self-reports: Stability, Concordance, Placement of Aggressive and Unpopular Children, and Centrality

This study compares three variations in how researchers construct middle childhood social networks: (1) with friendships or affiliations as a relational tie; (2) with children providing self reports of relationships, or in addition, multi-informant reports of relationships in which they are not involved; and (3) whether network computation is correlational or distance-based . The sample was 357 fourth- and fifth-grade students in 17 classrooms. The strongest differences were between self-reported friendship and affiliative networks. Results showed that compared with affiliations, friendship networks had smaller groups, more isolates, and lower fall-to-spring stability. Agreement in social placement between friendship and affiliative networks was generally average, but poor for unpopular and aggressive children. Multi-informant affiliative networks were most robust in their positioning of aggressive children. Multi-informant centrality was uniquely uncorrelated with aggression. Network computation differences were not substantial. Discussion focuses on recommendations for research and the educational promise of network technology.