Trajectory Modeling of Longitudinal Binary Data: Application of the EM Algorithm for Mixture Models

A developmental trajectory describes the course of behavior over time. Identifying multiple trajectories within an overall developmental process permits a focus on subgroups of particular interest. We introduce a framework for identifying trajectories by using the Expectation-Maximization (EM) algorithm to fit semiparametric mixtures of logistic distributions to longitudinal binary data. For performance comparison, we consider full maximization algorithms (PROC TRAJ in SAS), standard EM, and two other EM-based algorithms for speeding up convergence. Simulation shows that EM methods produce more accurate parameter estimates. The EM methodology is illustrated with a longitudinal dataset involving adolescents smoking behaviors.     

Bayesian estimation of sensitivity level and population proportion of a sensitive characteristic in a binary optional unrelated question RRT model

Sihm et al. (2016 Sihm, J. S., A. Chhabra, and S. N. Gupta. 2016. An optional unrelated question RRT model. Involve: A Journal of Mathematics 9 (2):195–209.[Crossref] , [Google Scholar]) proposed an unrelated question binary optional randomized response technique (RRT) model for estimating the proportion of population that possess a sensitive characteristic and the sensitivity level of the question. In our work, decision theoretic approach has been followed to obtain Bayes estimates of the two parameters along with their corresponding minimal Bayes posterior expected losses (BPEL) using beta prior and squared error loss function (SELF). Relative losses are also examined to compare the performances of the Bayes estimates with those of the classical estimates obtained by Sihm et al. (2016 Sihm, J. S., A. Chhabra, and S. N. Gupta. 2016. An optional unrelated question RRT model. Involve: A Journal of Mathematics 9 (2):195–209.[Crossref] , [Google Scholar]). The results obtained are illustrated with the help of real survey data using non informative prior.     

Bayesian analysis of agricultural field experiments

The paper describes Bayesian analysis for agricultural field experiments, a topic that has received very little previous attention, despite a vast frequentist literature. Adoption of the Bayesian paradigm simplifies the interpretation of the results, especially in ranking and selection. Also, complex formulations can be analysed with comparative ease, by using Markov chain Monte Carlo methods. A key ingredient in the approach is the need for spatial representations of the unobserved fertility patterns. This is discussed in detail. Problems caused by outliers and by jumps in fertility are tackled via hierarchical t formulations that may find use in other contexts. The paper includes three analyses of variety trials for yield and one example involving binary data; none is entirely straightforward. Some comparisons with frequentist analyses are made.     

Regularized robust estimation in binary regression models

In this paper, we investigate robust parameter estimation and variable selection for binary regression models with grouped data. We investigate estimation procedures based on the minimum-distance approach. In particular, we employ minimum Hellinger and minimum symmetric chi-squared distances criteria and propose regularized minimum-distance estimators. These estimators appear to possess a certain degree of automatic robustness against model misspecification and/or for potential outliers. We show that the proposed non-penalized and penalized minimum-distance estimators are efficient under the model and simultaneously have excellent robustness properties. We study their asymptotic properties such as consistency, asymptotic normality and oracle properties. Using Monte Carlo studies, we examine the small-sample and robustness properties of the proposed estimators and compare them with traditional likelihood estimators. We also study two real-data applications to illustrate our methods. The numerical studies indicate the satisfactory finite-sample performance of our procedures.     

Binary Mixtures of Polycyclic Aromatic Hydrocarbons Display Nonadditive Mixture Interactions in an In Vitro Liver Cell Model

Polycyclic aromatic hydrocarbons (PAHs) have been labeled contaminants of concern due to their carcinogenic potential, insufficient toxicological data, environmental ubiquity, and inconsistencies in the composition of environmental mixtures. The Environmental Protection Agency is reevaluating current methods for assessing the toxicity of PAHs, including the assumption of toxic additivity in mixtures. This study was aimed at testing mixture interactions through in vitro cell culture experimentation, and modeling the toxicity using quantitative structure‐activity relationships (QSAR). Clone‐9 rat liver cells were used to analyze cellular proliferation, viability, and genotoxicity of 15 PAHs in single doses and binary mixtures. Tests revealed that many mixtures have nonadditive toxicity, but display varying mixture effects depending on the mixture composition. Many mixtures displayed antagonism, similar to other published studies. QSARs were then developed using the genetic function approximation algorithm to predict toxic activity both in single PAH congeners and in binary mixtures. Effective concentrations inhibiting 50% of the cell populations were modeled, with R² = 0.90, 0.99, and 0.84, respectively. The QSAR mixture algorithms were then adjusted to account for the observed mixture interactions as well as the mixture composition (ratios) to assess the feasibility of QSARs for mixtures. Based on these results, toxic addition is improbable and therefore environmental PAH mixtures are likely to see nonadditive responses when complex interactions occur between components. Furthermore, QSAR may be a useful tool to help bridge these data gaps surrounding the assessment of human health risks that are associated with PAH exposures.     

Some bounds on balanced block designs

Bounds on the latest root of the C-matrix and the number of blocks for a variance-balanced block design are given. These results contain the well-known results as special cases.     

二元函数L’HOSPITAL法则初探

本文依据一元函数Ｌ’Ｈｏｓｐｉｔａｌ法则推导过程，给出了相应的二元函数Ｌ’Ｈｏｓｐｉｔａｌ法则。     

A Goodness of Fit Test for the Multilevel Logistic Model

It is crucial to test the goodness of fit of a model before it is used to make statistical inferences. However, no satisfactory goodness of fit test is available for the case of categorical multilevel data which occur when categorical data are clustered or hierarchical in nature. Hence the aim of this paper is to develop a new goodness of fit test for multilevel binary data based on Hosmer and Lemeshow and Lipsitz et.al. In order to identify the properties of the developed test, simulation studies were carried out to assess the Type I error and the power.     

Distance-Based Measures of Association with Applications in Relating Hyperspectral Images

We propose a distance-based method to relate two data sets. We define and study some measures of multivariate association based on distances between observations. The proposed approach can be used to deal with general data sets (e.g., observations on continuous, categorical or mixed variables). An application, using Hellinger distance, provides the relationships between two regions of hyperspectral images.     

Counting certain binary strings

Consider a sequence of exchangeable or independent binary (i.e. zero-one) random variables. Numbers of strings with a fixed number of ones between two subsequent zeros are studied under an overlapping enumeration scheme. The respective waiting times are examined as well. Exact probability functions are obtained by means of combinatorial analysis and via recursive schemes in the case of an exchangeable and of an independent sequence, respectively. Explicit formulae for the mean values and variances of the number of strings are provided for both types of the sequences. For a Bernoulli sequence the asymptotic normality of the numbers of strings is established too. Indicative exchangeable and independent sequences, combined with numerical examples, clarify further the theoretical results.