Detecting a Change in the Correlation Coefficient in a Sequence of Bivariate Normal Variables

We consider the problem of testing the hypothesis that the correlation coefficient is stable in a sequence of n observations of independent, bivariate normal random variables against the alternative that the correlation coefficient changes after an unknown point t(t < n). We propose an estimate of the changepoint t and report on power comparisons between the commonly used test for this problem and our proposed test. Some applications to finance are discussed.     

The large-sample performance of backwards variable elimination

Prior studies have shown that automated variable selection results in models with substantially inflated estimates of the model R ², and that a large proportion of selected variables are truly noise variables. These earlier studies used simulated data sets whose sample sizes were at most 100. We used Monte Carlo simulations to examine the large-sample performance of backwards variable elimination. We found that in large samples, backwards variable elimination resulted in estimates of R ² that were at most marginally biased. However, even in large samples, backwards elimination tended to identify the correct regression model in a minority of the simulated data sets.     

Estimation of a discriminant function from a mixture of two inverse Weibull distributions

The classification of a random variable based on a mixture can be meaningfully discussed only if the class of all finite mixtures is identifiable. In this paper, we find the maximum-likelihood estimates of the parameters of the mixture of two inverse Weibull distributions by using classified and unclassified observations. Next, we estimate the nonlinear discriminant function of the underlying model. Also, we calculate the total probabilities of misclassification as well as the percentage bias. In addition, we investigate the performance of all results through a series of simulation experiments by means of relative efficiencies. Finally, we analyse some simulated and real data sets through the findings of the paper.     

Approximate composite marginal likelihood inference in spatial generalized linear mixed models

Non-Gaussian spatial responses are usually modeled using spatial generalized linear mixed model with spatial random effects. The likelihood function of this model cannot usually be given in a closed form, thus the maximum likelihood approach is very challenging. There are numerical ways to maximize the likelihood function, such as Monte Carlo Expectation Maximization and Quadrature Pairwise Expectation Maximization algorithms. They can be applied but may in such cases be computationally very slow or even prohibitive. Gauss–Hermite quadrature approximation only suitable for low-dimensional latent variables and its accuracy depends on the number of quadrature points. Here, we propose a new approximate pairwise maximum likelihood method to the inference of the spatial generalized linear mixed model. This approximate method is fast and deterministic, using no sampling-based strategies. The performance of the proposed method is illustrated through two simulation examples and practical aspects are investigated through a case study on a rainfall data set.     

Publication bias and meta-analysis for 2×2 tables: an average Markov chain Monte Carlo EM algorithm

Summary. A major difficulty in meta-analysis is publication bias . Studies with positive outcomes are more likely to be published than studies reporting negative or inconclusive results. Correcting for this bias is not possible without making untestable assumptions. In this paper, a sensitivity analysis is discussed for the meta-analysis of 2×2 tables using exact conditional distributions. A Markov chain Monte Carlo EM algorithm is used to calculate maximum likelihood estimates. A rule for increasing the accuracy of estimation and automating the choice of the number of iterations is suggested.     

Reversible jump Markov chain Monte Carlo algorithms for Bayesian variable selection in logistic mixed models

In this article, to reduce computational load in performing Bayesian variable selection, we used a variant of reversible jump Markov chain Monte Carlo methods, and the Holmes and Held (HH) algorithm, to sample model index variables in logistic mixed models involving a large number of explanatory variables. Furthermore, we proposed a simple proposal distribution for model index variables, and used a simulation study and real example to compare the performance of the HH algorithm with our proposed and existing proposal distributions. The results show that the HH algorithm with our proposed proposal distribution is a computationally efficient and reliable selection method.     

Symmetric pattern models: a latent variable approach to item non-response in attitude scales

This paper proposes a new approach to the treatment of item non-response in attitude scales. It combines the ideas of latent variable identification with the issues of non-response adjustment in sample surveys. The latent variable approach allows missing values to be included in the analysis and, equally importantly, allows information about attitude to be inferred from non-response. We present a symmetric pattern methodology for handling item non-response in attitude scales. The methodology is symmetric in that all the variables are given equivalent status in the analysis (none is designated a 'dependent' variable) and is pattern based in that the pattern of responses and non-responses across individuals is a key element in the analysis. Our approach to the problem is through a latent variable model with two latent dimensions: one to summarize response propensity and the other to summarize attitude, ability or belief. The methodology presented here can handle binary, metric and mixed (binary and metric) manifest items with missing values. Examples using both artificial data sets and two real data sets are used to illustrate the mechanism and the advantages of the methodology proposed.     

Maximum likelihood estimation of the parameters of a multiple step-stress model from the Birnbaum-Saunders distribution under time-constraint: A comparative study

The cumulative exposure model (CEM) is a commonly used statistical model utilized to analyze data from a step-stress accelerated life testing which is a special class of accelerated life testing (ALT). In practice, researchers conduct ALT to: (1) determine the effects of extreme levels of stress factors (e.g., temperature) on the life distribution, and (2) to gain information on the parameters of the life distribution more rapidly than under normal operating (or environmental) conditions. In literature, researchers assume that the CEM is from well-known distributions, such as the Weibull family. This study, on the other hand, considers a p-step-stress model with q stress factors from the two-parameter Birnbaum-Saunders distribution when there is a time constraint on the duration of the experiment. In this comparison paper, we consider different frameworks to numerically compute the point estimation for the unknown parameters of the CEM using the maximum likelihood theory. Each framework implements at least one optimization method; therefore, numerical examples and extensive Monte Carlo simulations are considered to compare and numerically examine the performance of the considered estimation frameworks.     

Robust variable selection in finite mixture of regression models using the t distribution

Abstract

Variable selection in finite mixture of regression (FMR) models is frequently used in statistical modeling. The majority of applications of variable selection in FMR models use a normal distribution for regression error. Such assumptions are unsuitable for a set of data containing a group or groups of observations with heavy tails and outliers. In this paper, we introduce a robust variable selection procedure for FMR models using the t distribution. With appropriate selection of the tuning parameters, the consistency and the oracle property of the regularized estimators are established. To estimate the parameters of the model, we develop an EM algorithm for numerical computations and a method for selecting tuning parameters adaptively. The parameter estimation performance of the proposed model is evaluated through simulation studies. The application of the proposed model is illustrated by analyzing a real data set.     

Test for the equality of several correlation coefficients

We derive two C(α) statistics and the likelihood-ratio statistic for testing the equality of several correlation coefficients, from k ≥ 2 independent random samples from bivariate normal populations. The asymptotic relationship of the C(α) tests, the likelihood-ratio test, and a statistic based on the normality assumption of Fisher's Z-transform of the sample correlation coefficient is established. A comparative performance study, in terms of size and power, is then conducted by Monte Carlo simulations. The likelihood-ratio statistic is often too liberal, and the statistic based on Fisher's Z-transform is conservative. The performance of the two C(α) statistics is identical. They maintain significance level well and have almost the same power as the other statistics when empirically calculated critical values of the same size are used. The C(α) statistic based on a noniterative estimate of the common correlation coefficient (based on Fisher's Z-transform) is recommended.     

Non-ignorable missing covariate data in survival analysis: a case-study of an International Breast Cancer Study Group trial

Summary.  Non-ignorable missing data, a serious problem in both clinical trials and observational studies, can lead to biased inferences. Quality-of-life measures have become increasingly popular in clinical trials. However, these measures are often incompletely observed, and investigators may suspect that missing quality-of-life data are likely to be non-ignorable. Although several recent references have addressed missing covariates in survival analysis, they all required the assumption that missingness is at random or that all covariates are discrete. We present a method for estimating the parameters in the Cox proportional hazards model when missing covariates may be non-ignorable and continuous or discrete. Our method is useful in reducing the bias and improving efficiency in the presence of missing data. The methodology clearly specifies assumptions about the missing data mechanism and, through sensitivity analysis, helps investigators to understand the potential effect of missing data on study results.     

Gibbs sampling in DP-based nonlinear mixed effects models

This article uses several approaches to deal with the difficulty involved in evaluating the intractable integral when using Gibbs sampling to estimate the nonlinear mixed effects model (NLMM) based on the Dirichlet process (DP). For illustration, we applied these approaches to real data and simulations. Comparisons are then made between these methods with respect to estimation accuracy and computing efficiency.     

Bayesian semiparametric inference for the accelerated failure-time model

Bayesian semiparametric inference is considered for a loglinear model. This model consists of a parametric component for the regression coefficients and a nonparametric component for the unknown error distribution. Bayesian analysis is studied for the case of a parametric prior on the regression coefficients and a mixture-of-Dirichlet-processes prior on the unknown error distribution. A Markov-chain Monte Carlo (MCMC) method is developed to compute the features of the posterior distribution. A model selection method for obtaining a more parsimonious set of predictors is studied. The method adds indicator variables to the regression equation. The set of indicator variables represents all the possible subsets to be considered. A MCMC method is developed to search stochastically for the best subset. These procedures are applied to two examples, one with censored data.     

Estimating the Proportion of True Null Hypotheses in Nonparametric Exponential Mixture Model with Appication to the Leukemia Gene Expression Data

We revisit the problem of estimating the proportion π of true null hypotheses where a large scale of parallel hypothesis tests are performed independently. While the proportion is a quantity of interest in its own right in applications, the problem has arisen in assessing or controlling an overall false discovery rate. On the basis of a Bayes interpretation of the problem, the marginal distribution of the p-value is modeled in a mixture of the uniform distribution (null) and a non-uniform distribution (alternative), so that the parameter π of interest is characterized as the mixing proportion of the uniform component on the mixture. In this article, a nonparametric exponential mixture model is proposed to fit the p-values. As an alternative approach to the convex decreasing mixture model, the exponential mixture model has the advantages of identifiability, flexibility, and regularity. A computation algorithm is developed. The new approach is applied to a leukemia gene expression data set where multiple significance tests over 3,051 genes are performed. The new estimate for π with the leukemia gene expression data appears to be about 10% lower than the other three estimates that are known to be conservative. Simulation results also show that the new estimate is usually lower and has smaller bias than the other three estimates.     

Penalized and Shrinkage Estimation in the Cox Proportional Hazards Model

This article considers the shrinkage estimation procedure in the Cox's proportional hazards regression model when it is suspected that some of the parameters may be restricted to a subspace. We have developed the statistical properties of the shrinkage estimators including asymptotic distributional biases and risks. The shrinkage estimators have much higher relative efficiency than the classical estimator, furthermore, we consider two penalty estimators—the LASSO and adaptive LASSO—and compare their relative performance with that of the shrinkage estimators numerically. A Monte Carlo simulation experiment is conducted for different combinations of irrelevant predictors and the performance of each estimator is evaluated in terms of simulated mean squared error. Simulation study shows that the shrinkage estimators are comparable to the penalty estimators when the number of irrelevant predictors in the model is relatively large. The shrinkage and penalty methods are applied to two real data sets to illustrate the usefulness of the procedures in practice.     

Determination of a new mixed variable lot-size multiple dependent state sampling plan based on the process capability index

This article proposes a new mixed variable lot-size multiple dependent state sampling plan in which the attribute sampling plan can be used in the first stage and the variables multiple dependent state sampling plan based on the process capability index will be used in the second stage for the inspection of measurable quality characteristics. The proposed mixed plan is developed for both symmetric and asymmetric fraction non conforming. The optimal plan parameters can be determined by considering the satisfaction levels of the producer and the consumer simultaneously at an acceptable quality level and a limiting quality level, respectively. The performance of the proposed plan over the mixed single sampling plan based on C_pk and the mixed variable lot size plan based on C_pk with respect to the average sample number is also investigated. Tables are constructed for easy selection of plan parameters for both symmetric and asymmetric fraction non conforming and real world examples are also given for the illustration and practical implementation of the proposed mixed variable lot-size plan.     

Misspecification of a binary dependent variable in the logistic model controlling for the repeated longitudinal measures

Many medical applications are interested to know the disease status. The disease status can be related to multiple serial measurements. Nevertheless, owing to various reasons, the binary outcome can be measured incorrectly. The estimators derived from the misspecified outcome can be biased. This paper derives the complete data likelihood function to incorporate both the multiple serial measurements and the misspecified outcome. Owing to the latent variables, EM algorithm is used to derive the maximum-likelihood estimators. Monte Carlo simulations are conducted to compare the impact of misspecification on the estimates. A retrospective data for the recurrence of atrial fibrillation is used to illustrate the usage of the proposed model.     

Latent Variable Models in Heterogeneous Spaces for Observations of Mixed Types

The maximum likelihood approach to the estimation of factor analytic model parameters most commonly deals with outcomes that are assumed to be multivariate Gaussian random variables in a homogeneous input space. In many practical settings, however, many studies needing factor analytic modeling involve data that, not only are not multivariate Gaussian variables, but also come from a partitioned input space. This article introduces an extension of the maximum likelihood factor analysis that handles multivariate outcomes made up of attributes with different probability distributions, and originating from a partitioned input space. An EM Algorithm combined with Fisher Scoring is used to estimate the parameters of the derived model.     

A monte carlo study of variable selection and inferences in a two stage random coefficient linear regression model with unbalanced data

A growth curve analysis is often applied to estimate patterns of changes in a given characteristic of different individuals. It is also used to find out if the variations in the growth rates among individuals are due to effects of certain covariates. In this paper, a random coefficient linear regression model, as a special case of the growth curve analysis, is generalized to accommodate the situation where the set of influential covariates is not known a priori. Two different approaches for seleaing influential covariates (a weighted stepwise selection procedure and a modified version of Rao and Wu’s selection criterion) for the random slope coefficient of a linear regression model with unbalanced data are proposed. Performances of these methods are evaluated by means of Monte-Carlo simulation. In addition, several methods (Maximum Likelihood, Restricted Maximum Likelihood, Pseudo Maximum Likelihood and Method of Moments) for estimating the parameters of the selected model are compared Proposed variable selection schemes and estimators are appliedtotheactualindustrial problem which motivated this investigation.     

Estimating the Risk of a Down's Syndrome Term Pregnancy Using Age and Serum Markers: Comparison of Various Methods

The risk of an individual woman having a pregnancy associated with Down's syndrome is estimated given her age, α-fetoprotein, human chorionic gonadotropin, and pregnancy-specific β1-glycoprotein levels. The classical estimation method is based on discriminant analysis under the assumption of lognormality of the marker values, but logistic regression is also applied for data classification. In the present work, we compare the performance of the two methods using a dataset containing the data of almost 89,000 unaffected and 333 affected pregnancies. Assuming lognormality of the marker values, we also calculate the theoretical detection and false positive rates for both the methods.