Statistics and Probability Commons^™

Pseudo-Random Number Generation In R For Commonly Used Multivariate Distributions, Hakan Demirtas

Journal of Modern Applied Statistical Methods

An increasing number of practitioners and applied statisticians have started using the R programming system in recent years for their computing and data analysis needs. As far as pseudo-random number generation is concerned, the built-in generator in R does not contain multivariate distributions. In this article, R routines for widely used multivariate distributions are presented.

Confidence Intervals On Subsets May Be Misleading, Juliet Popper Shaffer

Journal of Modern Applied Statistical Methods

A combination of hypothesis testing and confidence interval construction is often used in social and behavioral science studies. Sometimes confidence intervals are computed or reported only if a null hypothesis is rejected, perhaps to see whether the range of values is of practical importance. Sometimes they are constructed or reported only if a null hypothesis is accepted, in order to assess the range of plausible nonnull values due to inadequate power to detect them. Even if always computed, they are interpreted differently, depending on whether the null value is or is not included. Furthermore, many studies in which the null …

Mentoring Doctoral Students: A Personal Perspective, Bruce W. Hall

Journal of Modern Applied Statistical Methods

In this brief essay, I reflect on the mentoring process based on advising over thirty doctoral students in measurement, evaluation, and research. There is considerable cause for optimism, and it is among the professors’ highest honor to mentor the doctoral student.

On A Simple Method For Analyzing Multivariate Survival Data Using Sample Survey Methods, Pingfu Fu, J. Sunil Rao

Journal of Modern Applied Statistical Methods

A simple technique is illustrated for analyzing multivariate survival data. The data situation arises when an individual records multiple survival events, or when individuals recording single survival events are grouped into clusters. Past work has focused on developing new methods to handle such data. Here, we use a connection between Poisson regression and survival modeling and a cluster sampling approach to adjust the variance estimates. The approach requires parametric assumption for the marginal hazard function, but avoids specification of a joint multivariate survival distribution. A simulation study demonstrates the proposed approach is a competing method of recent developed marginal approaches …

Monte Carlo Evaluation Of Ordinal D With Improved Confidence Interval, Du Feng, Norman Cliff

Journal of Modern Applied Statistical Methods

This article reports a Monte Carlo evaluation of ordinal statistic d with modified confidence intervals (CI) for location comparison of two independent groups under various conditions. Type I error rate, power, and coverage of CI of d were compared to those of the Welch's t-test.

Confidence Elicitation And Anchoring In The Respondent-Generated Intervals (Rgi) Protocol, Liping Chu, S. James Press, Judith M. Tanur

Journal of Modern Applied Statistical Methods

The Respondent-Generated Intervals protocol (RGI) has been used to have respondents recall the answer to a factual question by giving not only a point estimate but also bounds within which they feel it is almost certain that the true value of the quantity being reported upon falls. The RGI protocol is elaborated in this article with the goal of improving the accuracy of the estimators by introducing cueing mechanisms to direct confident (and thus presumably accurate) respondents to give shorter intervals and less confident (and thus presumably less accurate) respondents to give longer ones.

A Note On Extending Scheffé’S Modified Multiple-Comparison Procedure To Other Analysis Situations, Xinyue Zhou, Joel R. Levin

Journal of Modern Applied Statistical Methods

This article extends Scheffé’s modified (sequential) multiple-comparison procedure in one-way analysisof- variance to other analysis situations, including interaction comparisons in factorial ANOVA designs, tests of partial regression coefficients in multiple-regression analysis, and comparisons of means in onefactor multivariate analyses of variance. Researchers who are concerned with maintaining familywise Type I error rates while increasing statistical power relative to the original (simultaneous) Scheffé-based procedures are encouraged to consider these improved multiple-comparison methods.

A Modification Of The Em Algorithm To Estimate An Andersen-Gill Gamma Frailty Model For Multivariate Failure Time Data, Maria Antònia Barceló, Marc Saez

Journal of Modern Applied Statistical Methods

A modification of the Andersen-Gill gamma shared frailty model is presented. The variance of the frailty is directly modeled by means of a generalized linear model, the EM algorithm is modified in order to simultaneously estimate a semiparametric model for the failure times and a model for the variance of the frailty. A simulation study is conducted to evaluate the performance of the proposed algorithm (EMB algorithm) and compared with other methods, a marginal model, and a conditional model. Multivariate data from a nosocomial infection study is used to illustrate the methods. The EMB fit turned out to be better …

Laboratory Routines Cause Animal Stress, Jonathan P. Balcombe, Neal D. Barnard, Chad Sandusky

Laboratory Experiments Collection

Eighty published studies were appraised to document the potential stress associated with three routine laboratory procedures commonly performed on animals: handling, blood collection, and orogastric gavage. We defined handling as any non-invasive manipulation occurring as part of routine husbandry, including lifting an animal and cleaning or moving an animal's cage. Significant changes in physiologic parameters correlated with stress (e.g., serum or plasma concentrations of corticosterone, glucose, growth hormone or prolactin, heart rate, blood pressure, and behavior) were associated with all three procedures in multiple species in the studies we examined. The results of these studies demonstrated that animals responded with …

A Genetic Algorithm Hybrid For Constructing Optimal Response Surface Designs, David Drain, W. Matthew Carlyle, Douglas C. Montgomery, Connie Borror, Christine Anderson-Cook

Mathematics and Statistics Faculty Research & Creative Works

Hybrid heuristic optimization methods can discover efficient experiment designs in situations where traditional designs cannot be applied, exchange methods are ineffective, and simple heuristics like simulated annealing fail to find good solutions. One such heuristic hybrid is GASA (genetic algorithm-simulated annealing), developed to take advantage of the exploratory power of the genetic algorithm, while utilizing the local optimum exploitive properties of simulated annealing. the successful application of this method is demonstrated in a difficult design problem with multiple optimization criteria in an irregularly shaped design region. Copyright © 2004 John Wiley & Sons, Ltd.

An Overview Of The Respondent-Generated Intervals (Rgi) Approach To Sample Surveys, S. James Press, Judith M. Tanur

Journal of Modern Applied Statistical Methods

This article brings together many years of research on the Respondent-Generated Intervals (RGI) approach to recall in factual sample surveys. Additionally presented is new research on the use of RGI in opinion surveys and the use of RGI with gamma-distributed data. The research combines Bayesian hierarchical modeling with various cognitive aspects of sample surveys.

Statistics And Technology: Reflections On 35 Years Of Change, James J. Higgins

Journal of Modern Applied Statistical Methods

From the days when statistical calculations were done on mechanical calculators to today, technology has transformed the discipline of statistics. More than just giving statisticians the power to crunch numbers, it has fundamentally changed the way we teach, do research, and consult. In this article, I give some examples of this from my 35 years as an academic statistician.

“Teaching” In Honor Of Cliff Blair, Howard Stoker

Journal of Modern Applied Statistical Methods

In this article, I conceptualize teaching as the profession of facilitating and stimulating learning. As “teachers”, we help students acquire learning skills that they may expand on later in their life. I review fifteen principles that facilitate effective learning.

A New Goodness-Of-Fit Test For Item Response Theory, John H. Neel

Journal of Modern Applied Statistical Methods

Chi-square techniques for testing goodness-of-fit in item response theory are shown to give incorrect results. A new measure, CB, based on cumulants is proposed which avoids the arbitrary nature of interval creation found in chi-square techniques. The distribution of CB is estimated using Monte Carlo techniques and critical values for testing goodness-of-fit are given.

Modeling Incomplete Longitudinal Data, Hakan Demirtas

Journal of Modern Applied Statistical Methods

This article presents a review of popular parametric, semiparametric and ad-hoc approaches for analyzing incomplete longitudinal data.

Aligned Rank Tests As Robust Alternatives For Testing Interactions In Multiple Group Repeated Measures Designs With Heterogeneous Covariances, Xiaosheng Lei, Janet K. Holt, T. Mark Beasley

Journal of Modern Applied Statistical Methods

Data simulation was used to investigate whether tests performed on aligned ranks (Beasley, 2002) could be used as robust alternatives to parametric methods for testing a split-plot interaction with non-normal data and heterogeneous covariance matrices. Results indicated the aligned rank method do not have any distinct advantage over parametric methods in this situation.

Multivariate And Multistrata Nonparametric Tests: The Nonparametric Combination Method, Livio Corain, Luigi Salmaso

Journal of Modern Applied Statistical Methods

Researchers and practitioners in many scientific disciplines and industrial fields are often faced with complex problems when dealing with comparisons between two or more groups using classical parametric methods. The data arising from real problems rarely are in agreement with stringent parametric assumptions. The NonParametric Combination (NPC) methodology frees the researcher from stringent assumptions of parametric methods and allows a more flexible analysis, both in terms of specification of multivariate hypotheses and in terms of the nature of the variables involved in the analysis. An outline of NPC methodology is given, along with case studies.

On Comparison Of Hypothesis Tests In The Bayesian Framework Without Loss Function, Vladimir Gercsik, Mark Kelbert

Journal of Modern Applied Statistical Methods

The problem is how to compare the quality of different hypothesis tests in a Bayesian framework without introducing a loss function. Three different linear orders on the set of all possible hypothesis tests are studied. The most natural order estimates the Fisher information between indicators of event and decision.

The President’S Problem, Jann-Huei Jinn

Journal of Modern Applied Statistical Methods

A solution is offered in response to a complex combination problem challenged by Blom, Englund, and Sandell (1998). The problem is to determine the probability that a random permutation of the word BILLCLINTON has no equal neighbors.

A Conversation With R. Clifford Blair On The Occasion Of His Retirement, Shlomo S. Sawilowsky

Journal of Modern Applied Statistical Methods

An interview was conducted on 23 November 2003 with R. Clifford Blair on the occasion on his retirement from the University of South Florida. This article is based on that interview. Biographical sketches and images of members of his academic genealogy are provided.

Multivariate Stochastic Volatility Models: Bayesian Estimation And Model Comparison, Jun Yu, Renate Meyer

Research Collection School Of Economics

In this paper we show that fully likelihood-based estimation and comparison of multivariate stochastic volatility (SV) models can be easily performed via a freely available Bayesian software called WinBUGS. Moreover, we introduce to the literature several new specifications which are natural extensions to certain existing models, one of which allows for time varying correlation coefficients. Ideas are illustrated by fitting, to a bivariate time series data of weekly exchange rates, nine multivariate SV models, including the specifications with Granger causality in volatility, time varying correlations, heavy-tailed error distributions, additive factor structure, and multiplicative factor structure. Empirical results suggest that the …

Appeal Rates And Outcomes In Tried And Nontried Cases: Further Exploration Of Anti-Plaintiff Appellate Outcomes, Theodore Eisenberg

Cornell Law Faculty Publications

Federal data sets covering district court and appellate court civil cases for cases terminating in fiscal years 1988 through 2000 are analyzed. Appeals are filed in 10.9 percent of filed cases, and 21.0 percent of cases if one limits the sample to cases with a definitive judgment for plaintiff or defendant. The appeal rate is 39.6 percent in tried cases compared to 10.0 percent of nontried cases. For cases with definitive judgments, the appeal filing rate is 19.0 percent in nontried cases and 40.9 percent in tried cases. Tried cases with definitive judgments are appealed to a conclusion on the …

Bayesian Hierarchical Distributed Lag Models For Summer Ozone Exposure And Cardio-Respiratory Mortality, Yi Huang, Francesca Dominici, Michelle L. Bell

Johns Hopkins University, Dept. of Biostatistics Working Papers

In this paper, we develop Bayesian hierarchical distributed lag models for estimating associations between daily variations in summer ozone levels and daily variations in cardiovascular and respiratory (CVDRESP) mortality counts for 19 U.S. large cities included in the National Morbidity Mortality Air Pollution Study (NMMAPS) for the period 1987 - 1994.

At the first stage, we define a semi-parametric distributed lag Poisson regression model to estimate city-specific relative rates of CVDRESP associated with short-term exposure to summer ozone. At the second stage, we specify a class of distributions for the true city-specific relative rates to estimate an overall effect by …

Multiple Testing And Data Adaptive Regression: An Application To Hiv-1 Sequence Data, Merrill D. Birkner, Sandra E. Sinisi, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Analysis of viral strand sequence data and viral replication capacity could potentially lead to biological insights regarding the replication ability of HIV-1. Determining specific target codons on the viral strand will facilitate the manufacturing of target specific antiretrovirals. Various algorithmic and analysis techniques can be applied to this application. We propose using multiple testing to find codons which have significant univariate associations with replication capacity of the virus. We also propose using a data adaptive multiple regression algorithm to obtain multiple predictions of viral replication capacity based on an entire mutant/non-mutant sequence profile. The data set to which these techniques …

Gllamm Manual, Sophia Rabe-Hesketh, Anders Skrondal, Andrew Pickles

U.C. Berkeley Division of Biostatistics Working Paper Series

This manual describes a Stata program gllamm that can estimate Generalized Linear Latent and Mixed Models (GLLAMMs). GLLAMMs are a class of multilevel latent variable models for (multivariate) responses of mixed type including continuous responses, counts, duration/survival data, dichotomous, ordered and unordered categorical responses and rankings. The latent variables (common factors or random effects) can be assumed to be discrete or to have a multivariate normal distribution. Examples of models in this class are multilevel generalized linear models or generalized linear mixed models, multilevel factor or latent trait models, item response models, latent class models and multilevel structural equation models. …

Data Adaptive Estimation Of The Treatment Specific Mean, Yue Wang, Oliver Bembom, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

An important problem in epidemiology and medical research is the estimation of the causal effect of a treatment action at a single point in time on the mean of an outcome, possibly within strata of the target population defined by a subset of the baseline covariates. Current approaches to this problem are based on marginal structural models, i.e., parametric models for the marginal distribution of counterfactural outcomes as a function of treatment and effect modifiers. The various estimators developed in this context furthermore each depend on a high-dimensional nuisance parameter whose estimation currently also relies on parametric models. Since misspecification …

Finding Cancer Subtypes In Microarray Data Using Random Projections, Debashis Ghosh

The University of Michigan Department of Biostatistics Working Paper Series

One of the benefits of profiling of cancer samples using microarrays is the generation of molecular fingerprints that will define subtypes of disease. Such subgroups have typically been found in microarray data using hierarchical clustering. A major problem in interpretation of the output is determining the number of clusters. We approach the problem of determining disease subtypes using mixture models. A novel estimation procedure of the parameters in the mixture model is developed based on a combination of random projections and the expectation-maximization algorithm. Because the approach is probabilistic, our approach provides a measure for the number of true clusters …

Semiparametric Methods For The Binormal Model With Multiple Biomarkers, Debashis Ghosh

The University of Michigan Department of Biostatistics Working Paper Series

Abstract: In diagnostic medicine, there is great interest in developing strategies for combining biomarkers in order to optimize classification accuracy. A popular model that has been used when one biomarker is available is the binormal model. Extension of the model to accommodate multiple biomarkers has not been considered in this literature. Here, we consider a multivariate binormal framework for combining biomarkers using copula functions that leads to a natural multivariate extension of the binormal model. Estimation in this model will be done using rank-based procedures. We also discuss adjustment for covariates in this class of models and provide a simple …

Cholesky Residuals For Assessing Normal Errors In A Linear Model With Correlated Outcomes: Technical Report, E. Andres Houseman, Louise Ryan, Brent Coull

Harvard University Biostatistics Working Paper Series

Despite the widespread popularity of linear models for correlated outcomes (e.g. linear mixed models and time series models), distribution diagnostic methodology remains relatively underdeveloped in this context. In this paper we present an easy-to-implement approach that lends itself to graphical displays of model fit. Our approach involves multiplying the estimated margional residual vector by the Cholesky decomposition of the inverse of the estimated margional variance matrix. The resulting "rotated" residuals are used to construct an empirical cumulative distribution function and pointwise standard errors. The theoretical framework, including conditions and asymptotic properties, involves technical details that are motivated by Lange and …

Semiparametric Methods For Semi-Competing Risks Problem With Censoring And Truncation, Hongyu Jiang, Jason Fine, Richard J. Chappell

Harvard University Biostatistics Working Paper Series

Studies of chronic life-threatening diseases often involve both mortality and morbidity. In observational studies, the data may also be subject to administrative left truncation and right censoring. Since mortality and morbidity may be correlated and mortality may censor morbidity, the Lynden-Bell estimator for left truncated and right censored data may be biased for estimating the marginal survival function of the non-terminal event. We propose a semiparametric estimator for this survival function based on a joint model for the two time-to-event variables, which utilizes the gamma frailty specification in the region of the observable data. Firstly, we develop a novel estimator …