Statistical Theory Commons^™

On Additive Regression Of Expectancy, Ying Qing Chen

UW Biostatistics Working Paper Series

Regression models have been important tools to study the association between outcome variables and their covariates. The traditional linear regression models usually specify such an association by the expectations of the outcome variables as function of the covariates and some parameters. In reality, however, interests often focus on their expectancies characterized by the conditional means. In this article, a new class of additive regression models is proposed to model the expectancies. The model parameters carry practical implication, which may allow the models to be useful in applications such as treatment assessment, resource planning or short-term forecasting. Moreover, the new model …

An Empirical Process Limit Theorem For Sparsely Correlated Data, Thomas Lumley

UW Biostatistics Working Paper Series

We consider data that are dependent, but where most small sets of observations are independent. By extending Bernstein's inequality we prove a strong law of law numbers and an empirical process central limit theorem under bracketing entropy conditions.

New Statistical Paradigms Leading To Web-Based Tools For Clinical/Translational Science, Knut M. Wittkowski

COBRA Preprint Series

As the field of functional genetics and genomics is beginning to mature, we become confronted with new challenges. The constant drop in price for sequencing and gene expression profiling as well as the increasing number of genetic and genomic variables that can be measured makes it feasible to address more complex questions. The success with rare diseases caused by single loci or genes has provided us with a proof-of-concept that new therapies can be developed based on functional genomics and genetics.

Common diseases, however, typically involve genetic epistasis, genomic pathways, and proteomic pattern. Moreover, to better understand the underlying biologi-cal …

Multiple Imputation For Correcting Verification Bias, Ofer Harel, Xiao-Hua Zhou

UW Biostatistics Working Paper Series

In the case in which all subjects are screened using a common test, and only a subset of these subjects are tested using a golden standard test, it is well documented that there is a risk for bias, called verification bias. When the test has only two levels (e.g. positive and negative) and we are trying to estimate the sensitivity and specificity of the test, one is actually constructing a confidence interval for a binomial proportion. Since it is well documented that this estimation is not trivial even with complete data, we adopt Multiple imputation (MI) framework for verification bias …

On The Power Function Of Bayesian Tests With Application To Design Of Clinical Trials: The Fixed-Sample Case, Lyle Broemeling, Dongfeng Wu

Journal of Modern Applied Statistical Methods

Using a Bayesian approach to clinical trial design is becoming more common. For example, at the MD Anderson Cancer Center, Bayesian techniques are routinely employed in the design and analysis of Phase I and II trials. It is important that the operating characteristics of these procedures be determined as part of the process when establishing a stopping rule for a clinical trial. This study determines the power function for some common fixed-sample procedures in hypothesis testing, namely the one and two-sample tests involving the binomial and normal distributions. Also considered is a Bayesian test for multi-response (response and toxicity) in …

Two Sides Of The Same Coin: Bootstrapping The Restricted Vs. Unrestricted Model, Panagiotis Mantalos

Journal of Modern Applied Statistical Methods

The properties of the bootstrap test for restrictions are studied in two versions: 1) bootstrapping under the null hypothesis, restricted, and 2) bootstrapping under the alternative hypothesis, unrestricted. This article demonstrates the equivalence of these two methods, and illustrates the small sample properties of the Wald test for testing Granger-Causality in a stable stationary VAR system by Monte Carlo methods. The analysis regarding the size of the test reveals that, as expected, both bootstrap tests have actual sizes that lie close to the nominal size. Regarding the power of the test, the Wald and bootstrap tests share the same power …

Manifestation Of Differences In Item-Level Characteristics In Scale-Level Measurement Invariance Tests Of Multi-Group Confirmatory Factor Analyses, Bruno D. Zumbo, Kim H. Koh

Journal of Modern Applied Statistical Methods

If a researcher applies the conventional tests of scale-level measurement invariance through multi-group confirmatory factor analysis of a PC matrix and MLE to test hypotheses of strong and full measurement invariance when the researcher has a rating scale response format wherein the item characteristics are different for the two groups of respondents, do these scale-level analyses reflect (or ignore) differences in item threshold characteristics? Results of the current study demonstrate the inadequacy of judging the suitability of a measurement instrument across groups by only investigating the factor structure of the measure for the different groups with a PC matrix and …

Right-Tailed Testing Of Variance For Non-Normal Distributions, Michael C. Long, Ping Sa

Journal of Modern Applied Statistical Methods

A new test of variance for non-normal distribution with fewer restrictions than the current tests is proposed. Simulation study shows that the new test controls the Type I error rate well, and has power performance comparable to the competitors. In addition, it can be used without restrictions.

Multiple Imputation For Missing Ordinal Data, Ling Chen, Marian Toma-Drane, Robert F. Valois, J. Wanzer Drane

Journal of Modern Applied Statistical Methods

Simulations were used to compare complete case analysis of ordinal data with including multivariate normal imputations. MVN methods of imputation were not as good as using only complete cases. Bias and standard errors were measured against coefficients estimated from logistic regression and a standard data set.

Coverage Properties Of Optimized Confidence Intervals For Proportions, John P. Wendell, Sharon P. Cox

Journal of Modern Applied Statistical Methods

Wardell (1997) provided a method for constructing confidence intervals on a proportion that modifies the Clopper-Pearson (1934) interval by allowing for the upper and lower binomial tail probabilities to be set in a way that minimizes the interval width. This article investigates the coverage properties of these optimized intervals. It is found that the optimized intervals fail to provide coverage at or above the nominal rate over some portions of the binomial parameter space but may be useful as an approximate method.

Testing The Goodness Of Fit Of Multivariate Multiplicative-Intercept Risk Models Based On Case-Control Data, Biao Zhang

Journal of Modern Applied Statistical Methods

The validity of the multivariate multiplicative-intercept risk model with I +1 categories based on casecontrol data is tested. After reparametrization, the assumed risk model is equivalent to an (I +1) -sample semiparametric model in which the I ratios of two unspecified density functions have known parametric forms. By identifying this (I +1) -sample semiparametric model, which is of intrinsic interest in general (I +1) -sample problems, with an (I +1) -sample semiparametric selection bias model, we propose a weighted Kolmogorov-Smirnov-type statistic to test the validity of the multivariate multiplicativeintercept risk model. Established are some asymptotic results …

Within By Within Anova Based On Medians, Rand R. Wilcox

Journal of Modern Applied Statistical Methods

This article considers a J by K ANOVA design where all JK groups are dependent and where groups are to be compared based on medians. Two general approaches are considered. The first is based on an omnibus test for no main effects and no interactions and the other tests each member of a collection of relevant linear contrasts. Based on an earlier paper dealing with multiple comparisons, an obvious speculation is that a particular bootstrap method should be used. One of the main points here is that, in general, this is not the case for the problem at hand. The …

Testing The Casual Relation Between Sunspots And Temperature Using Wavelets Analysis, Abdullah Almasri, Ghazi Shukur

Journal of Modern Applied Statistical Methods

Investigated and tested in this article are the causal nexus between sunspots and temperature by using statistical methodology and causality tests. Because this kind of relationship cannot be properly captured in the short run (daily, monthly or yearly data), the relationship is investigated in the long run using a very low frequency Wavelets-based decomposed data such as D8 (128 - 256 months). Results indicate that during the period 1854-1989, the causality nexus between these two series is as expected of onedirectional form, i.e., from sunspots to temperature.

Model-Selection-Based Monitoring Of Structural Change, Kosei Fukuda

Journal of Modern Applied Statistical Methods

Monitoring structural change is performed not by hypothesis testing but by model selection using a modified Bayesian information criterion. It is found that concerning detection accuracy and detection speed, the proposed method shows better performance than the hypothesis-testing method. Two advantages of the proposed method are also discussed.

Using Scale Mixtures Of Normals To Model Continuously Compounded Returns, Hasan Hamdan, John Nolan, Melanie Wilson, Kristen Dardia

Journal of Modern Applied Statistical Methods

A new method for estimating the parameters of scale mixtures of normals (SMN) is introduced and evaluated. The new method is called UNMIX and is based on minimizing the weighted square distance between exact values of the density of the scale mixture and estimated values using kernel smoothing techniques over a specified grid of x-values and a grid of potential scale values. Applications of the method are made in modeling the continuously compounded return, CCR, of stock prices. Modeling this ratio with UNMIX proves promising in comparison with other existing techniques that use only one normal component, or those that …

Bayesian Reliability Modeling Using Monte Carlo Integration, Vincent A. R. Camara, Chris P. Tsokos

Journal of Modern Applied Statistical Methods

Bayesian Reliability Modeling Using Monte Carlo IntegrationThe aim of this article is to introduce the concept of Monte Carlo Integration in Bayesian estimation and Bayesian reliability analysis. Using the subject concept, approximate estimates of parameters and reliability functions are obtained for the three-parameter Weibull and the gamma failure models. Four different loss functions are used: square error, Higgins-Tsokos, Harris, and a logarithmic loss function proposed in this article. Relative efficiency is used to compare results obtained under the above mentioned loss functions.

Exploratory Factor Analysis In Two Measurement Journals: Hegemony By Default, J. Thomas Kellow

Journal of Modern Applied Statistical Methods

Exploratory factor analysis studies in two prominent measurement journals were explored. Issues addressed were: (a) factor extraction methods, (b) factor retention rules, (c) factor rotation strategies, and (d) saliency criteria for including variables. Many authors continue to use principal components extraction, orthogonal (varimax) rotation, and retain factors with eigenvalues greater than 1.0.

An Algorithm For Generating Unconditional Exact Permutation Distribution For A Two-Sample Experiment, Justice I. Odiase, Sunday M. Ogbonmwan

Journal of Modern Applied Statistical Methods

An Algorithm that generates the unconditional exact permutation distribution of a 2 x n experiment is presented. The algorithm is able to handle ranks as well as actual observations. It makes it possible to obtain exact p-values for several statistics, especially when sample sizes are small and the application of large sample approximation is unreliable. An illustrative implementation is achieved and leads to the computation of exact p-values for the Mood test when the sample size is small.

A Comparison Of Nonlinear Regression Codes, Paul Fredrick Mondragon, Brian Borchers

Journal of Modern Applied Statistical Methods

Five readily available software packages were tested on nonlinear regression test problems from the NIST Statistical Reference Datasets. None of the packages was consistently able to obtain solutions accurate to at least three digits. However, two of the packages were somewhat more reliable than the others.

Bias Of The Cox Model Hazard Ratio, Inger Persson, Harry Khamis

Journal of Modern Applied Statistical Methods

The hazard ratio estimated with the Cox model is investigated under proportional and five forms of nonproportional hazards. Results indicate that the highest bias occurs for diverging hazards with early censoring, and for increasing and crossing hazards under a high censoring rate.

Bias Affiliated With Two Variants Of Cohen’S D When Determining U1 As A Measure Of The Percent Of Non-Overlap, David A. Walker

Journal of Modern Applied Statistical Methods

Variants of Cohen’s d, in this instance dt and d_{adj, has the largest influence on U1 measures used with smaller sample sizes, specifically when n1 and n2 = 10. This study indicated that bias for variants of d, which influence U1 measures, tends to subside and become more manageable, in terms of precision of estimation, around 1% to 2% when n1 and n2 = 20. Thus, depending on the direction of the influence, both dt and dadj are likely to manage bias in the U1 measure quite well for smaller to …}

Some Guidelines For Using Nonparametric Methods For Modeling Data From Response Surface Designs, Christine M. Anderson-Cook, Kathryn Prewitt

Journal of Modern Applied Statistical Methods

Traditional response surface methodology focuses on modeling responses using parametric models with designs chosen to balance cost with adequate estimation of parameters and prediction in the design space. Using nonparametric smoothing to approximate the response surface offers both opportunities as well as problems. This article explores some conditions under which these methods can be appropriately used to increase the flexibility of surfaces modeled. The Box and Draper (1987) printing ink study is considered to illustrate the methods.

Determining The Correct Number Of Components To Extract From A Principal Components Analysis: A Monte Carlo Study Of The Accuracy Of The Scree Plot, Gibbs Y. Kanyongo

Journal of Modern Applied Statistical Methods

This article pertains to the accuracy of the of the scree plot in determining the correct number of components to retain under different conditions of sample size, component loading and variable-tocomponent ratio. The study employs use of Monte Carlo simulations in which the population parameters were manipulated, and data were generated, and then the scree plot applied to the generated scores.

Bayesian Wavelet Estimation Of Long Memory Parameter, Leming Qu

Journal of Modern Applied Statistical Methods

A Bayesian wavelet estimation method for estimating parameters of a stationary I(d) process is represented as an useful alternative to the existing frequentist wavelet estimation methods. The effectiveness of the proposed method is demonstrated through Monte Carlo simulations. The sampling from the posterior distribution is through the Markov Chain Monte Carlo (MCMC) easily implemented in the WinBUGS software package.

Enhancing The Performance Of A Short Run Multivariate Control Chart For The Process Mean, Michael B. C. Khoo, T. F. Ng

Journal of Modern Applied Statistical Methods

No abstract provided.

Jmasm16: Pseudo-Random Number Generation In R For Some Univariate Distributions, Hakan Demirtas

Journal of Modern Applied Statistical Methods

An increasing number of practitioners and applied researchers 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 some important univariate distributions. In this article, complementary R routines that could potentially be useful for simulation and computation purposes are provided.

Jmasm17: An Algorithm And Code For Computing Exact Critical Values For Friedman’S Nonparametric Anova, Sikha Bagui, Sbuhash Bagui

Journal of Modern Applied Statistical Methods

Provided in this article is an algorithm and code for computing exact critical values (or percentiles) for Friedman’s nonparametric rank test for k related treatment populations using Visual Basic (VB.NET). This program has the ability to calculate critical values for any number of treatment populations ( k ) and block sizes (b) at any significance level (α ) . We developed an exact critical value table for k = 2(1)5 and b = 2(1)15. This table will be useful to practitioners since it is not available in standard nonparametric statistics texts. The program can also be used to compute any …

Jmasm19: A Spss Matrix For Determining Effect Sizes From Three Categories: R And Functions Of R, Differences Between Proportions, And Standardized Differences Between Means, David A. Walker

Journal of Modern Applied Statistical Methods

The program is intended to provide editors, manuscript reviewers, students, and researchers with an SPSS matrix to determine an array of effect sizes not reported or the correctness of those reported, such as rrelated indices, r-related squared indices, and measures of association, when the only data provided in the manuscript or article are the n, M, and SD (and sometimes proportions and t and F (1) values) for twogroup designs. This program can create an internal matrix table to assist researchers in determining the size of an effect for commonly utilized r-related, mean difference, and difference in proportions indices when …

Letter To The Editor, Jmasm Editors

Journal of Modern Applied Statistical Methods

No abstract provided.

An Exploration Of Using Data Mining In Educational Research, Yonghong Jade Xu

Journal of Modern Applied Statistical Methods

Technology advances popularized large databases in education. Traditional statistics have limitations for analyzing large quantities of data. This article discusses data mining by analyzing a data set with three models: multiple regression, data mining, and a combination of the two. It is concluded that data mining is applicable in educational research.