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Multiple Regression In Pair Correlation Solution, Stan Lipovetsky

Journal of Modern Applied Statistical Methods

Behavior of the coefficients of ordinary least squares (OLS) regression with the coefficients regularized by the one-parameter ridge (Ridge-1) and two-parameter ridge (Ridge-2) regressions are compared. The ridge models are not prone to multicollinearity. The fit quality of Ridge-2 does not decrease with the profile parameter increase, but the Ridge-2 model converges to a solution proportional to the coefficients of pair correlation between the dependent variable and predictors. The Correlation-Regression (CORE) model suggests meaningful coefficients and net effects for the individual impact of the predictors, high quality model fit, and convenient analysis and interpretation of the regression. Simulation with three …

Bayesian Inference On The Variance Of Normal Distribution Using Moving Extremes Ranked Set Sampling, Said Ali Al-Hadhrami, Amer Ibrahim Al-Omari

Journal of Modern Applied Statistical Methods

Bayesian inference of the variance of the normal distribution is considered using moving extremes ranked set sampling (MERSS) and is compared with the simple random sampling (SRS) method. Generalized maximum likelihood estimators (GMLE), confidence intervals (CI), and different testing hypotheses are considered using simple hypothesis versus simple hypothesis, simple hypothesis versus composite alternative, and composite hypothesis versus composite alternative based on MERSS and compared with SRS. It is shown that modified inferences using MERSS are more efficient than their counterparts based on SRS.

Quantifying Bimodality Part 2: A Likelihood Ratio Test For The Comparison Of A Unimodal Normal Distribution And A Bimodal Mixture Of Two Normal Distributions. Bruno D. Zumbo Is, B. W. Frankland, Bruno D. Zumbo

Journal of Modern Applied Statistical Methods

Scientists in a variety of fields are often faced with the question of whether a sample is best described as unimodal or bimodal. In an earlier paper (Frankland & Zumbo, 2002), a simple and convenient method for assessing bimodality was described. That method is extended by developing and demonstrating a likelihood ratio test (LRT) for bimodality for the comparison of a unimodal normal distribution and a bimodal mixture of two normal distributions. As in Frankland and Zumbo (2002), the LRT approach is demonstrated using algorithms in SPSS.

Email: A Note On Hypothesis Tests After Correction For Autocorrelation: Solace For The Cochrane-Orcutt Method?, Terry E. Dielman

Journal of Modern Applied Statistical Methods

The behavior of the t test in small samples for coefficient significance in time-series regressions is examined after using the Prais-Winsten (PW) and Cochrane-Orcutt (CO) corrections for autocorrelation. Results are compared to ordinary least squares and generalized least squares.

Quel Test For Two Linear Restrictions In The Nonlinear Models, Krishna K. Saha

Journal of Modern Applied Statistical Methods

An alternative Wald type test called the quel test is developed for two linear restrictions by finding the critical region based on the quel utilizing the repeated values of estimated parameters of interest under the null. Simulation shows evidence that the full quel test performs best in that it holds nominal level well and shows monotonic increasing power properties.

Comparative Power Of The Independent T, Permutation T, And Wilcoxontests, Michèle Weber, Shlomo Sawilowsky

Journal of Modern Applied Statistical Methods

The nonparametric Wilcoxon Rank Sum (also known as the Mann-Whitney U) and the permutation t-tests are robust with respect to Type I error for departures from population normality, and both are powerful alternatives to the independent samples Student’s t-test for detecting shift in location. The question remains regarding their comparative statistical power for small samples, particularly for non-normal distributions. Monte Carlo simulations indicated the rank-based Wilcoxon test was found to be more powerful than both the t and the permutation t-tests.

Industrialization In Animal Agriculture: A Kalman Filter Analysis, Oya S. Erdogdu, Levent Ozbek

Journal of Modern Applied Statistical Methods

Studies discussing the effects of technological developments on (animal) agricultural production argue that the effective usage of chemicals and genetic engineering increase control over production processes, which in turn decreases seasonality (one significant factor defining agricultural production) significantly and brings standardization to production. Studies on broilery also show that production is not limited by nature determined seasons. Supply side changes accompanied by changes in demand have led to more healthier, standardized products. Using tools of economics and statistics, this study documents this transformation in animal agricultural production of beef, pork and milk. Results indicate decreasing seasonality, thus the industralization of …

Aligned Rank Tests For Interactions In Split-Plot Designs: Distributional Assumptions And Stochastic Heterogeneity, T. Mark Beasley, Bruno D. Zumbo

Journal of Modern Applied Statistical Methods

Three aligned rank methods for transforming data from multiple group repeated measures (split-plot) designs are reviewed. Univariate and multivariate statistics for testing the interaction in split-plot designs are elaborated. Computational examples are presented to provide a context for performing these ranking procedures and statistical tests. SAS/IML and SPSS syntax code to perform the procedures is included in the Appendix.

Pain As A Predictor Of Depression Treatment Outcomes In Women With Childhood Sexual Abuse, Ellen L. Poleshuck, Nancy L. Talbot, Haiyan Su, Xin Tu, Linda Chaudron, Stephanie Gamble, Donna E. Giles

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

Objectives: Childhood sexual abuse (CSA) increases risk for both depression and pain in women. Pain is associated with worse depression treatment response. The contribution of pain to depression treatment outcomes in women with histories of CSA is unknown. This study examined whether clinically significant pain would be associated with worse depression and functioning outcomes among women with CSA histories treated with interpersonal psychotherapy. Method: Participants were 66 women with major depression and CSA who presented to a community mental health center. An interpersonal psychotherapy protocol planned for 14 weekly sessions followed by 2 biweekly sessions. Patients were classified as experiencing …

The Comparison Of Model Selection Criteria When Selecting Among Competing Hierarchical Linear Models, Tiffany A. Whittaker, Carolyn F. Furlow

Journal of Modern Applied Statistical Methods

Little is known about the use and accuracy of model selection criteria when selecting among a set of competing multilevel models. The practices of applied researchers and the performance of five model selection criteria are examined when selecting the correct multilevel model using simulation techniques.

Bias In Stabilized Sieve Sampling, Liming Guan, John P. Wendell

Journal of Modern Applied Statistical Methods

The stabilized sieve sample selection method (SSM) is considered to be a probability proportional to size (PPS) sampling method with an unbiased estimator (Horgan 1997, 1998). This article demonstrates that SSM does not select items with PPS and that the point estimator is biased.

A New Approximate Bayesian Approach For Decision Making About The Variance Of A Gaussian Distribution Versus The Classical Approach, Vincent A. R. Camara

Journal of Modern Applied Statistical Methods

Rules of decision-making about the variance of a Gaussian distribution are obtained and compared. Considering the square error loss function, an approximate Bayesian decision rule for the variance of a normal population is derived. Using normal data and SAS software, the obtained approximate Bayesian test results were compared to their counterparts obtained with the well-known classical decision rule. It is shown that the proposed approximate Bayesian decision rule relies only on observations. The classical decision rule, which uses the Chi-square statistic, does not always yield the best results: the proposed approach often performs better.

Which Is The Best Parametric Statistical Method For Analyzing Delphi Data?, Hiral A. Shah, Sema A. Kalaian

Journal of Modern Applied Statistical Methods

This study compares the three parametric statistical methods: coefficient of variation, Pearson correlation coefficient, and F-test to obtain reliability in a Delphi study that involved more than 100 participants. The results of this study indicated that coefficient of variation was the best procedure to obtain reliability in such a study.

A Socratic Dialogue, Vance W. Berger

Journal of Modern Applied Statistical Methods

Socrates has found some aspects of medical biostatistics a bit confusing, and wishes to discuss some of these issues with Simplicio, a prominent medical researcher. This Socratic dialogue will shed some light on the errant use of parametric analyses in clinical trials.

A Comparison Of Maximum Likelihood And Expected A Posteriori Estimation For Polychoric Correlation Using Monte Carlo Simulation, Jinsong Chen, Jaehwa Choi

Journal of Modern Applied Statistical Methods

This study aims to compare the maximum likelihood (ML) and expected a posterior (EAP) estimation for polychoric correlation (PCC) under diverse conditions, especially when considering a sample size. As the ML is the classical solution to estimate PCC, the EAP is a new method based on Bayes’ theorem. Different types of prior distributions are also adapted to investigate the sensitivity of prior distribution onto the PCC estimate for the EAP case. The Monte Carlo simulation is used for this comparison by a specialized program code in MATLAB.

Tandem Queues With Non-Stationary Arrivals, Senthil Balaji Girimurugan

All Theses

We consider a network of K queues in tandem labeled Q₁, Q₂, ..,Q_K. The arrivals to Q ₁ form a non-homogeneous Poisson process whose intensity is periodic. We conjecture that asymptotically the arrival process A_j to Q_j, j= 1,2,..,K is cycle stationary. In addition, we conjecture that asymptotically as 'j' gets larger, the arrival process at the jth queue gets closer to a stationary point process. Hence, the queue performance measures become more stationary as 'j' increases. We perform Monte-Carlo simulations and design statistical tests whose results support the conjecture.

The Effectiveness Of Institutional Intervention At Minimizing Demographic Inertia And Improving The Representation Of Women Faculty In Higher Education, Amanda V. Bakian

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Across all science and engineering disciplines, women currently receive 46% of the doctoral degrees granted annually. Despite gains in doctoral degrees earned by women over the past 30 years, they remain under-represented among full time tenured /tenure-track science and engineering faculty compared to their presence among degree recipients. The inequality gap is widest among full professors at 4 year research universities where women account for a mere 16% of all S&E full time full professors. Multiple hypothesis have been proposed to account for women's under-representation relative to men including those based on human capital/economic theory, feminist theory, innate biological gender …

Time Series Analysis: A New Look At Some Old Problems, Ferebee Tunno

All Dissertations

This dissertation gives a comprehensive report of my doctoral research in time series analysis from summer 2006 to spring 2009. It is comprised of two main efforts: interval estimation for an autoregressive parameter and arc length tests for equivalent ARIMA dynamics. Such problems are traditional in statistics, but three new theorems and several simulations are presented here that help elucidate new ways to handle them.

Investigations Of Variable Importance Measures Within Random Forests, Andrew C. Merrill

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Random Forests (RF) (Breiman 2001; Breiman and Cutler 2004) is a completely nonparametric statistical learning procedure that may be used for regression analysis and. A feature of RF that is drawing a lot of attention is the novel algorithm that is used to evaluate the relative importance of the predictor/explanatory variables. Other machine learning algorithms for regression and classification, such as support vector machines and artificial neural networks (Hastie et al. 2009), exhibit high predictive accuracy but provide little insight into predictive power of individual variables. In contrast, the permutation algorithm of RF has already established a track record for …

Resampling-Based Multiple Hypothesis Testing With Applications To Genomics: New Developments In The R/Bioconductor Package Multtest, Houston N. Gilbert, Katherine S. Pollard, Mark J. Van Der Laan, Sandrine Dudoit

U.C. Berkeley Division of Biostatistics Working Paper Series

The multtest package is a standard Bioconductor package containing a suite of functions useful for executing, summarizing, and displaying the results from a wide variety of multiple testing procedures (MTPs). In addition to many popular MTPs, the central methodological focus of the multtest package is the implementation of powerful joint multiple testing procedures. Joint MTPs are able to account for the dependencies between test statistics by effectively making use of (estimates of) the test statistics joint null distribution. To this end, two additional bootstrap-based estimates of the test statistics joint null distribution have been developed for use in the …

A Class Of Semiparametric Mixture Cure Survival Models With Dependent Censoring, Megan Othus, Yi Li, Ram C. Tiwari

Harvard University Biostatistics Working Paper Series

No abstract provided.

Application Of Time-To-Event Methods In The Assessment Of Safety In Clinical Trials, Kelly L. Moore, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Since randomized controlled trials (RCT) are typically designed and powered for efficacy rather than safety, power is an important concern in the analysis of the effect of treatment on the occurrence of adverse events (AE). These outcomes are often time-to-event outcomes which will naturally be subject to right-censoring due to early patient withdrawals. In the analysis of the treatment effect on such an outcome, gains in efficiency, and thus power, can be achieved by exploiting covariate information. We apply the targeted maximum likelihood methodology to the estimation of treatment specific survival at a fixed end point for right-censored survival outcomes. …

Interval Estimation For The Difference In Paired Areas Under The Roc Curves In The Absence Of A Gold Standard Test, Hsin-Neng Hsieh, Hsiu-Yuan Su, Xiao-Hua Zhou

UW Biostatistics Working Paper Series

Receiver operating characteristic (ROC) curves can be used to assess the accuracy of tests measured on ordinal or continuous scales. The most commonly used measure for the overall diagnostic accuracy of diagnostic tests is the area under the ROC curve (AUC). A gold standard test on the true disease status is required to estimate the AUC. However, a gold standard test may sometimes be too expensive or infeasible. Therefore, in many medical research studies, the true disease status of the subjects may remain unknown. Under the normality assumption on test results from each disease group of subjects, using the expectation-maximization …

Bilinear Immersed Finite Elements For Interface Problems, Xiaoming He

Mathematics and Statistics Faculty Research & Creative Works

In this dissertation we discuss bilinear immersed finite elements (IFE) for solving interface problems. The related research works can be categorized into three aspects: (1) the construction of the bilinear immersed finite element spaces; (2) numerical methods based on these IFE spaces for solving interface problems; and (3) the corresponding error analysis. All of these together form a solid foundation for the bilinear IFEs.

The research on immersed finite elements is motivated by many real world applications, in which a simulation domain is often formed by several materials separated from each other by curves or surfaces while a mesh independent …

Collaborative Targeted Maximum Likelihood Estimation, Mark J. Van Der Laan, Susan Gruber

U.C. Berkeley Division of Biostatistics Working Paper Series

Collaborative double robust targeted maximum likelihood estimators represent a fundamental further advance over standard targeted maximum likelihood estimators of causal inference and variable importance parameters. The targeted maximum likelihood approach involves fluctuating an initial density estimate, (Q), in order to make a bias/variance tradeoff targeted towards a specific parameter in a semi-parametric model. The fluctuation involves estimation of a nuisance parameter portion of the likelihood, g. TMLE and other double robust estimators have been shown to be consistent and asymptotically normally distributed (CAN) under regularity conditions, when either one of these two factors of the likelihood of the data is …

A Semi-Parametric Two-Part Mixed-Effects Heteroscedastic Transformation Model For Correlated Right-Skewed Semi-Continuous Data, Huazhen Lin, Xiao-Hua Zhou

UW Biostatistics Working Paper Series

In longitudinal or hierarchical structure studies, we often encounter a semi-continuous variable that has a certain proportion of a single value and a continuous and skewed distribution among the rest of values. In the paper, we propose a new semi-parametric two-part mixed-effects transformation model to fit correlated skewed semi-continuous data. In our model, we allow the transformation to be non-parametric. Fitting the proposed model faces computational challenges due to intractable numerical integrations. We derive the estimates for the parameter and the transformation function based on an approximate likelihood, which has high order accuracy but less computational burden. We also propose …

Xprime: A Method Incorporating Expert Prior Information Into Motif Exploration, Rachel Lynn Poulsen

Theses and Dissertations

One of the primary goals of active research in molecular biology is to better understand the process of transcription regulation. An important objective in understanding transcription is identifying transcription factors that directly regulate target genes. Identifying these transcription factors is a key step toward eliminating genetic diseases or disease susceptibilities that are encoded inside deoxyribonucleic acid (DNA). There is much uncertainty and variation associated with transcription factor binding sites, requiring these sites to be represented stochastically. Although typically each transcription factor prefers to bind to a specific DNA word, it can bind to different variations of that DNA word. In …

Composite Likelihood Bayesian Information Criteria For Model Selection In High Dimensional Data, X Gao, Peter Xuekun Song

The University of Michigan Department of Biostatistics Working Paper Series

For high-dimensional data set with complicated dependency structures, the full likelihood approach often renders to intractable computational complexity. This imposes di±culty on model selection as most of the traditionally used information criteria require the evaluation of the full likelihood. We propose a composite likelihood version of the Bayesian information criterion (BIC) and establish its consistency property for the selection of the true underlying model. Under some mild regularity conditions, the proposed BIC is shown to be selection consistent, where the number of potential model parameters is allowed to increase to in¯nity at a certain rate of the sample size. Simulation …

Longitudinal Image Analysis Of Tumor/Brain Change In Contrast Uptake Induced By Radiation, Xiaoxi Zhang, Tim Johnson, Rod Little, Yue Cao

The University of Michigan Department of Biostatistics Working Paper Series

This work is motivated by a quantitative Magnetic Resonance Imaging study of the differential tumor/healthy tissue change in contrast uptake induced by radiation. The goal is to determine the time in which there is maximal contrast uptake, a surrogate for permeability, in the tumor relative to healthy tissue. A notable feature of the data is its spatial heterogeneity. Zhang, Johnson, Little, and Cao (2008a and 2008b) discuss two parallel approaches to “denoise” a single image of change in contrast uptake from baseline to a single follow-up visit of interest. In this work we explore the longitudinal profile of the tumor/healthy …

Joint Multiple Testing Procedures For Graphical Model Selection With Applications To Biological Networks, Houston N. Gilbert, Mark J. Van Der Laan, Sandrine Dudoit

U.C. Berkeley Division of Biostatistics Working Paper Series

Gaussian graphical models have become popular tools for identifying relationships between genes when analyzing microarray expression data. In the classical undirected Gaussian graphical model setting, conditional independence relationships can be inferred from partial correlations obtained from the concentration matrix (= inverse covariance matrix) when the sample size n exceeds the number of parameters p which need to estimated. In situations where n < p, another approach to graphical model estimation may rely on calculating unconditional (zero-order) and first-order partial correlations. In these settings, the goal is to identify a lower-order conditional independence graph, sometimes referred to as a ‘0-1 graphs’. For either choice of graph, model selection may involve a multiple testing problem, in which edges in a graph are drawn only after rejecting hypotheses involving (saturated or lower-order) partial correlation parameters. Most multiple testing procedures applied in previously proposed graphical model selection algorithms rely on standard, marginal testing methods which do not take into account the joint distribution of the test statistics derived from (partial) correlations. We propose and implement a multiple testing framework useful when testing for edge inclusion during graphical model selection. Two features of our methodology include (i) a computationally efficient and asymptotically valid test statistics joint null distribution derived from influence curves for correlation-based parameters, and (ii) the application of empirical Bayes joint multiple testing procedures which can effectively control a variety of popular Type I error rates by incorpo- rating joint null distributions such as those described here (Dudoit and van der Laan, 2008). Using a dataset from Arabidopsis thaliana, we observe that the use of more sophisticated, modular approaches to multiple testing allows one to identify greater numbers of edges when approximating an undirected graphical model using a 0-1 graph. Our framework may also be extended to edge testing algorithms for other types of graphical models (e.g., for classical undirected, bidirected, and directed acyclic graphs).