Introduction Interactions between Continuous Predictors in Multiple Regression The Effects of Predictor Scaling on Coefficients of Regression Equations Testing and Probing Three-Way Interactions Structuring Regression Equations to Reflect Higher Order Relationships Model and Effect Testing with Higher Order Terms Interactions between Categorical and Continuous Variables Reliability and Statistical Power Conclusion Some Contrasts Between ANOVA and MR in Practice

Multiple Regression: Testing and Interpreting Interactions

Correlation networks are increasingly being used in bioinformatics applications For example, weighted gene co-expression network analysis is a systems biology method for describing the correlation patterns among genes across microarray samples Weighted correlation network analysis (WGCNA) can be used for finding clusters (modules) of highly correlated genes, for summarizing such clusters using the module eigengene or an intramodular hub gene, for relating modules to one another and to external sample traits (using eigengene network methodology), and for calculating module membership measures Correlation networks facilitate network based gene screening methods that can be used to identify candidate biomarkers or therapeutic targets These methods have been successfully applied in various biological contexts, eg cancer, mouse genetics, yeast genetics, and analysis of brain imaging data While parts of the correlation network methodology have been described in separate publications, there is a need to provide a user-friendly, comprehensive, and consistent software implementation and an accompanying tutorial The WGCNA R software package is a comprehensive collection of R functions for performing various aspects of weighted correlation network analysis The package includes functions for network construction, module detection, gene selection, calculations of topological properties, data simulation, visualization, and interfacing with external software Along with the R package we also present R software tutorials While the methods development was motivated by gene expression data, the underlying data mining approach can be applied to a variety of different settings The WGCNA package provides R functions for weighted correlation network analysis, eg co-expression network analysis of gene expression data The R package along with its source code and additional material are freely available at http://wwwgeneticsuclaedu/labs/horvath/CoexpressionNetwork/Rpackages/WGCNA
 

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WGCNA: an R package for weighted correlation network analysis.

An essential textbook for any student or researcher in biology needing to design experiments, sample programs or analyse the resulting data The text begins with a revision of estimation and hypothesis testing methods, covering both classical and Bayesian philosophies, before advancing to the analysis of linear and generalized linear models Topics covered include linear and logistic regression, simple and complex ANOVA models (for factorial, nested, block, split-plot and repeated measures and covariance designs), and log-linear models Multivariate techniques, including classification and ordination, are then introduced Special emphasis is placed on checking assumptions, exploratory data analysis and presentation of results The main analyses are illustrated with many examples from published papers and there is an extensive reference list to both the statistical and biological literature The book is supported by a website that provides all data sets, questions for each chapter and links to software

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Experimental Design and Data Analysis for Biologists

In Acemoglu, Johnson, and Robinson, henceforth AJR, (2001), we advanced the hypothesis that the mortality rates faced by Europeans in different parts of the world after 1500 affected their willingness to establish settlements and choice of colonization strategy. Places that were relatively healthy (for Europeans) were—when they fell under European control—more likely to receive better economic and political institutions. In contrast, places where European settlers were less likely to go were more likely to have “extractive” institutions imposed. We also posited that this early pattern of institutions has persisted over time and influences the extent and nature of institutions in the modern world. On this basis, we proposed using estimates of potential European settler mortality as an instrument for institutional variation in former European colonies today. Data on settlers themselves are unfortunately patchy—particularly because not many went to places they believed, with good reason, to be most unhealthy. We therefore followed the lead of Curtin (1989 and 1998) who compiled data on the death rates faced by European soldiers in various overseas postings. 1 Curtin’s data were based on pathbreaking data collection and statistical work initiated by the British military in the mid-nineteenth century. These data became part of the foundation of both contemporary thinking about public health (for soldiers and for civilians) and the life insurance industry (as actuaries and executives considered the

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The Colonial Origins of Comparative Development: An Empirical Investigation

Although intraclass correlation coefficients (ICCs) are commonly used in behavioral measurement, psychometrics, and behavioral genetics, procedures available for forming inferences about ICCs are not widely known. Following a review of the distinction between various forms of the ICC, this article p

https://psycnet.apa.org/journals/met/1/1/30.pdf

Forming inferences about some intraclass correlation coefficients.

Preface 1 Introduction 2 A Foundation for Robust Methods 3 Estimating Measures of Location and Scale 4 Confidence Intervals in the One-Sample Case 5 Comparing Two Groups 6 Some Multivariate Methods 7 One-Way and Higher Designs for Independent Groups 8 Comparing Multiple Dependent Groups 9 Correlation and Tests of Independence 10 Robust Regression 11 More Regression Methods

Introduction to Robust Estimation and Hypothesis Testing

This paper introduces the R package WRS2 that implements various robust statistical methods. It elaborates on the basics of robust statistics by introducing robust location, dispersion, and correlation measures. The location and dispersion measures are then used in robust variants of independent and dependent samples t tests and ANOVA, including between-within subject designs and quantile ANOVA. Further, robust ANCOVA as well as robust mediation models are introduced. The paper targets applied researchers; it is therefore kept rather non-technical and written in a tutorial style. Special emphasis is placed on applications in the social and behavioral sciences and illustrations of how to perform corresponding robust analyses in R. The R code for reproducing the results in the paper is given in the Supplementary Materials.

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Robust statistical methods in R using the WRS2 package.

Pearson’s correlation measures the strength of the association between two variables. The technique is, however, restricted to linear associations and is overly sensitive to outliers. Indeed, a single outlier can result in a highly inaccurate summary of the data. Yet, it remains the most commonly used measure of association in psychology research. Here we describe a free Matlab(R) based toolbox (http://sourceforge.net/projects/robustcorrtool/) that computes robust measures of association between two or more random variables: the percentage-bend correlation and skipped-correlations. After illustrating how to use the toolbox, we show that robust methods, where outliers are down weighted or removed and accounted for in significance testing, provide better estimates of the true association with accurate false positive control and without loss of power. The different correlation methods were tested with normal data and normal data contaminated with marginal or bivariate outliers. We report estimates of effect size, false positive rate and power, and advise on which technique to use depending on the data at hand.

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Robust Correlation Analyses: False Positive and Power Validation Using a New Open Source Matlab Toolbox

Part I: Genesis of a Science. Derivation Curve. What Am I Holding.- Least Squares. Quantifying Accuracy. Solving Bernoulli's Problem. Promoting Normality.- Part II: Exploiting Normality. Dealing with Small Samples Sizes. Correlation.- Part III: Dealing with Nonnormality. Revolution with a Whimper. Robust Methods. Bootstrap. Conclusion.

Fundamentals of Modern Statistical Methods: Substantially Improving Power and Accuracy

Various statistical methods, developed after 1970, offer the opportunity to substantially improve upon the power and accuracy of the conventional t test and analysis of variance methods for a wide range of commonly occurring situations. The authors briefly review some of the more fundamental problems with conventional methods based on means; provide some indication of why recent advances, based on robust measures of location (or central tendency), have practical value; and describe why modern investigations dealing with nonnormality find practical problems when comparing means, in contrast to earlier studies. Some suggestions are made about how to proceed when using modern methods.

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Rand R. Wilcox

Papers

Introduction to Robust Estimation and Hypothesis Testing

Robust statistical methods in R using the WRS2 package.

Robust Correlation Analyses: False Positive and Power Validation Using a New Open Source Matlab Toolbox

Fundamentals of Modern Statistical Methods: Substantially Improving Power and Accuracy

Modern robust data analysis methods: measures of central tendency.