Applied Multivariate Analysis


 Kelly Shelton
 2 years ago
 Views:
Transcription
1 Neil H. Timm Applied Multivariate Analysis With 42 Figures Springer
2 Contents Preface Acknowledgments List of Tables List of Figures vii ix xix xxiii 1 Introduction Overview Multivariate Models and Methods Scope of the Book 3 2 Vectors and Matrices Introduction Vectors, Vector Spaces, and Vector Subspaces 7 a. Vectors 7 b. Vector Spaces 8 c. Vector Subspaces Bases, Vector Norms, and the Algebra of Vector Spaces 12 a. Bases 13 b. Lengths, Distances, and Angles 13 c. GramSchmidt Orthogonalization Process 15 d. Orthogonal Spaces 17 e. Vector Inequalities, Vector Norms, and Statistical Distance 21
3 xii Contents 2.4 Basic Matrix Operations 25 a. Equality, Addition, and Multiplication of Matrices 26 b. Matrix Transposition 28 c. Some Special Matrices 29 d. Trace and the Euclidean Matrix Norm 30 e. Kronecker and Hadamard Products 32 f. Direct Sums 35 g. The Vec() and Vech() Operators Rank, Inverse, and Determinant 41 a. Rank and Inverse 41 b. Generalized Inverses 47 c. Determinants Systems of Equations, Transformations, and Quadratic Forms 55 a. Systems of Equations 55 b. Linear Transformations 61 c. Projection Transformations 63 d. Eigenvalues and Eigenvectors 67 e. Matrix Norms 71 f. Quadratic Forms and Extrema 72 g. Generalized Projectors Limits and Asymptotics 76 3 Multivariate Distributions and the Linear Model Introduction Random Vectors and Matrices The Multivariate Normal (MVN) Distribution 84 a. Properties of the Multivariate Normal Distribution 86 b. Estimating /x and E 88 c. The Matrix Normal Distribution The ChiSquare and Wishart Distributions 93 a. ChiSquare Distribution 93 b. The Wishart Distribution Other Multivariate Distributions 99 a. The Univariate t and F Distributions 99 b. Hotelling's T 2 Distribution 99 c. The Beta Distribution 101 d. Multivariate t, F, and / 2 Distributions The General Linear Model 106 a. Regression, ANOVA, and ANCOVA Models 107 b. Multivariate Regression, MANOVA, and MANCOVA Models c. The Seemingly Unrelated Regression (SUR) Model 114 d. The General MANOVA Model (GMANOVA) Evaluating Normality Tests of Covariance Matrices 133 a. Tests of Covariance Matrices 133
4 Contents xiii b. Equality of Covariance Matrices 133 c. Testing for a Specific Covariance Matrix 137 d. Testing for Compound Symmetry 138 e. Tests of Sphericity 139 f. Tests of Independence 143 g. Tests for Linear Structure Tests of Location 149 a. TwoSample Case, Ei = E 2 = 149 b. TwoSample Case, Ei ^ E c. TwoSample Case, Nonnormality 160 d. Profile Analysis, One Group 160 e. Profile Analysis, Two Groups 165 f. Profile Analysis, Ei ^ E Univariate Profile Analysis 181 a. Univariate OneGroup Profile Analysis 182 b. Univariate TwoGroup Profile Analysis Power Calculations 182 Multivariate Regression Models Introduction Multivariate Regression 186 a. Multiple Linear Regression 186 b. Multivariate Regression Estimation and Testing Hypotheses 187 c. Multivariate Influence Measures 193 d. Measures of Association, Variable Selection and LackofFit Tests e. Simultaneous Confidence Sets for a New Observation y new and the Elements of B 204 f. Random X Matrix and Model Validation: Mean Squared Error of Prediction in Multivariate Regression 206 g. Exogeniety in Regression Multivariate Regression Example OneWay MANOVA and MANCOVA 218 a. OneWay MANOVA 218 b. OneWay MANCOVA 225 c. Simultaneous Test Procedures (STP) for OneWay MANOVA /MANCOVA OneWay MANOVA/MANCOVA Examples 234 a. MANOVA (Example 4.5.1) 234 b. MANCOVA (Example 4.5.2) MANOVA/MANCOVA with Unequal E, or Nonnormal Data OneWay MANOVA with Unequal E, Example TwoWay MANOVA/MANCOVA 246 a. TwoWay MANOVA with Interaction 246 b. Additive TwoWay MANOVA 252 c. TwoWay MANCOVA 256
5 xiv Contents d. Tests of Nonadditivity TwoWay MANOVA/MANCOVA Example 257 a. TwoWay MANOVA (Example 4.9.1) 257 b. TwoWay MANCOVA (Example 4.9.2) Nonorthogonal TwoWay MANOVA Designs 264 a. Nonorthogonal TwoWay MANOVA Designs with and Without Empty Cells, and Interaction 265 b. Additive TwoWay MANOVA Designs With Empty Cells Unbalance, Nonorthogonal Designs Example Higher Ordered Fixed Effect, Nested and Other Designs Complex Design Examples 276 a. Nested Design (Example ) 276 b. Latin Square Design (Example ) Repeated Measurement Designs 282 a. OneWay Repeated Measures Design 282 b. Extended Linear Hypotheses Repeated Measurements and Extended Linear Hypotheses Example a. Repeated Measures (Example ) 294 b. Extended Linear Hypotheses (Example ) Robustness and Power Analysis for MR Models Power Calculations Power.sas Testing for Mean Differences with Unequal Covariance Matrices Seemingly Unrelated Regression Models Introduction The SUR Model 312 a. Estimation and Hypothesis Testing 312 b. Prediction Seeming Unrelated Regression Example The CGMANOVA Model CGMANOVA Example The GMANOVA Model 320 a. Overview 320 b. Estimation and Hypothesis Testing 321 c. Test of Fit 324 d. Subsets of Covariates 324 e. GMANOVA vs SUR 326 f. Missing Data GMANOVA Example 327 a. One Group Design (Example 5.7.1) 328 b. Two Group Design (Example 5.7.2) Tests of Nonadditivity Testing for Nonadditivity Example Lack of Fit Test Sum of Profile Designs 338
6 Contents xv 5.12 The Multivariate SUR (MSUR) Model Sum of Profile Example Testing Model Specification in SUR Models Miscellanea 348 Multivariate Random and Mixed Models Introduction Random Coefficient Regression Models 352 a. Model Specification 352 b. Estimating the Parameters 353 c. Hypothesis Testing Univariate General Linear Mixed Models 357 a. Model Specification 357 b. Covariance Structures and Model Fit 359 c. Model Checking 361 d. Balanced Variance Component Experimental Design Models 366 e. Multilevel Hierarchical Models 367 f. Prediction Mixed Model Examples 369 a. Random Coefficient Regression (Example 6.4.1) 371 b. Generalized Randomized Block Design (Example 6.4.2) 376 c. Repeated Measurements (Example 6.4.3) 380 d. HLM Model (Example 6.4.4) Mixed Multivariate Models 385 a. Model Specification 386 b. Hypothesis Testing 388 c. Evaluating Expected Mean Square 391 d. Estimating the Mean 392 e. Repeated Measurements Model Balanced Mixed Multivariate Models Examples 394 a. Twoway Mixed MANOVA 395 b. Multivariate SplitPlot Design Double Multivariate Model (DMM) Double Multivariate Model Examples 403 a. Double Multivariate MANOVA (Example 6.8.1) 404 b. SplitPlot Design (Example 6.8.2) Multivariate Hierarchical Linear Models Tests of Means with Unequal Covariance Matrices 417 Discriminant and Classification Analysis Introduction Two Group Discrimination and Classification 420 a. Fisher's Linear Discriminant Function 421 b. Testing Discriminant Function Coefficients 422 c. Classification Rules 424
7 xvi Contents d. Evaluating Classification Rules Two Group Discriminant Analysis Example 429 a. Egyptian Skull Data (Example 7.3.1) 429 b. Brain Size (Example 7.3.2) Multiple Group Discrimination and Classification 434 a. Fisher's Linear Discriminant Function 434 b. Testing Discriminant Functions for Significance 435 c. Variable Selection 437 d. Classification Rules 438 e. Logistic Discrimination and Other Topics Multiple Group Discriminant Analysis Example Principal Component, Canonical Correlation, and Exploratory Factor Analysis Introduction Principal Component Analysis 445 a. Population Model for PCA 446 b. Number of Components and Component Structure 449 c. Principal Components with Covariates 453 d. Sample PCA 455 e. Plotting Components 458 f. Additional Comments 458 g. Outlier Detection Principal Component Analysis Examples 460 a. Test Battery (Example 8.3.1) 460 b. Semantic Differential Ratings (Example 8.3.2) 461 c. Performance Assessment Program (Example 8.3.3) Statistical Tests in Principal Component Analysis 468 a. Tests Using the Covariance Matrix 468 b. Tests Using a Correlation Matrix Regression on Principal Components 474 a. GMANOVA Model 475 b. The PCA Model Multivariate Regression on Principal Components Example Canonical Correlation Analysis 477 a. Population Model for CCA 477 b. Sample CCA 482 c. Tests of Significance 483 d. Association and Redundancy 485 e. Partial, Part and Bipartial Canonical Correlation 487 f. Predictive Validity in Multivariate Regression using CCA 490 g. Variable Selection and Generalized Constrained CCA Canonical Correlation Analysis Examples 492 a. Rohwer CCA (Example 8.8.1) 492 b. Partial and Part CCA (Example 8.8.2) 494
8 Contents xvii 8.9 Exploratory Factor Analysis 496 a. Population Model for EFA 497 b. Estimating Model Parameters 502 c. Determining Model Fit 506 d. Factor Rotation 507 e. Estimating Factor Scores 509 f. Additional Comments Exploratory Factor Analysis Examples 511 a. Performance Assessment Program (PAP Example ) 511 b. Di Vesta and Walls (Example ) 512 c. Shin (Example ) Cluster Analysis and Multidimensional Scaling Introduction Proximity Measures 516 a. Dissimilarity Measures 516 b. Similarity Measures 519 c. Clustering Variables Cluster Analysis 522 a. Agglomerative Hierarchical Clustering Methods 523 b. Nonhierarchical Clustering Methods 530 c. Number of Clusters 531 d. Additional Comments Cluster Analysis Examples 533 a. Protein Consumption (Example 9.4.1) 534 b. Nonhierarchical Method (Example 9.4.2) 536 c. Teacher Perception (Example 9.4.3) 538 d. Cedar Project (Example 9.4.4) Multidimensional Scaling 541 a. Classical Metric Scaling 542 b. Nonmetric Scaling 544 c. Additional Comments Multidimensional Scaling Examples 548 a. Classical Metric Scaling (Example 9.6.1) 549 b. Teacher Perception (Example 9.6.2) 550 c. Nation (Example 9.6.3) Structural Equation Models Introduction Path Diagrams, Basic Notation, and the General Approach Confirmatory Factor Analysis Confirmatory Factor Analysis Examples 575 a. Performance Assessment 3  Factor Model (Example ) 575 b. Performance Assessment 5Factor Model (Example ) Path Analysis 580
9 xviii Contents 10.6 Path Analysis Examples 586 a. Community Structure and Industrial Conflict (Example ) b. Nonrecursive Model (Example ) Structural Equations with Manifest and Latent Variables Structural Equations with Manifest and Latent Variables Example Longitudinal Analysis with Latent Variables Exogeniety in Structural Equation Models 604 Appendix 609 References 625 Author Index 667 Subject Index 675
Multivariate Statistical Inference and Applications
Multivariate Statistical Inference and Applications ALVIN C. RENCHER Department of Statistics Brigham Young University A WileyInterscience Publication JOHN WILEY & SONS, INC. New York Chichester Weinheim
More informationMULTIVARIATE DATA ANALYSIS i.*.'.. ' 4
SEVENTH EDITION MULTIVARIATE DATA ANALYSIS i.*.'.. ' 4 A Global Perspective Joseph F. Hair, Jr. Kennesaw State University William C. Black Louisiana State University Barry J. Babin University of Southern
More informationStatistics Graduate Courses
Statistics Graduate Courses STAT 7002Topics in StatisticsBiological/Physical/Mathematics (cr.arr.).organized study of selected topics. Subjects and earnable credit may vary from semester to semester.
More informationReview Jeopardy. Blue vs. Orange. Review Jeopardy
Review Jeopardy Blue vs. Orange Review Jeopardy Jeopardy Round Lectures 03 Jeopardy Round $200 How could I measure how far apart (i.e. how different) two observations, y 1 and y 2, are from each other?
More informationMATHEMATICAL METHODS OF STATISTICS
MATHEMATICAL METHODS OF STATISTICS By HARALD CRAMER TROFESSOK IN THE UNIVERSITY OF STOCKHOLM Princeton PRINCETON UNIVERSITY PRESS 1946 TABLE OF CONTENTS. First Part. MATHEMATICAL INTRODUCTION. CHAPTERS
More informationApplied Regression Analysis and Other Multivariable Methods
THIRD EDITION Applied Regression Analysis and Other Multivariable Methods David G. Kleinbaum Emory University Lawrence L. Kupper University of North Carolina, Chapel Hill Keith E. Muller University of
More informationInstitute of Actuaries of India Subject CT3 Probability and Mathematical Statistics
Institute of Actuaries of India Subject CT3 Probability and Mathematical Statistics For 2015 Examinations Aim The aim of the Probability and Mathematical Statistics subject is to provide a grounding in
More informationExploratory Data Analysis with MATLAB
Computer Science and Data Analysis Series Exploratory Data Analysis with MATLAB Second Edition Wendy L Martinez Angel R. Martinez Jeffrey L. Solka ( r ec) CRC Press VV J Taylor & Francis Group Boca Raton
More informationCONTENTS PREFACE 1 INTRODUCTION 1 2 DATA VISUALIZATION 19
PREFACE xi 1 INTRODUCTION 1 1.1 Overview 1 1.2 Definition 1 1.3 Preparation 2 1.3.1 Overview 2 1.3.2 Accessing Tabular Data 3 1.3.3 Accessing Unstructured Data 3 1.3.4 Understanding the Variables and Observations
More information(and sex and drugs and rock 'n' roll) ANDY FIELD
DISCOVERING USING SPSS STATISTICS THIRD EDITION (and sex and drugs and rock 'n' roll) ANDY FIELD CONTENTS Preface How to use this book Acknowledgements Dedication Symbols used in this book Some maths revision
More informationService courses for graduate students in degree programs other than the MS or PhD programs in Biostatistics.
Course Catalog In order to be assured that all prerequisites are met, students must acquire a permission number from the education coordinator prior to enrolling in any Biostatistics course. Courses are
More informationADVANCED LINEAR ALGEBRA FOR ENGINEERS WITH MATLAB. Sohail A. Dianat. Rochester Institute of Technology, New York, U.S.A. Eli S.
ADVANCED LINEAR ALGEBRA FOR ENGINEERS WITH MATLAB Sohail A. Dianat Rochester Institute of Technology, New York, U.S.A. Eli S. Saber Rochester Institute of Technology, New York, U.S.A. (g) CRC Press Taylor
More informationData Analysis in Management with SPSS Software
Data Analysis in Management with SPSS Software J.P. Verma Data Analysis in Management with SPSS Software J.P. Verma Research and Advanced Studies Lakshmibai National University of Physical Education Gwalior,
More informationWhen to Use Which Statistical Test
When to Use Which Statistical Test Rachel Lovell, Ph.D., Senior Research Associate Begun Center for Violence Prevention Research and Education Jack, Joseph, and Morton Mandel School of Applied Social Sciences
More informationApplied Multiple Regression/Correlation Analysis for the Behavioral Sciences
Applied Multiple Regression/Correlation Analysis for the Behavioral Sciences Third Edition Jacob Cohen (deceased) New York University Patricia Cohen New York State Psychiatric Institute and Columbia University
More informationOverview of Factor Analysis
Overview of Factor Analysis Jamie DeCoster Department of Psychology University of Alabama 348 Gordon Palmer Hall Box 870348 Tuscaloosa, AL 354870348 Phone: (205) 3484431 Fax: (205) 3488648 August 1,
More informationDATA ANALYTICS USING R
DATA ANALYTICS USING R Duration: 90 Hours Intended audience and scope: The course is targeted at fresh engineers, practicing engineers and scientists who are interested in learning and understanding data
More informationMultivariate Normal Distribution
Multivariate Normal Distribution Lecture 4 July 21, 2011 Advanced Multivariate Statistical Methods ICPSR Summer Session #2 Lecture #47/21/2011 Slide 1 of 41 Last Time Matrices and vectors Eigenvalues
More informationMultivariate Analysis of Variance (MANOVA)
Multivariate Analysis of Variance (MANOVA) Aaron French, Marcelo Macedo, John Poulsen, Tyler Waterson and Angela Yu Keywords: MANCOVA, special cases, assumptions, further reading, computations Introduction
More informationAnalysing Ecological Data
Alain F. Zuur Elena N. Ieno Graham M. Smith Analysing Ecological Data University una Landesbibliothe;< Darmstadt Eibliothek Biologie tov.nr. 4y Springer Contents Contributors xix 1 Introduction 1 1.1
More informationC: LEVEL 800 {MASTERS OF ECONOMICS( ECONOMETRICS)}
C: LEVEL 800 {MASTERS OF ECONOMICS( ECONOMETRICS)} 1. EES 800: Econometrics I Simple linear regression and correlation analysis. Specification and estimation of a regression model. Interpretation of regression
More informationRegression Modeling Strategies
Frank E. Harrell, Jr. Regression Modeling Strategies With Applications to Linear Models, Logistic Regression, and Survival Analysis With 141 Figures Springer Contents Preface Typographical Conventions
More informationData analysis process
Data analysis process Data collection and preparation Collect data Prepare codebook Set up structure of data Enter data Screen data for errors Exploration of data Descriptive Statistics Graphs Analysis
More informationREVIEWING THREE DECADES WORTH OF STATISTICAL ADVANCEMENTS IN INDUSTRIALORGANIZATIONAL PSYCHOLOGICAL RESEARCH
1 REVIEWING THREE DECADES WORTH OF STATISTICAL ADVANCEMENTS IN INDUSTRIALORGANIZATIONAL PSYCHOLOGICAL RESEARCH Nicholas Wrobel Faculty Sponsor: Kanako Taku Department of Psychology, Oakland University
More informationDesign & Analysis of Ecological Data. Landscape of Statistical Methods...
Design & Analysis of Ecological Data Landscape of Statistical Methods: Part 3 Topics: 1. Multivariate statistics 2. Finding groups  cluster analysis 3. Testing/describing group differences 4. Unconstratined
More information1 Introduction. 2 Matrices: Definition. Matrix Algebra. Hervé Abdi Lynne J. Williams
In Neil Salkind (Ed.), Encyclopedia of Research Design. Thousand Oaks, CA: Sage. 00 Matrix Algebra Hervé Abdi Lynne J. Williams Introduction Sylvester developed the modern concept of matrices in the 9th
More informationIntroduction to Principal Components and FactorAnalysis
Introduction to Principal Components and FactorAnalysis Multivariate Analysis often starts out with data involving a substantial number of correlated variables. Principal Component Analysis (PCA) is a
More informationSemester 2 Statistics Short courses
Semester 2 Statistics Short courses Course: STAA0001  Basic Statistics Blackboard Site: STAA0001 Dates: Sat 10 th Sept and 22 Oct 2016 (9 am 5 pm) Room EN409 Assumed Knowledge: None Day 1: Exploratory
More informationIntroduction to Statistics with SPSS for Social Science
New Introduction to Statistics with SPSS for Social Science Gareth Norris Faiza Qureshi Dennis Howitt Duncan Cramer Aberystwyth University City University London University of Loughborough University of
More informationA Introduction to Matrix Algebra and Principal Components Analysis
A Introduction to Matrix Algebra and Principal Components Analysis Multivariate Methods in Education ERSH 8350 Lecture #2 August 24, 2011 ERSH 8350: Lecture 2 Today s Class An introduction to matrix algebra
More informationDISCRIMINANT FUNCTION ANALYSIS (DA)
DISCRIMINANT FUNCTION ANALYSIS (DA) John Poulsen and Aaron French Key words: assumptions, further reading, computations, standardized coefficents, structure matrix, tests of signficance Introduction Discriminant
More informationChapter 14: Analyzing Relationships Between Variables
Chapter Outlines for: Frey, L., Botan, C., & Kreps, G. (1999). Investigating communication: An introduction to research methods. (2nd ed.) Boston: Allyn & Bacon. Chapter 14: Analyzing Relationships Between
More information1. Complete the sentence with the correct word or phrase. 2. Fill in blanks in a source table with the correct formuli for df, MS, and F.
Final Exam 1. Complete the sentence with the correct word or phrase. 2. Fill in blanks in a source table with the correct formuli for df, MS, and F. 3. Identify the graphic form and nature of the source
More informationMultivariate Analysis. Overview
Multivariate Analysis Overview Introduction Multivariate thinking Body of thought processes that illuminate the interrelatedness between and within sets of variables. The essence of multivariate thinking
More informationEconometric Analysis of Cross Section and Panel Data Second Edition. Jeffrey M. Wooldridge. The MIT Press Cambridge, Massachusetts London, England
Econometric Analysis of Cross Section and Panel Data Second Edition Jeffrey M. Wooldridge The MIT Press Cambridge, Massachusetts London, England Preface Acknowledgments xxi xxix I INTRODUCTION AND BACKGROUND
More informationIntroduction to Longitudinal Data Analysis
Introduction to Longitudinal Data Analysis Longitudinal Data Analysis Workshop Section 1 University of Georgia: Institute for Interdisciplinary Research in Education and Human Development Section 1: Introduction
More informationFactor Analysis. Chapter 420. Introduction
Chapter 420 Introduction (FA) is an exploratory technique applied to a set of observed variables that seeks to find underlying factors (subsets of variables) from which the observed variables were generated.
More informationCommon factor analysis
Common factor analysis This is what people generally mean when they say "factor analysis" This family of techniques uses an estimate of common variance among the original variables to generate the factor
More information1. Students will demonstrate an understanding of the real number system as evidenced by classroom activities and objective tests
MATH 102/102L InterAlgebra/Lab Properties of the real number system, factoring, linear and quadratic equations polynomial and rational expressions, inequalities, systems of equations, exponents, radicals,
More informationQUALITY ENGINEERING PROGRAM
QUALITY ENGINEERING PROGRAM Production engineering deals with the practical engineering problems that occur in manufacturing planning, manufacturing processes and in the integration of the facilities and
More informationPrincipal Components Analysis (PCA)
Principal Components Analysis (PCA) Janette Walde janette.walde@uibk.ac.at Department of Statistics University of Innsbruck Outline I Introduction Idea of PCA Principle of the Method Decomposing an Association
More informationIntroduction to Multivariate Models: Modeling Multivariate Outcomes with Mixed Model Repeated Measures Analyses
Introduction to Multivariate Models: Modeling Multivariate Outcomes with Mixed Model Repeated Measures Analyses Applied Multilevel Models for Cross Sectional Data Lecture 11 ICPSR Summer Workshop University
More informationSPSS ADVANCED ANALYSIS WENDIANN SETHI SPRING 2011
SPSS ADVANCED ANALYSIS WENDIANN SETHI SPRING 2011 Statistical techniques to be covered Explore relationships among variables Correlation Regression/Multiple regression Logistic regression Factor analysis
More informationEconomic Order Quantity and Economic Production Quantity Models for Inventory Management
Economic Order Quantity and Economic Production Quantity Models for Inventory Management Inventory control is concerned with minimizing the total cost of inventory. In the U.K. the term often used is stock
More informationGraduate Programs in Statistics
Graduate Programs in Statistics Course Titles STAT 100 CALCULUS AND MATR IX ALGEBRA FOR STATISTICS. Differential and integral calculus; infinite series; matrix algebra STAT 195 INTRODUCTION TO MATHEMATICAL
More informationSemester 1 Statistics Short courses
Semester 1 Statistics Short courses Course: STAA0001 Basic Statistics Blackboard Site: STAA0001 Dates: Sat. March 12 th and Sat. April 30 th (9 am 5 pm) Assumed Knowledge: None Course Description Statistical
More informationComputerAided Multivariate Analysis
ComputerAided Multivariate Analysis FOURTH EDITION Abdelmonem Af if i Virginia A. Clark and Susanne May CHAPMAN & HALL/CRC A CRC Press Company Boca Raton London New York Washington, D.C Contents Preface
More informationStep 5: Conduct Analysis. The CCA Algorithm
Model Parameterization: Step 5: Conduct Analysis P Dropped species with fewer than 5 occurrences P Logtransformed species abundances P Rownormalized species log abundances (chord distance) P Selected
More informationUnivariate and Multivariate Methods PEARSON. Addison Wesley
Time Series Analysis Univariate and Multivariate Methods SECOND EDITION William W. S. Wei Department of Statistics The Fox School of Business and Management Temple University PEARSON Addison Wesley Boston
More informationANSWERS TO EXERCISES AND REVIEW QUESTIONS
ANSWERS TO EXERCISES AND REVIEW QUESTIONS PART FIVE: STATISTICAL TECHNIQUES TO COMPARE GROUPS Before attempting these questions read through the introduction to Part Five and Chapters 1621 of the SPSS
More informationTtest & factor analysis
Parametric tests Ttest & factor analysis Better than non parametric tests Stringent assumptions More strings attached Assumes population distribution of sample is normal Major problem Alternatives Continue
More informationStatistical Models in R
Statistical Models in R Some Examples Steven Buechler Department of Mathematics 276B Hurley Hall; 16233 Fall, 2007 Outline Statistical Models Structure of models in R Model Assessment (Part IA) Anova
More information15.062 Data Mining: Algorithms and Applications Matrix Math Review
.6 Data Mining: Algorithms and Applications Matrix Math Review The purpose of this document is to give a brief review of selected linear algebra concepts that will be useful for the course and to develop
More informationMathematics (MAT) MAT 061 Basic Euclidean Geometry 3 Hours. MAT 051 PreAlgebra 4 Hours
MAT 051 PreAlgebra Mathematics (MAT) MAT 051 is designed as a review of the basic operations of arithmetic and an introduction to algebra. The student must earn a grade of C or in order to enroll in MAT
More informationStatistics in Psychosocial Research Lecture 8 Factor Analysis I. Lecturer: Elizabeth GarrettMayer
This work is licensed under a Creative Commons AttributionNonCommercialShareAlike License. Your use of this material constitutes acceptance of that license and the conditions of use of materials on this
More informationTeaching Multivariate Analysis to BusinessMajor Students
Teaching Multivariate Analysis to BusinessMajor Students WingKeung Wong and TeckWong Soon  Kent Ridge, Singapore 1. Introduction During the last two or three decades, multivariate statistical analysis
More informationDimensionality Reduction: Principal Components Analysis
Dimensionality Reduction: Principal Components Analysis In data mining one often encounters situations where there are a large number of variables in the database. In such situations it is very likely
More informationGeneralized Inverse of Matrices and its Applications
Generalized Inverse of Matrices and its Applications C. RADHAKRISHNA RAO, Sc.D., F.N.A., F.R.S. Director, Research and Training School Indian Statistical Institute SUJIT KUMAR MITRA, Ph.D. Professor of
More informationAdvanced Linear Modeling
Ronald Christensen Advanced Linear Modeling Multivariate, Time Series, and Spatial Data; Nonparametric Regression and Response Surface Maximization Second Edition Springer Preface to the Second Edition
More informationINTRODUCTORY STATISTICS
INTRODUCTORY STATISTICS FIFTH EDITION Thomas H. Wonnacott University of Western Ontario Ronald J. Wonnacott University of Western Ontario WILEY JOHN WILEY & SONS New York Chichester Brisbane Toronto Singapore
More informationBusiness Statistics. Successful completion of Introductory and/or Intermediate Algebra courses is recommended before taking Business Statistics.
Business Course Text Bowerman, Bruce L., Richard T. O'Connell, J. B. Orris, and Dawn C. Porter. Essentials of Business, 2nd edition, McGrawHill/Irwin, 2008, ISBN: 9780073319889. Required Computing
More informationFactor Analysis. Principal components factor analysis. Use of extracted factors in multivariate dependency models
Factor Analysis Principal components factor analysis Use of extracted factors in multivariate dependency models 2 KEY CONCEPTS ***** Factor Analysis Interdependency technique Assumptions of factor analysis
More informationPrincipal Component Analysis Application to images
Principal Component Analysis Application to images Václav Hlaváč Czech Technical University in Prague Faculty of Electrical Engineering, Department of Cybernetics Center for Machine Perception http://cmp.felk.cvut.cz/
More informationCourse Agenda. First Day. 4 th February  Monday 14.3019.00. 14:3015.30 Students Registration Polo Didattico Laterino
Course Agenda First Day 4 th February  Monday 14.3019.00 14:3015.30 Students Registration Main Entrance Registration Desk 15.3017.00 Opening Works Teacher presentation Brief Students presentation Course
More informationLecture  32 Regression Modelling Using SPSS
Applied Multivariate Statistical Modelling Prof. J. Maiti Department of Industrial Engineering and Management Indian Institute of Technology, Kharagpur Lecture  32 Regression Modelling Using SPSS (Refer
More informationbusiness statistics using Excel OXFORD UNIVERSITY PRESS Glyn Davis & Branko Pecar
business statistics using Excel Glyn Davis & Branko Pecar OXFORD UNIVERSITY PRESS Detailed contents Introduction to Microsoft Excel 2003 Overview Learning Objectives 1.1 Introduction to Microsoft Excel
More informationMultivariate Analysis of Variance. The general purpose of multivariate analysis of variance (MANOVA) is to determine
2  Manova 4.3.05 25 Multivariate Analysis of Variance What Multivariate Analysis of Variance is The general purpose of multivariate analysis of variance (MANOVA) is to determine whether multiple levels
More informationSTATISTICA Formula Guide: Logistic Regression. Table of Contents
: Table of Contents... 1 Overview of Model... 1 Dispersion... 2 Parameterization... 3 SigmaRestricted Model... 3 Overparameterized Model... 4 Reference Coding... 4 Model Summary (Summary Tab)... 5 Summary
More information1 2 3 1 1 2 x = + x 2 + x 4 1 0 1
(d) If the vector b is the sum of the four columns of A, write down the complete solution to Ax = b. 1 2 3 1 1 2 x = + x 2 + x 4 1 0 0 1 0 1 2. (11 points) This problem finds the curve y = C + D 2 t which
More informationWhen to Use a Particular Statistical Test
When to Use a Particular Statistical Test Central Tendency Univariate Descriptive Mode the most commonly occurring value 6 people with ages 21, 22, 21, 23, 19, 21  mode = 21 Median the center value the
More informationAnalysis of Variance. MINITAB User s Guide 2 31
3 Analysis of Variance Analysis of Variance Overview, 32 OneWay Analysis of Variance, 35 TwoWay Analysis of Variance, 311 Analysis of Means, 313 Overview of Balanced ANOVA and GLM, 318 Balanced
More informationWednesday PM. Multiple regression. Multiple regression in SPSS. Presentation of AM results Multiple linear regression. Logistic regression
Wednesday PM Presentation of AM results Multiple linear regression Simultaneous Stepwise Hierarchical Logistic regression Multiple regression Multiple regression extends simple linear regression to consider
More informationInferential Statistics. Probability. From Samples to Populations. Katie RommelEsham Education 504
Inferential Statistics Katie RommelEsham Education 504 Probability Probability is the scientific way of stating the degree of confidence we have in predicting something Tossing coins and rolling dice
More informationMATH BOOK OF PROBLEMS SERIES. New from Pearson Custom Publishing!
MATH BOOK OF PROBLEMS SERIES New from Pearson Custom Publishing! The Math Book of Problems Series is a database of math problems for the following courses: Prealgebra Algebra Precalculus Calculus Statistics
More informationCourse Text. Required Computing Software. Course Description. Course Objectives. StraighterLine. Business Statistics
Course Text Business Statistics Lind, Douglas A., Marchal, William A. and Samuel A. Wathen. Basic Statistics for Business and Economics, 7th edition, McGrawHill/Irwin, 2010, ISBN: 9780077384470 [This
More informationStatistical Machine Learning
Statistical Machine Learning UoC Stats 37700, Winter quarter Lecture 4: classical linear and quadratic discriminants. 1 / 25 Linear separation For two classes in R d : simple idea: separate the classes
More informationHow to Use a Monte Carlo Study to Decide on Sample Size and Determine Power
STRUCTURAL EQUATION MODELING, 9(4), 599 620 Copyright 2002, Lawrence Erlbaum Associates, Inc. TEACHER S CORNER How to Use a Monte Carlo Study to Decide on Sample Size and Determine Power Linda K. Muthén
More informationHow To Use A Monte Carlo Study To Decide On Sample Size and Determine Power
How To Use A Monte Carlo Study To Decide On Sample Size and Determine Power Linda K. Muthén Muthén & Muthén 11965 Venice Blvd., Suite 407 Los Angeles, CA 90066 Telephone: (310) 3919971 Fax: (310) 3918971
More informationINTERPRETING THE REPEATEDMEASURES ANOVA
INTERPRETING THE REPEATEDMEASURES ANOVA USING THE SPSS GENERAL LINEAR MODEL PROGRAM RM ANOVA In this scenario (based on a RM ANOVA example from Leech, Barrett, and Morgan, 2005) each of 12 participants
More informationMultivariate Analysis of Variance (MANOVA): I. Theory
Gregory Carey, 1998 MANOVA: I  1 Multivariate Analysis of Variance (MANOVA): I. Theory Introduction The purpose of a t test is to assess the likelihood that the means for two groups are sampled from the
More informationIntroduction to Matrix Algebra
Psychology 7291: Multivariate Statistics (Carey) 8/27/98 Matrix Algebra  1 Introduction to Matrix Algebra Definitions: A matrix is a collection of numbers ordered by rows and columns. It is customary
More informationContents. Gbur, Gregory J. Mathematical methods for optical physics and engineering digitalisiert durch: IDS Basel Bern
Preface page xv 1 Vector algebra 1 1.1 Preliminaries 1 1.2 Coordinate System invariance 4 1.3 Vector multiplication 9 1.4 Useful products of vectors 12 1.5 Linear vector Spaces 13 1.6 Focus: periodic media
More information11/20/2014. Correlational research is used to describe the relationship between two or more naturally occurring variables.
Correlational research is used to describe the relationship between two or more naturally occurring variables. Is age related to political conservativism? Are highly extraverted people less afraid of rejection
More informationOrthogonal Diagonalization of Symmetric Matrices
MATH10212 Linear Algebra Brief lecture notes 57 Gram Schmidt Process enables us to find an orthogonal basis of a subspace. Let u 1,..., u k be a basis of a subspace V of R n. We begin the process of finding
More informationExamples on Variable Selection in PCA in Sensory Descriptive and Consumer Data
Examples on Variable Selection in PCA in Sensory Descriptive and Consumer Data Per Lea, Frank Westad, Margrethe Hersleth MATFORSK, Ås, Norway Harald Martens KVL, Copenhagen, Denmark 6 th Sensometrics Meeting
More informationPrincipal Component Analysis
Principal Component Analysis Principle Component Analysis: A statistical technique used to examine the interrelations among a set of variables in order to identify the underlying structure of those variables.
More informationIntroduction to General and Generalized Linear Models
Introduction to General and Generalized Linear Models General Linear Models  part I Henrik Madsen Poul Thyregod Informatics and Mathematical Modelling Technical University of Denmark DK2800 Kgs. Lyngby
More informationMultivariate Analysis of Variance (MANOVA)
Chapter 415 Multivariate Analysis of Variance (MANOVA) Introduction Multivariate analysis of variance (MANOVA) is an extension of common analysis of variance (ANOVA). In ANOVA, differences among various
More informationAdvanced Algebra 2. I. Equations and Inequalities
Advanced Algebra 2 I. Equations and Inequalities A. Real Numbers and Number Operations 6.A.5, 6.B.5, 7.C.5 1) Graph numbers on a number line 2) Order real numbers 3) Identify properties of real numbers
More informationTutorial for proteome data analysis using the Perseus software platform
Tutorial for proteome data analysis using the Perseus software platform Laboratory of Mass Spectrometry, LNBio, CNPEM Tutorial version 1.0, January 2014. Note: This tutorial was written based on the information
More informationMehtap Ergüven Abstract of Ph.D. Dissertation for the degree of PhD of Engineering in Informatics
INTERNATIONAL BLACK SEA UNIVERSITY COMPUTER TECHNOLOGIES AND ENGINEERING FACULTY ELABORATION OF AN ALGORITHM OF DETECTING TESTS DIMENSIONALITY Mehtap Ergüven Abstract of Ph.D. Dissertation for the degree
More informationUsing Multivariate Statistics
/ K FIFTH EDITION 2008 AGIInformation Management Consultants May be used for personal purporses only or by libraries associated to dandelon.com network. Using Multivariate Statistics Barbara G. Tabachnick
More informationHow to report the percentage of explained common variance in exploratory factor analysis
UNIVERSITAT ROVIRA I VIRGILI How to report the percentage of explained common variance in exploratory factor analysis Tarragona 2013 Please reference this document as: LorenzoSeva, U. (2013). How to report
More informationDATA MINING CLUSTER ANALYSIS: BASIC CONCEPTS
DATA MINING CLUSTER ANALYSIS: BASIC CONCEPTS 1 AND ALGORITHMS Chiara Renso KDDLAB ISTI CNR, Pisa, Italy WHAT IS CLUSTER ANALYSIS? Finding groups of objects such that the objects in a group will be similar
More informationExample: Credit card default, we may be more interested in predicting the probabilty of a default than classifying individuals as default or not.
Statistical Learning: Chapter 4 Classification 4.1 Introduction Supervised learning with a categorical (Qualitative) response Notation:  Feature vector X,  qualitative response Y, taking values in C
More informationMetric Multidimensional Scaling (MDS): Analyzing Distance Matrices
Metric Multidimensional Scaling (MDS): Analyzing Distance Matrices Hervé Abdi 1 1 Overview Metric multidimensional scaling (MDS) transforms a distance matrix into a set of coordinates such that the (Euclidean)
More informationSTUDY GUIDE LINEAR ALGEBRA. David C. Lay University of Maryland College Park AND ITS APPLICATIONS THIRD EDITION UPDATE
STUDY GUIDE LINEAR ALGEBRA AND ITS APPLICATIONS THIRD EDITION UPDATE David C. Lay University of Maryland College Park Copyright 2006 Pearson AddisonWesley. All rights reserved. Reproduced by Pearson AddisonWesley
More informationCanonical Correlation Analysis
Canonical Correlation Analysis Lecture 11 August 4, 2011 Advanced Multivariate Statistical Methods ICPSR Summer Session #2 Lecture #118/4/2011 Slide 1 of 39 Today s Lecture Canonical Correlation Analysis
More informationALGEBRAIC EIGENVALUE PROBLEM
ALGEBRAIC EIGENVALUE PROBLEM BY J. H. WILKINSON, M.A. (Cantab.), Sc.D. Technische Universes! Dsrmstedt FACHBEREICH (NFORMATiK BIBL1OTHEK Sachgebieto:. Standort: CLARENDON PRESS OXFORD 1965 Contents 1.
More information10. Analysis of Longitudinal Studies Repeatmeasures analysis
Research Methods II 99 10. Analysis of Longitudinal Studies Repeatmeasures analysis This chapter builds on the concepts and methods described in Chapters 7 and 8 of Mother and Child Health: Research methods.
More information