Factor Analysis and Structural equation modelling

Size: px
Start display at page:

Download "Factor Analysis and Structural equation modelling"

Transcription

1 Factor Analysis and Structural equation modelling Herman Adèr Previously: Department Clinical Epidemiology and Biostatistics, VU University medical center, Amsterdam Stavanger July 4 13, 2006 Herman Adèr 1

2 Overview 1 E C 2 EFA 3 CFA 4 SEM Exploratory Confirmatory methods Exploratory Factor Analysis Confirmatory Factor Analysis Structural Equation Modelling Herman Adèr 2

3 Overview 1 E C 2 EFA 3 CFA 4 SEM Exploratory Confirmatory methods Exploratory Factor Analysis Confirmatory Factor Analysis Structural Equation Modelling Herman Adèr 2

4 Overview 1 E C 2 EFA 3 CFA 4 SEM Exploratory Confirmatory methods Exploratory Factor Analysis Confirmatory Factor Analysis Structural Equation Modelling Herman Adèr 2

5 Overview 1 E C 2 EFA 3 CFA 4 SEM Exploratory Confirmatory methods Exploratory Factor Analysis Confirmatory Factor Analysis Structural Equation Modelling Herman Adèr 2

6 Overview 1 E C 2 EFA 3 CFA 4 SEM Exploratory Confirmatory methods Exploratory Factor Analysis Confirmatory Factor Analysis Structural Equation Modelling Herman Adèr 2

7 Part VI Factor analysis and Herman Adèr Factor Analysis and SEM 3

8 Detective Judge Herman Adèr Factor Analysis and SEM 5

9 Characterization of Tukey (1977) Exploratory data analysis is detective in character. Confirmatory data analysis is judicial or quasi-judicial in character... Unless the detective finds the clues, judge or jury has nothing to consider. Unless exploratory data analysis uncovers indications, usually quantitative ones, there is likely to be nothing for confirmatory data analysis to consider. On the other hand: Exploratory data analysis can never be the whole story, but nothing else can serve as the foundation stone the first step. Herman Adèr Factor Analysis and SEM 7

10 Characterization of Tukey (1977) Exploratory data analysis is detective in character. Confirmatory data analysis is judicial or quasi-judicial in character... Unless the detective finds the clues, judge or jury has nothing to consider. Unless exploratory data analysis uncovers indications, usually quantitative ones, there is likely to be nothing for confirmatory data analysis to consider. On the other hand: Exploratory data analysis can never be the whole story, but nothing else can serve as the foundation stone the first step. Herman Adèr Factor Analysis and SEM 7

11 Questions and answers Three steps Determining the meaningful factors Rotation Interpretation of the factor structure F = M U E, of which M indicate the meaningful factors, U so-called unique factors (factors on which only one item loads) and E error factors. Questions we try to settle using EFA 1 How many meaningful dimensions are present? 2 What is the structure of those dimensions? Herman Adèr Factor Analysis and SEM 8

12 Questions and answers Three steps Determining the meaningful factors Rotation Interpretation of the factor structure F = M U E, of which M indicate the meaningful factors, U so-called unique factors (factors on which only one item loads) and E error factors. Questions we try to settle using EFA 1 How many meaningful dimensions are present? 2 What is the structure of those dimensions? Herman Adèr Factor Analysis and SEM 8

13 Questions and answers Three steps Determining the meaningful factors Rotation Interpretation of the factor structure Data set: { } D = Subject Items Exploratory Factor Analysis factor structure determine meaningful factors unrotated Three steps 1 Determine the meaningful factors rotate factor structure k meaningful factors 2 Rotate 3 Interpret the factor structure determine factor meaning final factor solution Herman Adèr Factor Analysis and SEM 9

14 Questions and answers Three steps Determining the meaningful factors Rotation Interpretation of the factor structure determine meaningful factors: scree plot eigenvalues larger than 1 GoF change significant between solutions total variance explained more than 50% select factors with intelligible loading patterns and name them communalities reliabilities doubtful Herman Adèr Factor Analysis and SEM 10

15 Questions and answers Three steps Determining the meaningful factors Rotation Interpretation of the factor structure CES-D: A multidimensional scale to assess Depression FACTOR /VARIABLES cesd1 cesd2 cesd3 cesd4 cesd5 cesd6 cesd7 cesd8 cesd9 cesd10 cesd11 cesd12 cesd13 cesd14 cesd15 cesd16 cesd17 cesd18 cesd19 cesd20 /MISSING LISTWISE /ANALYSIS cesd1 cesd2 cesd3 cesd4 cesd5 cesd6 cesd7 cesd8 cesd9 cesd10 cesd11 cesd12 cesd13 cesd14 cesd15 cesd16 cesd17 cesd18 cesd19 cesd20 /PRINT all /FORMAT BLANK(.30) /PLOT EIGEN /CRITERIA MINEIGEN(0) ITERATE(100) factors(3) /EXTRACTION pc /ROTATION norotate. Herman Adèr Factor Analysis and SEM 12

16 Questions and answers Three steps Determining the meaningful factors Rotation Interpretation of the factor structure CES-D: A multidimensional scale to assess Depression FACTOR /VARIABLES cesd1 cesd2 cesd3 cesd4 cesd5 cesd6 cesd7 cesd8 cesd9 cesd10 cesd11 cesd12 cesd13 cesd14 cesd15 cesd16 cesd17 cesd18 cesd19 cesd20 /MISSING LISTWISE /ANALYSIS cesd1 cesd2 cesd3 cesd4 cesd5 cesd6 cesd7 cesd8 cesd9 cesd10 cesd11 cesd12 cesd13 cesd14 cesd15 cesd16 cesd17 cesd18 cesd19 cesd20 /PRINT all /FORMAT BLANK(.30) /PLOT EIGEN /CRITERIA MINEIGEN(0) ITERATE(100) factors(3) /EXTRACTION pc /ROTATION norotate. Herman Adèr Factor Analysis and SEM 12

17 Questions and answers Three steps Determining the meaningful factors Rotation Interpretation of the factor structure 10 Scree Plot Eigenvalue Component Number Herman Adèr Factor Analysis and SEM 13

18 Questions and answers Three steps Determining the meaningful factors Rotation Interpretation of the factor structure Component Initial Eigenvalues Total % of Variance Cumulative % Extraction Method: Principal Component Analysis. Herman Adèr Factor Analysis and SEM 14

19 Questions and answers Three steps Determining the meaningful factors Rotation Interpretation of the factor structure Interpretation of the unrotated factor structure Component CESD CESD CESD CESD CESD CESD6 CESD CESD CESD CESD CESD CESD CESD CESD CESD CESD CESD CESD CESD CESD Extraction Method: Principal Component Analysis. Herman Adèr Factor Analysis and SEM 15

20 Questions and answers Three steps Determining the meaningful factors Rotation Interpretation of the factor structure Communalities: four factors and all factors Communalities Initial Extraction CESD CESD CESD CESD CESD CESD CESD CESD CESD CESD CESD CESD CESD CESD CESD CESD CESD CESD CESD CESD Extraction Method: Principal Component Analysis. Communalities Initial Extraction CESD CESD CESD CESD CESD CESD CESD CESD CESD CESD CESD CESD CESD CESD CESD CESD CESD CESD CESD CESD Extraction Method: Principal Component Analysis. Herman Adèr Factor Analysis and SEM 16

21 Questions and answers Three steps Determining the meaningful factors Rotation Interpretation of the factor structure Communalities: two and three factors Communalities Initial Extraction CESD CESD E-02 CESD CESD CESD CESD CESD CESD CESD CESD CESD CESD CESD CESD CESD CESD CESD CESD CESD CESD Extraction Method: Principal Component Analysis. Communalities Initial Extraction CESD CESD CESD CESD CESD CESD CESD CESD CESD CESD CESD CESD CESD CESD CESD CESD CESD CESD CESD CESD Extraction Method: Principal Component Analysis. Herman Adèr Factor Analysis and SEM 17

22 Questions and answers Three steps Determining the meaningful factors Rotation Interpretation of the factor structure Goodness-of-fit criterium # Facts GoF χ 2 Df χ 2 change Df χ 2 α= As one can see by comparing the 0.05 threshold χ 2 in the last column Herman Adèr Factor Analysis and SEM 18

23 Questions and answers Three steps Determining the meaningful factors Rotation Interpretation of the factor structure Unrotated Rotated Factor Factor Item I II III I II III CESD CESD CESD CESD04 + CESD CESD CESD CESD08 + CESD CESD CESD CESD12 + CESD CESD CESD CESD16 + CESD CESD CESD CESD Herman Adèr Factor Analysis and SEM 19

24 Questions and answers Three steps Determining the meaningful factors Rotation Interpretation of the factor structure Interpretation of table I Unrotated Rotated Factor Factor Item I II III I II III CESD CESD CESD CESD04 + CESD CESD CESD CESD08 + CESD CESD CESD CESD12 + CESD CESD CESD CESD16 + CESD CESD CESD CESD All items with high positive loadings on the unrotated Factor I still load on this factor after rotation, but some of them (5, 6, 7, 9, 17, 18 and 20) also load on factor II. This makes that Factor I is now separated into two sublists, of which the above could be called the pure depression scale while (1, 3, 10, 11, 13, 14, 15, 19) includes a sublist indicating less severe symptoms of depression. Herman Adèr Factor Analysis and SEM 20

25 Questions and answers Three steps Determining the meaningful factors Rotation Interpretation of the factor structure Interpretation of table II Unrotated Rotated Factor Factor Item I II III I II III CESD CESD CESD CESD04 + CESD CESD CESD CESD08 + CESD CESD CESD CESD12 + CESD CESD CESD CESD16 + CESD CESD CESD CESD Factor II now also contains all the items that loaded negatively on Factor I before (4, 8, 12 and 16). We called this a factor that measures: general attitude towards life. Herman Adèr Factor Analysis and SEM 21

26 Questions and answers Three steps Determining the meaningful factors Rotation Interpretation of the factor structure Interpretation of table III Unrotated Rotated Factor Factor Item I II III I II III CESD CESD CESD CESD04 + CESD CESD CESD CESD08 + CESD CESD CESD CESD12 + CESD CESD CESD CESD16 + CESD CESD CESD CESD After rotation, Factor III now contains only item 2 ( I did not feel like eating: my appetite was poor ) and item 11 ( My sleep was restless ), suggesting that it is a factor that has to do with physical aspects of depression. Herman Adèr Factor Analysis and SEM 22

27 Example of EQS input Example of EQS input Conclusions of EFA and CFA combined Example of EQS input /TITLE Cesd; /SPECIFICATIONS VARIABLES=6; CASES= 200; DATAFILE= cesd.ess ; MATRIX=RAW; ME = ML; /EQUATIONS V1 = 2 * F1 + E1; V2 = 2 * F1 + E2; V3 = 2 * F2 + E3; V4 = 2 * F2 + E4; V5 = 2 * F3 + E5; V6 = 2 * F3 + E6; F1 = 2 * F2 + 2*F3+ D1; /VARIANCES E1 to E10 = 0.2*; D1, D2, D3 = 0.2*; /COVARIANCES F2,F3 =.5*; /END Herman Adèr Factor Analysis and SEM 23

28 Example of EQS input Example of EQS input Conclusions of EFA and CFA combined CES-D: Conclusions of the CFA The varimax solution is not fully confirmed: item 5, 6, 7, 18 and 20 have negligible coefficients on the second factor. The assumption of a orthogonal factor structure is unfounded: The correlations between the factors are (F1, F2) = 0.241; (F1, F3) = and (F2, F3) = Herman Adèr Factor Analysis and SEM 24

29 Example of EQS input Example of EQS input Conclusions of EFA and CFA combined CES-D: Conclusions of the CFA The varimax solution is not fully confirmed: item 5, 6, 7, 18 and 20 have negligible coefficients on the second factor. The assumption of a orthogonal factor structure is unfounded: The correlations between the factors are (F1, F2) = 0.241; (F1, F3) = and (F2, F3) = Herman Adèr Factor Analysis and SEM 24

30 Example of EQS input Example of EQS input Conclusions of EFA and CFA combined Conclusions of EFA and CFA combined 1 The first factor is a general depression factor (item 1, 3, 5, 6, 7, 10, 13, 14, 15, 18, 19 and 20) 2 The second factor contains the positively formulated items (4, 8, 9, 12, 16, 17). It represents a general attitude towards life. 3 The third factor contains items that have to do with physical aspects of depression. Herman Adèr Factor Analysis and SEM 25

31 Example: Post-traumatic stress disorder Example of a postulated structure Draw pictures! Herman Adèr Factor Analysis and SEM 26

32 Example: Post-traumatic stress disorder Example of a postulated structure Draw pictures! Herman Adèr Factor Analysis and SEM 26

33 Example: Post-traumatic stress disorder Example of a postulated structure Draw pictures! Herman Adèr Factor Analysis and SEM 26

34 Postulated structure Structure found Herman Adèr Factor Analysis and SEM 27

35 Recommended literature Factor analysis: Friendly (1995) (http://www.psych.yorku.ca/lab/psy6140/fa/factorbi.htm) Principal component analysis: Jackson (1991) : Bollen (1989), Kaplan (2000) Herman Adèr Factor Analysis and SEM 28

36 Summary Herman Adèr Factor Analysis and SEM 29

37 Summary In factor analysis the contrast between exploratory and confirmatory approaches is quite clear: the available techniques are different although related. can well be performed with principal component analysis, possibly combined with Maximum likelihood factor analysis. PCA is first used to determine the meaningful factors, MLFA for the final factor structure. Structural Equation Modelling makes it possible to analyze a research problem that has been represented as a diagram. Herman Adèr Factor Analysis and SEM 30

38 Bollen, K. A. (1989). Structural equations with latent variables. New York: John Wiley and Sons. Friendly, M. (1995). Annotated Factor Analysis Bibliography. Jackson, J. E. (1991). A user s guide to principal components. New York: Wiley. Kaplan, D. (2000). Structural Equation Modeling. Foundations and Extensions. Thousand Oaks London New Delhi: Sage Publications. Tukey, J. W. (1977). Exploratory data analysis. Reading, MA: Addison Wesley. Herman Adèr Factor Analysis and SEM 31

Overview of Factor Analysis

Overview of Factor Analysis Overview of Factor Analysis Jamie DeCoster Department of Psychology University of Alabama 348 Gordon Palmer Hall Box 870348 Tuscaloosa, AL 35487-0348 Phone: (205) 348-4431 Fax: (205) 348-8648 August 1,

More information

FACTOR ANALYSIS EXPLORATORY APPROACHES. Kristofer Årestedt

FACTOR ANALYSIS EXPLORATORY APPROACHES. Kristofer Årestedt FACTOR ANALYSIS EXPLORATORY APPROACHES Kristofer Årestedt 2013-04-28 UNIDIMENSIONALITY Unidimensionality imply that a set of items forming an instrument measure one thing in common Unidimensionality is

More information

Rachel J. Goldberg, Guideline Research/Atlanta, Inc., Duluth, GA

Rachel J. Goldberg, Guideline Research/Atlanta, Inc., Duluth, GA PROC FACTOR: How to Interpret the Output of a Real-World Example Rachel J. Goldberg, Guideline Research/Atlanta, Inc., Duluth, GA ABSTRACT THE METHOD This paper summarizes a real-world example of a factor

More information

Doing Quantitative Research 26E02900, 6 ECTS Lecture 2: Measurement Scales. Olli-Pekka Kauppila Rilana Riikkinen

Doing Quantitative Research 26E02900, 6 ECTS Lecture 2: Measurement Scales. Olli-Pekka Kauppila Rilana Riikkinen Doing Quantitative Research 26E02900, 6 ECTS Lecture 2: Measurement Scales Olli-Pekka Kauppila Rilana Riikkinen Learning Objectives 1. Develop the ability to assess a quality of measurement instruments

More information

Factor 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 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 information

A Brief Introduction to SPSS Factor Analysis

A Brief Introduction to SPSS Factor Analysis A Brief Introduction to SPSS Factor Analysis SPSS has a procedure that conducts exploratory factor analysis. Before launching into a step by step example of how to use this procedure, it is recommended

More information

Chapter 7 Factor Analysis SPSS

Chapter 7 Factor Analysis SPSS Chapter 7 Factor Analysis SPSS Factor analysis attempts to identify underlying variables, or factors, that explain the pattern of correlations within a set of observed variables. Factor analysis is often

More information

Common factor analysis

Common 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 information

Factor Analysis. Advanced Financial Accounting II Åbo Akademi School of Business

Factor Analysis. Advanced Financial Accounting II Åbo Akademi School of Business Factor Analysis Advanced Financial Accounting II Åbo Akademi School of Business Factor analysis A statistical method used to describe variability among observed variables in terms of fewer unobserved variables

More information

Introduction to Principal Components and FactorAnalysis

Introduction 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 information

T-test & factor analysis

T-test & factor analysis Parametric tests T-test & factor analysis Better than non parametric tests Stringent assumptions More strings attached Assumes population distribution of sample is normal Major problem Alternatives Continue

More information

Exploratory Factor Analysis

Exploratory Factor Analysis Exploratory Factor Analysis ( 探 索 的 因 子 分 析 ) Yasuyo Sawaki Waseda University JLTA2011 Workshop Momoyama Gakuin University October 28, 2011 1 Today s schedule Part 1: EFA basics Introduction to factor

More information

An introduction to. Principal Component Analysis & Factor Analysis. Using SPSS 19 and R (psych package) Robin Beaumont robin@organplayers.co.

An introduction to. Principal Component Analysis & Factor Analysis. Using SPSS 19 and R (psych package) Robin Beaumont robin@organplayers.co. An introduction to Principal Component Analysis & Factor Analysis Using SPSS 19 and R (psych package) Robin Beaumont robin@organplayers.co.uk Monday, 23 April 2012 Acknowledgment: The original version

More information

To do a factor analysis, we need to select an extraction method and a rotation method. Hit the Extraction button to specify your extraction method.

To do a factor analysis, we need to select an extraction method and a rotation method. Hit the Extraction button to specify your extraction method. Factor Analysis in SPSS To conduct a Factor Analysis, start from the Analyze menu. This procedure is intended to reduce the complexity in a set of data, so we choose Data Reduction from the menu. And the

More information

5.2 Customers Types for Grocery Shopping Scenario

5.2 Customers Types for Grocery Shopping Scenario ------------------------------------------------------------------------------------------------------- CHAPTER 5: RESULTS AND ANALYSIS -------------------------------------------------------------------------------------------------------

More information

Factor Analysis Using SPSS

Factor Analysis Using SPSS Psychology 305 p. 1 Factor Analysis Using SPSS Overview For this computer assignment, you will conduct a series of principal factor analyses to examine the factor structure of a new instrument developed

More information

Applications of Structural Equation Modeling in Social Sciences Research

Applications of Structural Equation Modeling in Social Sciences Research American International Journal of Contemporary Research Vol. 4 No. 1; January 2014 Applications of Structural Equation Modeling in Social Sciences Research Jackson de Carvalho, PhD Assistant Professor

More information

CHAPTER 4 EXAMPLES: EXPLORATORY FACTOR ANALYSIS

CHAPTER 4 EXAMPLES: EXPLORATORY FACTOR ANALYSIS Examples: Exploratory Factor Analysis CHAPTER 4 EXAMPLES: EXPLORATORY FACTOR ANALYSIS Exploratory factor analysis (EFA) is used to determine the number of continuous latent variables that are needed to

More information

FACTOR ANALYSIS. Factor Analysis is similar to PCA in that it is a technique for studying the interrelationships among variables.

FACTOR ANALYSIS. Factor Analysis is similar to PCA in that it is a technique for studying the interrelationships among variables. FACTOR ANALYSIS Introduction Factor Analysis is similar to PCA in that it is a technique for studying the interrelationships among variables Both methods differ from regression in that they don t have

More information

Factor Analysis. Sample StatFolio: factor analysis.sgp

Factor Analysis. Sample StatFolio: factor analysis.sgp STATGRAPHICS Rev. 1/10/005 Factor Analysis Summary The Factor Analysis procedure is designed to extract m common factors from a set of p quantitative variables X. In many situations, a small number of

More information

Exploratory Factor Analysis of Demographic Characteristics of Antenatal Clinic Attendees and their Association with HIV Risk

Exploratory Factor Analysis of Demographic Characteristics of Antenatal Clinic Attendees and their Association with HIV Risk Doi:10.5901/mjss.2014.v5n20p303 Abstract Exploratory Factor Analysis of Demographic Characteristics of Antenatal Clinic Attendees and their Association with HIV Risk Wilbert Sibanda Philip D. Pretorius

More information

Lecture 7: Factor Analysis. Laura McAvinue School of Psychology Trinity College Dublin

Lecture 7: Factor Analysis. Laura McAvinue School of Psychology Trinity College Dublin Lecture 7: Factor Analysis Laura McAvinue School of Psychology Trinity College Dublin The Relationship between Variables Previous lectures Correlation Measure of strength of association between two variables

More information

Research Methodology: Tools

Research Methodology: Tools MSc Business Administration Research Methodology: Tools Applied Data Analysis (with SPSS) Lecture 02: Item Analysis / Scale Analysis / Factor Analysis February 2014 Prof. Dr. Jürg Schwarz Lic. phil. Heidi

More information

Social Media Marketing Management 社 會 媒 體 行 銷 管 理 確 認 性 因 素 分 析. (Confirmatory Factor Analysis) 1002SMMM12 TLMXJ1A Tue 12,13,14 (19:20-22:10) D325

Social Media Marketing Management 社 會 媒 體 行 銷 管 理 確 認 性 因 素 分 析. (Confirmatory Factor Analysis) 1002SMMM12 TLMXJ1A Tue 12,13,14 (19:20-22:10) D325 Social Media Marketing Management 社 會 媒 體 行 銷 管 理 確 認 性 因 素 分 析 (Confirmatory Factor Analysis) 1002SMMM12 TLMXJ1A Tue 12,13,14 (19:20-22:10) D325 Min-Yuh Day 戴 敏 育 Assistant Professor 專 任 助 理 教 授 Dept.

More information

Principal Component Analysis

Principal 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 information

PRINCIPAL COMPONENT ANALYSIS

PRINCIPAL COMPONENT ANALYSIS 1 Chapter 1 PRINCIPAL COMPONENT ANALYSIS Introduction: The Basics of Principal Component Analysis........................... 2 A Variable Reduction Procedure.......................................... 2

More information

A Brief Introduction to Factor Analysis

A Brief Introduction to Factor Analysis 1. Introduction A Brief Introduction to Factor Analysis Factor analysis attempts to represent a set of observed variables X 1, X 2. X n in terms of a number of 'common' factors plus a factor which is unique

More information

Factor Analysis Example: SAS program (in blue) and output (in black) interleaved with comments (in red)

Factor Analysis Example: SAS program (in blue) and output (in black) interleaved with comments (in red) Factor Analysis Example: SAS program (in blue) and output (in black) interleaved with comments (in red) The following DATA procedure is to read input data. This will create a SAS dataset named CORRMATR

More information

Current Topics in Statistics for Applied Researchers Factor Analysis

Current Topics in Statistics for Applied Researchers Factor Analysis Current Topics in Statistics for Applied Researchers Factor Analysis George J. Knafl, PhD Professor & Senior Scientist knaflg@ohsu.edu Purpose to describe and demonstrate factor analysis of survey instrument

More information

CFA/SEM Using Stata. Basic CFA/SEM Syntax Using Stata:

CFA/SEM Using Stata. Basic CFA/SEM Syntax Using Stata: CFA/SEM Using Stata Five Main Points: 1. Basics of Stata CFA/SEM syntax 2. One Factor CFA 3. Two Factor CFA 4. Structural Equation Modeling 5. A little bit of cross-group invariance To begin, we should

More information

What is Rotating in Exploratory Factor Analysis?

What is Rotating in Exploratory Factor Analysis? A peer-reviewed electronic journal. Copyright is retained by the first or sole author, who grants right of first publication to the Practical Assessment, Research & Evaluation. Permission is granted to

More information

MULTIVARIATE DATA ANALYSIS i.-*.'.. ' -4

MULTIVARIATE 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 information

Partial Least Squares (PLS) Regression.

Partial Least Squares (PLS) Regression. Partial Least Squares (PLS) Regression. Hervé Abdi 1 The University of Texas at Dallas Introduction Pls regression is a recent technique that generalizes and combines features from principal component

More information

The president of a Fortune 500 firm wants to measure the firm s image.

The president of a Fortune 500 firm wants to measure the firm s image. 4. Factor Analysis A related method to the PCA is the Factor Analysis (FA) with the crucial difference that in FA a statistical model is constructed to explain the interrelations (correlations) between

More information

Exploratory Factor Analysis

Exploratory Factor Analysis Introduction Principal components: explain many variables using few new variables. Not many assumptions attached. Exploratory Factor Analysis Exploratory factor analysis: similar idea, but based on model.

More information

Constructing Indices and Scales. Hsueh-Sheng Wu CFDR Workshop Series Summer 2012

Constructing Indices and Scales. Hsueh-Sheng Wu CFDR Workshop Series Summer 2012 Constructing Indices and Scales Hsueh-Sheng Wu CFDR Workshop Series Summer 2012 1 Outline What are scales and indices? Graphical presentation of relations between items and constructs for scales and indices

More information

Part 2: EFA Outline. Exploratory and Confirmatory Factor Analysis. Basic Ideas of Factor Analysis. Basic ideas: 1. Linear regression on common factors

Part 2: EFA Outline. Exploratory and Confirmatory Factor Analysis. Basic Ideas of Factor Analysis. Basic ideas: 1. Linear regression on common factors Exploratory and Confirmatory Factor Analysis Michael Friendly Feb. 25, Mar. 3, 10, 2008 SCS Short Course web notes: http://www.math.yorku.ca/scs/courses/factor/ Part 2: EFA Outline 1 Linear regression

More information

Factor Analysis. Chapter 420. Introduction

Factor 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 information

Running head: ONLINE VALUE AND SELF-EFFICACY SCALE

Running head: ONLINE VALUE AND SELF-EFFICACY SCALE Online Value and Self-Efficacy Scale Running head: ONLINE VALUE AND SELF-EFFICACY SCALE Development and Initial Validation of the Online Learning Value and Self-Efficacy Scale Anthony R. Artino Jr. and

More information

Exploratory Factor Analysis and Principal Components. Pekka Malo & Anton Frantsev 30E00500 Quantitative Empirical Research Spring 2016

Exploratory Factor Analysis and Principal Components. Pekka Malo & Anton Frantsev 30E00500 Quantitative Empirical Research Spring 2016 and Principal Components Pekka Malo & Anton Frantsev 30E00500 Quantitative Empirical Research Spring 2016 Agenda Brief History and Introductory Example Factor Model Factor Equation Estimation of Loadings

More information

4. There are no dependent variables specified... Instead, the model is: VAR 1. Or, in terms of basic measurement theory, we could model it as:

4. There are no dependent variables specified... Instead, the model is: VAR 1. Or, in terms of basic measurement theory, we could model it as: 1 Neuendorf Factor Analysis Assumptions: 1. Metric (interval/ratio) data 2. Linearity (in the relationships among the variables--factors are linear constructions of the set of variables; the critical source

More information

Using Principal Components Analysis in Program Evaluation: Some Practical Considerations

Using Principal Components Analysis in Program Evaluation: Some Practical Considerations http://evaluation.wmich.edu/jmde/ Articles Using Principal Components Analysis in Program Evaluation: Some Practical Considerations J. Thomas Kellow Assistant Professor of Research and Statistics Mercer

More information

Statistics in Psychosocial Research Lecture 8 Factor Analysis I. Lecturer: Elizabeth Garrett-Mayer

Statistics in Psychosocial Research Lecture 8 Factor Analysis I. Lecturer: Elizabeth Garrett-Mayer This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike License. Your use of this material constitutes acceptance of that license and the conditions of use of materials on this

More information

Principal Components Analysis (PCA)

Principal 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 information

Principal Component Analysis

Principal Component Analysis Principal Component Analysis ERS70D George Fernandez INTRODUCTION Analysis of multivariate data plays a key role in data analysis. Multivariate data consists of many different attributes or variables recorded

More information

Multivariate Analysis

Multivariate Analysis Table Of Contents Multivariate Analysis... 1 Overview... 1 Principal Components... 2 Factor Analysis... 5 Cluster Observations... 12 Cluster Variables... 17 Cluster K-Means... 20 Discriminant Analysis...

More information

O n g o i n g D i s c u s s i o n

O n g o i n g D i s c u s s i o n O n g o i n g D i s c u s s i o n Université de Genève, Switzerland Abstract: Utilisation of structural equations with latent variables is one promising strategy for social representation theory development.

More information

Tjalling C. Koopmans Research Institute

Tjalling C. Koopmans Research Institute Tjalling C. Koopmans Research Institute Tjalling C. Koopmans Research Institute Utrecht School of Economics Utrecht University Kriekenpitplein 21-22 3584 TC Utrecht The Netherlands telephone +31 30 253

More information

Introduction to Confirmatory Factor Analysis and Structural Equation Modeling

Introduction to Confirmatory Factor Analysis and Structural Equation Modeling Introduction to Confirmatory Factor Analysis and Structural Equation Modeling Lecture 12 August 7, 2011 Advanced Multivariate Statistical Methods ICPSR Summer Session #2 Today s Class An Introduction to:

More information

USEFULNESS AND BENEFITS OF E-BANKING / INTERNET BANKING SERVICES

USEFULNESS AND BENEFITS OF E-BANKING / INTERNET BANKING SERVICES CHAPTER 6 USEFULNESS AND BENEFITS OF E-BANKING / INTERNET BANKING SERVICES 6.1 Introduction In the previous two chapters, bank customers adoption of e-banking / internet banking services and functional

More information

Questionnaire Evaluation with Factor Analysis and Cronbach s Alpha An Example

Questionnaire Evaluation with Factor Analysis and Cronbach s Alpha An Example Questionnaire Evaluation with Factor Analysis and Cronbach s Alpha An Example - Melanie Hof - 1. Introduction The pleasure writers experience in writing considerably influences their motivation and consequently

More information

Exploratory Factor Analysis

Exploratory Factor Analysis Exploratory Factor Analysis Definition Exploratory factor analysis (EFA) is a procedure for learning the extent to which k observed variables might measure m abstract variables, wherein m is less than

More information

Table of Contents. Abstract. Abstrak. Publications. Acknowledgement. List of Tables. List of Figures. List of Abbreviations

Table of Contents. Abstract. Abstrak. Publications. Acknowledgement. List of Tables. List of Figures. List of Abbreviations Table of Contents Abstract Abstrak Publications Acknowledgement List of Tables List of Figures Appendix List of Abbreviations i ii iii iv x xii xiii xiii CHAPTER 1 BACKGROUND TO THE STUDY 1.1 Introduction

More information

Exploratory Factor Analysis Brian Habing - University of South Carolina - October 15, 2003

Exploratory Factor Analysis Brian Habing - University of South Carolina - October 15, 2003 Exploratory Factor Analysis Brian Habing - University of South Carolina - October 15, 2003 FA is not worth the time necessary to understand it and carry it out. -Hills, 1977 Factor analysis should not

More information

Getting Started in Factor Analysis (using Stata 10) (ver. 1.5)

Getting Started in Factor Analysis (using Stata 10) (ver. 1.5) Getting Started in Factor Analysis (using Stata 10) (ver. 1.5) Oscar Torres-Reyna Data Consultant otorres@princeton.edu http://dss.princeton.edu/training/ Factor analysis is used mostly for data reduction

More information

CUNNINGHAM, Everarda G and WANG, Wei C Swinburne University of Technology Australia

CUNNINGHAM, Everarda G and WANG, Wei C Swinburne University of Technology Australia USING AMOS GRAPHICS TO ENHANCE THE UNDERSTANDING AND COMMUNICATION OF MULTIPLE REGRESSION CUNNINGHAM, Everarda G and WANG, Wei C Swinburne University of Technology Australia Support for the saying a picture

More information

FACTOR ANALYSIS NASC

FACTOR ANALYSIS NASC FACTOR ANALYSIS NASC Factor Analysis A data reduction technique designed to represent a wide range of attributes on a smaller number of dimensions. Aim is to identify groups of variables which are relatively

More information

Effectiveness of Performance Appraisal: Its Outcomes and Detriments in Pakistani Organizations

Effectiveness of Performance Appraisal: Its Outcomes and Detriments in Pakistani Organizations Effectiveness of Performance Appraisal: Its Outcomes and Detriments in Pakistani Organizations Hafiz Muhammad Ishaq Federal Urdu University of Arts, Science and Technology, Islamabad, Pakistan E-mail:

More information

SPSS and AMOS. Miss Brenda Lee 2:00p.m. 6:00p.m. 24 th July, 2015 The Open University of Hong Kong

SPSS and AMOS. Miss Brenda Lee 2:00p.m. 6:00p.m. 24 th July, 2015 The Open University of Hong Kong Seminar on Quantitative Data Analysis: SPSS and AMOS Miss Brenda Lee 2:00p.m. 6:00p.m. 24 th July, 2015 The Open University of Hong Kong SBAS (Hong Kong) Ltd. All Rights Reserved. 1 Agenda MANOVA, Repeated

More information

Factor Analysis: Statnotes, from North Carolina State University, Public Administration Program. Factor Analysis

Factor Analysis: Statnotes, from North Carolina State University, Public Administration Program. Factor Analysis Factor Analysis Overview Factor analysis is used to uncover the latent structure (dimensions) of a set of variables. It reduces attribute space from a larger number of variables to a smaller number of

More information

Rockefeller College University at Albany

Rockefeller College University at Albany Rockefeller College University at Albany PAD 705 Handout: Throughout this course, I have emphasized that statistical analysis is part science, part art. Our final topic, factor analysis, strays the farthest

More information

Factor analysis. Angela Montanari

Factor analysis. Angela Montanari Factor analysis Angela Montanari 1 Introduction Factor analysis is a statistical model that allows to explain the correlations between a large number of observed correlated variables through a small number

More information

2. Linearity (in relationships among the variables--factors are linear constructions of the set of variables) F 2 X 4 U 4

2. Linearity (in relationships among the variables--factors are linear constructions of the set of variables) F 2 X 4 U 4 1 Neuendorf Factor Analysis Assumptions: 1. Metric (interval/ratio) data. Linearity (in relationships among the variables--factors are linear constructions of the set of variables) 3. Univariate and multivariate

More information

Data analysis process

Data 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 information

Psychology 7291, Multivariate Analysis, Spring 2003. SAS PROC FACTOR: Suggestions on Use

Psychology 7291, Multivariate Analysis, Spring 2003. SAS PROC FACTOR: Suggestions on Use : Suggestions on Use Background: Factor analysis requires several arbitrary decisions. The choices you make are the options that you must insert in the following SAS statements: PROC FACTOR METHOD=????

More information

CHAPTER V ANALYSIS & INTERPRETATION

CHAPTER V ANALYSIS & INTERPRETATION CHAPTER V ANALYSIS & INTERPRETATION In this chapter the analysis of the data collected based on the frame of reference of this thesis is presented. First the empirical analysis of the proposed theoretical

More information

I n d i a n a U n i v e r s i t y U n i v e r s i t y I n f o r m a t i o n T e c h n o l o g y S e r v i c e s

I n d i a n a U n i v e r s i t y U n i v e r s i t y I n f o r m a t i o n T e c h n o l o g y S e r v i c e s I n d i a n a U n i v e r s i t y U n i v e r s i t y I n f o r m a t i o n T e c h n o l o g y S e r v i c e s Confirmatory Factor Analysis using Amos, LISREL, Mplus, SAS/STAT CALIS* Jeremy J. Albright

More information

Brief report: Intimacy, passion, and commitment in romantic relationships Validation of a triangular love scale for adolescents $

Brief report: Intimacy, passion, and commitment in romantic relationships Validation of a triangular love scale for adolescents $ Journal of Adolescence Journal of Adolescence 30 (2007) 523 528 www.elsevier.com/locate/jado Brief report: Intimacy, passion, and commitment in romantic relationships Validation of a triangular love scale

More information

Understanding and Using Factor Scores: Considerations for the Applied Researcher

Understanding and Using Factor Scores: Considerations for the Applied Researcher A peer-reviewed electronic journal. Copyright is retained by the first or sole author, who grants right of first publication to the Practical Assessment, Research & Evaluation. Permission is granted to

More information

Structural Equation Modelling (SEM)

Structural Equation Modelling (SEM) (SEM) Aims and Objectives By the end of this seminar you should: Have a working knowledge of the principles behind causality. Understand the basic steps to building a Model of the phenomenon of interest.

More information

FEATURE. Abstract. Introduction. Background

FEATURE. Abstract. Introduction. Background FEATURE From Data to Information: Using Factor Analysis with Survey Data Ronald D. Fricker, Jr., Walter W. Kulzy, and Jeffrey A. Appleget, Naval Postgraduate School; rdfricker@nps.edu Abstract In irregular

More information

Topic 10: Factor Analysis

Topic 10: Factor Analysis Topic 10: Factor Analysis Introduction Factor analysis is a statistical method used to describe variability among observed variables in terms of a potentially lower number of unobserved variables called

More information

About Me (Reynolds Child Depression Scale) Grade 3 / Year 4 Fast Track Project Technical Report Stephanie Little & Grace Yan Fang December, 2000

About Me (Reynolds Child Depression Scale) Grade 3 / Year 4 Fast Track Project Technical Report Stephanie Little & Grace Yan Fang December, 2000 About Me (Reynolds Child Depression Scale) Grade 3 / Year 4 Fast Track Project Technical Report Stephanie Little & Grace Yan Fang December, 2000 Table of Contents: I. Introduction II. Report Sample and

More information

Factor analysis and Concurrent Validity of a University Counseling Center Presenting Problems Checklist

Factor analysis and Concurrent Validity of a University Counseling Center Presenting Problems Checklist A RESEARCH REPORT OF THE RESEARCH CONSORTIUM OF COUNSELING & PSYCHOLOGICAL SERVICES IN HIGHER EDUCATION Factor analysis and Concurrent Validity of a University Counseling Center Presenting Problems Checklist

More information

How to report the percentage of explained common variance in exploratory factor analysis

How 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: Lorenzo-Seva, U. (2013). How to report

More information

EXPLORATORY FACTOR ANALYSIS IN MPLUS, R AND SPSS. sigbert@wiwi.hu-berlin.de

EXPLORATORY FACTOR ANALYSIS IN MPLUS, R AND SPSS. sigbert@wiwi.hu-berlin.de EXPLORATORY FACTOR ANALYSIS IN MPLUS, R AND SPSS Sigbert Klinke 1,2 Andrija Mihoci 1,3 and Wolfgang Härdle 1,3 1 School of Business and Economics, Humboldt-Universität zu Berlin, Germany 2 Department of

More information

What Are Principal Components Analysis and Exploratory Factor Analysis?

What Are Principal Components Analysis and Exploratory Factor Analysis? Statistics Corner Questions and answers about language testing statistics: Principal components analysis and exploratory factor analysis Definitions, differences, and choices James Dean Brown University

More information

Confirmatory factor analysis in MPlus

Confirmatory factor analysis in MPlus Jan Štochl, Ph.D. Department of Psychiatry University of Cambridge Email: js883@cam.ac.uk Confirmatory factor analysis in MPlus The Psychometrics Centre Agenda of day 1 General ideas and introduction to

More information

Factor Analysis. Factor Analysis

Factor Analysis. Factor Analysis Factor Analysis Principal Components Analysis, e.g. of stock price movements, sometimes suggests that several variables may be responding to a small number of underlying forces. In the factor model, we

More information

SPSS ADVANCED ANALYSIS WENDIANN SETHI SPRING 2011

SPSS 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 information

Hatice Camgöz Akdağ. findings of previous research in which two independent firm clusters were

Hatice Camgöz Akdağ. findings of previous research in which two independent firm clusters were Innovative Culture and Total Quality Management as a Tool for Sustainable Competitiveness: A Case Study of Turkish Fruit and Vegetable Processing Industry SMEs, Sedef Akgüngör Hatice Camgöz Akdağ Aslı

More information

The Effectiveness of Ethics Program among Malaysian Companies

The Effectiveness of Ethics Program among Malaysian Companies 2011 2 nd International Conference on Economics, Business and Management IPEDR vol.22 (2011) (2011) IACSIT Press, Singapore The Effectiveness of Ethics Program among Malaysian Companies Rabiatul Alawiyah

More information

Part III. Item-Level Analysis

Part III. Item-Level Analysis Part III Item-Level Analysis 6241-029-P3-006-2pass-r02.indd 169 1/16/2013 9:14:56 PM 6241-029-P3-006-2pass-r02.indd 170 1/16/2013 9:14:57 PM 6 Exploratory and Confirmatory Factor Analysis Rex Kline 6.1

More information

Data Analysis in Mixed Research: A Primer

Data Analysis in Mixed Research: A Primer Data Analysis in Mixed Research: A Primer Anthony J. Onwuegbuzie (Corresponding author) & Julie P. Combs Department of Educational Leadership and Counseling Sam Houston State University, USA Box 2119,

More information

RR765 Applied Multivariate Analysis

RR765 Applied Multivariate Analysis Semester: Fall 2007 RR765 Applied Multivariate Analysis Course Instructor: Dr. Jerry J. Vaske 491-2360 email: jerryv@cnr.colostate.edu Office: 244 Forestry Bldg. Office Hours: Tuesday/Thursdays 1:00 2:00

More information

A Casual Structure Analysis of Smart phone Addiction: Use Motives of Smart phone Users and Psychological Characteristics

A Casual Structure Analysis of Smart phone Addiction: Use Motives of Smart phone Users and Psychological Characteristics A Casual Structure Analysis of Smart phone Addiction: Use Motives of Smart phone Users and Psychological Characteristics Dept. of Social Welfare, BaekSeok Culture University, ijoo65@hanmail.net Abstract

More information

Empirical Model-Building and Response Surfaces

Empirical Model-Building and Response Surfaces Empirical Model-Building and Response Surfaces GEORGE E. P. BOX NORMAN R. DRAPER Technische Universitat Darmstadt FACHBEREICH INFORMATIK BIBLIOTHEK Invortar-Nf.-. Sachgsbiete: Standort: New York John Wiley

More information

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.

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. 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 information

Introduction to Principal Component Analysis: Stock Market Values

Introduction to Principal Component Analysis: Stock Market Values Chapter 10 Introduction to Principal Component Analysis: Stock Market Values The combination of some data and an aching desire for an answer does not ensure that a reasonable answer can be extracted from

More information

Review Jeopardy. Blue vs. Orange. Review Jeopardy

Review Jeopardy. Blue vs. Orange. Review Jeopardy Review Jeopardy Blue vs. Orange Review Jeopardy Jeopardy Round Lectures 0-3 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 information

Chapter VIII Customers Perception Regarding Health Insurance

Chapter VIII Customers Perception Regarding Health Insurance Chapter VIII Customers Perception Regarding Health Insurance This chapter deals with the analysis of customers perception regarding health insurance and involves its examination at series of stages i.e.

More information

The Development of One Dimensional Scales for Assessing Stakeholder Perceptions of Academic Ethical Codes

The Development of One Dimensional Scales for Assessing Stakeholder Perceptions of Academic Ethical Codes Michael A. Yahr Lois D. Bryan Kurt Schimmel Robert Morris University 6001 University Blvd. Moon Township, PA 15108 yahr@rmu.edu bryan@rmu.edu schimmel@rmu.edu Michael A. Yahr Lois D. Bryan Kurt Schimmel

More information

Succession planning in Chinese family-owned businesses in Hong Kong: an exploratory study on critical success factors and successor selection criteria

Succession planning in Chinese family-owned businesses in Hong Kong: an exploratory study on critical success factors and successor selection criteria Succession planning in Chinese family-owned businesses in Hong Kong: an exploratory study on critical success factors and successor selection criteria By Ling Ming Chan BEng (University of Newcastle upon

More information

Applied Multivariate Analysis

Applied Multivariate Analysis Neil H. Timm Applied Multivariate Analysis With 42 Figures Springer Contents Preface Acknowledgments List of Tables List of Figures vii ix xix xxiii 1 Introduction 1 1.1 Overview 1 1.2 Multivariate Models

More information

Psychology 405: Psychometric Theory Homework on Factor analysis and structural equation modeling

Psychology 405: Psychometric Theory Homework on Factor analysis and structural equation modeling Psychology 405: Psychometric Theory Homework on Factor analysis and structural equation modeling William Revelle Department of Psychology Northwestern University Evanston, Illinois USA June, 2014 1 / 20

More information

PRINCIPAL COMPONENTS AND THE MAXIMUM LIKELIHOOD METHODS AS TOOLS TO ANALYZE LARGE DATA WITH A PSYCHOLOGICAL TESTING EXAMPLE

PRINCIPAL COMPONENTS AND THE MAXIMUM LIKELIHOOD METHODS AS TOOLS TO ANALYZE LARGE DATA WITH A PSYCHOLOGICAL TESTING EXAMPLE PRINCIPAL COMPONENTS AND THE MAXIMUM LIKELIHOOD METHODS AS TOOLS TO ANALYZE LARGE DATA WITH A PSYCHOLOGICAL TESTING EXAMPLE Markela Muca Llukan Puka Klodiana Bani Department of Mathematics, Faculty of

More information

The Factor Structure of the System Usability Scale

The Factor Structure of the System Usability Scale The Factor Structure of the System Usability Scale James R. Lewis 1 and Jeff Sauro 2 1 IBM Software Group, 8051 Congress Ave, Suite 2227 Boca Raton, FL 33487, jimlewis@us.ibm.com 2 Oracle, 1 Technology

More information

Missing Data: Part 1 What to Do? Carol B. Thompson Johns Hopkins Biostatistics Center SON Brown Bag 3/20/13

Missing Data: Part 1 What to Do? Carol B. Thompson Johns Hopkins Biostatistics Center SON Brown Bag 3/20/13 Missing Data: Part 1 What to Do? Carol B. Thompson Johns Hopkins Biostatistics Center SON Brown Bag 3/20/13 Overview Missingness and impact on statistical analysis Missing data assumptions/mechanisms Conventional

More information

EM Clustering Approach for Multi-Dimensional Analysis of Big Data Set

EM Clustering Approach for Multi-Dimensional Analysis of Big Data Set EM Clustering Approach for Multi-Dimensional Analysis of Big Data Set Amhmed A. Bhih School of Electrical and Electronic Engineering Princy Johnson School of Electrical and Electronic Engineering Martin

More information

When to Use Which Statistical Test

When 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 information