Applied Univariate, Bivariate, and Multivariate Statistics. Daniel J. Denis
href="#ulink_f6d57851-4a98-5638-99be-c7c0c02646e4">14.4 THEORY OF FACTOR ANALYSIS: THE EXPLORATORY FACTOR‐ANALYTIC MODEL 14.5 THE COMMON FACTOR‐ANALYTIC MODEL 14.6 ASSUMPTIONS OF THE FACTOR‐ANALYTIC MODEL 14.7 WHY MODEL ASSUMPTIONS ARE IMPORTANT 14.8 THE FACTOR MODEL AS AN IMPLICATION FOR THE COVARIANCE MATRIX ∑ 14.9 AGAIN, WHY IS ∑ = ΛΛ′ + ψ SO IMPORTANT A RESULT? 14.10 THE MAJOR CRITIQUE AGAINST FACTOR ANALYSIS: INDETERMINACY AND THE NONUNIQUENESS OF SOLUTIONS 14.11 HAS YOUR FACTOR ANALYSIS BEEN SUCCESSFUL? 14.12 ESTIMATION OF PARAMETERS IN EXPLORATORY FACTOR ANALYSIS 14.13 PRINCIPAL FACTOR 14.14 MAXIMUM LIKELIHOOD 14.15 THE CONCEPTS (AND CRITICISMS) OF FACTOR ROTATION 14.16 VARIMAX AND QUARTIMAX ROTATION 14.17 SHOULD FACTORS BE ROTATED? IS THAT NOT CHEATING? 14.18 SAMPLE SIZE FOR FACTOR ANALYSIS 14.19 PRINCIPAL COMPONENTS ANALYSIS VERSUS FACTOR ANALYSIS: TWO KEY DIFFERENCES 14.20 PRINCIPAL FACTOR IN SPSS: PRINCIPAL AXIS FACTORING 14.21 BARTLETT TEST OF SPHERICITY AND KAISER–MEYER–OLKIN MEASURE OF SAMPLING ADEQUACY (MSA) 14.22 FACTOR ANALYSIS IN R: HOLZINGER AND SWINEFORD (1939) 14.23 CLUSTER ANALYSIS 14.24 WHAT IS CLUSTER ANALYSIS? THE BIG PICTURE 14.25 MEASURING PROXIMITY 14.26 HIERARCHICAL CLUSTERING APPROACHES 14.27 NONHIERARCHICAL CLUSTERING APPROACHES 14.28 K‐MEANS CLUSTER ANALYSIS IN R 14.29 GUIDELINES AND WARNINGS ABOUT CLUSTER ANALYSIS 14.30 A BRIEF LOOK AT MULTIDIMENSIONAL SCALING 14.31 CHAPTER SUMMARY AND HIGHLIGHTS REVIEW EXERCISES Further Discussion and Activities
21 15 PATH ANALYSIS AND STRUCTURAL EQUATION MODELING 15.1 PATH ANALYSIS: A MOTIVATING EXAMPLE—PREDICTING IQ ACROSS GENERATIONS 15.2 PATH ANALYSIS AND “CAUSAL MODELING” 15.3 EARLY POST‐WRIGHT PATH ANALYSIS: PREDICTING CHILD'S IQ (Burks, 1928) 15.4 DECOMPOSING PATH COEFFICIENTS 15.5 PATH COEFFICIENTS AND WRIGHT'S CONTRIBUTION 15.6 PATH ANALYSIS IN R—A QUICK OVERVIEW: MODELING GALTON'S DATA 15.7 CONFIRMATORY FACTOR ANALYSIS: THE MEASUREMENT MODEL 15.8 STRUCTURAL EQUATION MODELS 15.9 DIRECT, INDIRECT, AND TOTAL EFFECTS 15.10 THEORY OF STATISTICAL MODELING: A DEEPER LOOK INTO COVARIANCE STRUCTURES AND GENERAL MODELING 15.11 THE DISCREPANCY FUNCTION AND CHI‐SQUARE 15.12 IDENTIFICATION 15.13 DISTURBANCE VARIABLES 15.14 MEASURES AND INDICATORS OF MODEL FIT 15.15 OVERALL MEASURES OF MODEL FIT 15.16 MODEL COMPARISON MEASURES: INCREMENTAL FIT INDICES 15.17 WHICH INDICATOR OF MODEL FIT IS BEST? 15.18 STRUCTURAL EQUATION MODEL IN R 15.19 HOW ALL VARIABLES ARE LATENT: A SUGGESTION FOR RESOLVING THE MANIFEST‐LATENT DISTINCTION 15.20 THE STRUCTURAL EQUATION MODEL AS A GENERAL MODEL: SOME CONCLUDING THOUGHTS ON STATISTICS AND SCIENCE 15.21 CHAPTER SUMMARY AND HIGHLIGHTS REVIEW EXERCISES Further Discussion and Activities
22 REFERENCES
23 INDEX
List of Tables
1 Chapter 2Table 2.1 Contingency Table for 2 × 2 DesignTable 2.2 Contingency Table for 2 × 2 × 2 Design...Table 2.3 Contingency Table for 2 × 2 Diagnostic DesignTable 2.4 Mathematical versus Discrete Random VariableTable 2.5 Favorability of Movies for Two Individuals in Terms of RanksTable 2.6 Power Estimates as a Function of Sample Size and Estimated Magnitud...Table 2.7 Conversions for r → r2→ d.11Table 2.8 Matched-Pairs Design