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Multivariate Data Analysis Chapter 8 - Canonical Correlation Analysis

Multivariate Data Analysis Chapter 8 - Canonical Correlation Analysis. Chapter 8. What Is Canonical Correlation? Interrelationships between sets of multiple independent variables and multiple dependent measures (quantify the strength of the relationship) General form of canonical analysis

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Multivariate Data Analysis Chapter 8 - Canonical Correlation Analysis

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  1. Multivariate Data AnalysisChapter 8 - Canonical Correlation Analysis

  2. Chapter 8 • What Is Canonical Correlation? • Interrelationships between sets of multiple independent variables and multiple dependent measures (quantify the strength of the relationship) • General form of canonical analysis • Hypothetical Example of Canonical Correlation • HATCO’s case: credit usage • Table 8.1 (p.445) • Canonical coefficient (Rc)

  3. Comparisons with Other Methods • Similar to regression • Quantify the relationship between i.v.s and d.v.s • Corresponds to factor analysis • Create composites of variables • Resembles discriminant analysis • Determine independent dimensions (discrimant functions) for each variable set • Maximize the relationship between i.v. and d.v. sets

  4. Analyzing Relationships with Canonical Correlation • Stage 1: Objectives of Canonical Correlation Analysis • Determine relationships among sets of variables • Achieve maximal correlation • Explain nature of relationships among sets of variables • Stage 2: Designing a Canonical Correlation Analysis • Sample size • Stage 3: 3 Assumptions in Canonical Correlation

  5. Analyzing Relationships with Canonical Correlation (Cont.) • Stage 4: Deriving the Canonical Functions and Assessing Overall Fit • Deriving Canonical Variates (Functions) • Each of the pairs of variates is orthogonal and independent of all other variates derived from the same set of data • Which Canonical Functions Should Be Interpreted? • Level of Significance • Magnitude of the Canonical Relationships • Redundancy Measure of Shared Variance

  6. Analyzing Relationships with Canonical Correlation (Cont.) • Stage 5: Interpreting the Canonical Variate • Canonical Weights (standardized coefficients) • Canonical Loadings (structure correlations) • Canonical Cross-Loadings • Which Interpretation Approach to Use • Stage 6: Validation and Diagnosis

  7. An Illustrative Example • HATCO: 7 attributes (metric i.v.s), 2 measures of efforts (metric d.v.s); 100 customers • Stage 1: Objectives of Canonical Correlation Analysis • Identify the relationship between a customer’s perceptions about HATCO and the customers’ level of usage and satisfaction • Stages 2 and 3: Designing a Canonical Correlation Analysis and Testing thee Assumptions • 13-to-1 ratio of observations to variables; exceeding 10 observations per variables • Stage 4: Deriving the Canonical Functions and Assessing Overall Fit • Statistical and Practical Significance • Redundancy Analysis

  8. An Illustrative Example (Cont.) • Stage 5: Interpreting the Canonical Variates • Canonical Weights (derive two canonical functions based on Table 8.5) • Canonical Loadings (Table 8.6 part I) • Canonical Cross-Loadings (Table 8.6 part II) • Stage 6: Validation and Diagnosis • Sensitivity analysis (Table 8.7) • A Managerial Overview (redundancy value > = 0.75)

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