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 Hypothetical Example of Canonical Correlation  HATCO’s case: credit usage  Table 8.1 (p.445)  Canonical coefficient (R c )

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

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

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

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

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

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)