Multivariate Data Analysis Chapter 3 – Factor Analysis

Chapter 3 What is Factor Analysis? – Interrelationships (correlations) among a large number of variables – Interdependence technique in which all variables are simultaneously considered, each related to all others. – Factors are formed to maximize their explanation of the entire variable set, not to predict a dependent variable(s). An example of Factor Analysis (p. 92)

Factor Analysis Decision Process Stage 1: Objectives of Factor Analysis – Identifying Structure Through Data Summarization – Data Reduction – Using Factor Analysis With Other Multivariate Techniques – Variable Selection

Factor Analysis Decision Process (Cont.) Stage 2: Designing a Factor Analysis – Correlations Among Variables or Respondents – Variable Selection and Measurement Issues – Sample Size Stage 3: Assumptions in Factor Analysis

Factor Analysis Decision Process (Cont.) Stage 4: Deriving Factors and Assessing Overall Fit – Common Factor Analysis Versus Component Analysis – Criteria for the Number of Factors to Be Extracted Latent Root Criterion Percentage of Variance Criterion Scree Test Criterion Heterogeneity of the Respondents Summary of Factor Selection Criteria

Factor Analysis Decision Process (Cont.) Stage 5: Interpreting the Factors – Rotation of Factors An Illustration of Factor Rotation Orthogonal Rotation Methods – QUARTIMAX – VARIMAX – EQUIMAX Oblique Rotation Methods Selecting Among Rotational Methods

Factor Analysis Decision Process (Cont.) Stage 5: Interpreting the Factors (Cont.) – Criteria for the Significance of Factor Loadings Ensuring Practical Significance Assessing Statistical Significance Adjustments Based on the Number of Variables – Interpreting a Factor Matrix Examine the Factor Matrix of Loadings Identify the Highest Leading For Each Variables Assess Communalities of the Variables Label the Factors

Factor Analysis Decision Process (Cont.) Stage 6: Validation of Factor Analysis Stage 7: Additional Uses of the Factor Analysis Results – Selecting Surrogate Variables for Subsequent Analysis – Creating Summated Scales Conceptual Definition Dimensionality Reliability Validity Summary Computing Factor Scores Selecting Among the Three Methods

An Illustrative Example Stage 1: Objectives of Factor Analysis Stage 2: Designing a Factor Analysis Stage 3: Assumptions in Factor Analysis Component Factor Analysis: Stages 4 through Stage 7

An Illustrative Example (Cont.) Stage 4: Deriving Factors and Assessing Overall Fit Stage 5: Interpreting the Factors – Applying an Orthogonal (VARIMAX) Rotation – Naming the Factors – Applying an Oblique Rotation Stage 6: Validation of Factor Analysis

An Illustrative Example (Cont.) Stage 7: Additional Users of the Factor Analysis Results – Selecting Surrogate Variables for Subsequent Analysis – Creating Summated Scales – Use of Factor Scores – Selecting the Data Reduction Method

An Illustrative Example Common Factor Analysis Stages 4 and 5 Stage 4: Deriving Factors and Assessing Overall Fit Stage 5: Interpreting the Factors A Managerial Overview of the Results