Intro to Marketing Research: Factor Analysis - Key Decisions, Correlation Matrix Extraction Method Number of Factors Eigenvalues 1 Scree Plot Parallel Analysis Rotation Orthogonal Varimax vs. Oblique Promax

What It Is

Key Decisions in Factor Analysis refer to the critical steps involved in determining the number of factors to retain in a factor analysis. This method is used to reduce a large number of variables into a smaller set of underlying factors. A famous example of factor analysis in marketing is the Aaker and Day (1986) study on the dimensions of brand personality. They used factor analysis to identify five dimensions of brand personality: sincerity, excitement, competence, sophistication, and ruggedness. This matters for marketing decision-making as it helps in understanding consumer perceptions and preferences, ultimately informing brand positioning and marketing strategies.

Key Terms & Concepts

• Factor Analysis: A statistical method used to reduce a large number of variables into a smaller set of underlying factors.
  • Example: Aaker and Day (1986) used factor analysis to identify dimensions of brand personality.
• Correlation Matrix: A table showing the correlation coefficients between all pairs of variables.
  • Formula: r = ?[(xi - x?)(yi - ?)] / ?[?(xi - x?)² * ?(yi - ?)²]
  • Symbols: r = correlation coefficient, xi = individual data point, x? = mean of x, yi = individual data point,-= mean of y
• Extraction Method: A method used to extract the underlying factors from the correlation matrix.
  • Types: Principal Component Analysis (PCA), Maximum Likelihood Estimation (MLE)
  • Example: PCA is commonly used in factor analysis.
• Number of Factors – Eigenvalues > 1: A rule of thumb used to determine the number of factors to retain.
  • Formula: Eigenvalue > 1
  • Example: If an eigenvalue is greater than 1, it indicates that the factor explains more variance than a single variable.
• Scree Plot: A graphical representation of the eigenvalues.
  • Example: A scree plot can help identify the number of factors to retain by showing the point at which the eigenvalues level off.
• Parallel Analysis: A method used to determine the number of factors to retain.
  • Example: Parallel analysis involves comparing the eigenvalues of the original correlation matrix with those of a random correlation matrix.
• Rotation – Orthogonal (Varimax): A method used to rotate the factors to improve interpretability.
  • Example: Varimax rotation is commonly used in factor analysis.
• Rotation – Oblique (Promax): A method used to rotate the factors to improve interpretability.
  • Example: Promax rotation is used when the factors are expected to be correlated.
• Kaiser Criterion: A rule of thumb used to determine the number of factors to retain.
  • Formula: Eigenvalue > 1
  • Example: The Kaiser criterion is a common method used to determine the number of factors to retain.
• Cattell's Scree Test: A method used to determine the number of factors to retain.
  • Example: Cattell's scree test involves looking for the point at which the eigenvalues level off.
• Exploratory Factor Analysis (EFA): A type of factor analysis used to identify the underlying factors.
  • Example: EFA is commonly used in marketing research to identify the underlying dimensions of consumer preferences.
• Confirmatory Factor Analysis (CFA): A type of factor analysis used to test a hypothesized factor structure.
  • Example: CFA is commonly used in marketing research to test the validity of a hypothesized factor structure.

Common Misunderstandings

• Misunderstanding: The number of factors to retain is determined by the number of variables in the analysis.
• Correction: The number of factors to retain is determined by the eigenvalues and the scree plot, not by the number of variables.
• Misunderstanding: Factor analysis is only used for exploratory purposes.
• Correction: Factor analysis can be used for both exploratory and confirmatory purposes.
• Misunderstanding: The Kaiser criterion is the only method used to determine the number of factors to retain.
• Correction: There are several methods used to determine the number of factors to retain, including the Kaiser criterion, Cattell's scree test, and parallel analysis.

Quick Application / Identification

Scenario: A marketing researcher wants to identify the underlying dimensions of consumer preferences for a new product. The researcher has collected data on 10 variables related to the product. Using factor analysis, the researcher identifies 3 underlying factors. What type of factor analysis was used?

Answer: Exploratory Factor Analysis (EFA)

Explanation: EFA was used to identify the underlying factors, as the researcher was not testing a hypothesized factor structure.

Last-Minute Revision

• Factor analysis is a statistical method used to reduce a large number of variables into a smaller set of underlying factors.
• The correlation matrix is a table showing the correlation coefficients between all pairs of variables.
• The extraction method is used to extract the underlying factors from the correlation matrix.
• The number of factors to retain is determined by the eigenvalues and the scree plot.
• Parallel analysis is a method used to determine the number of factors to retain.
• Rotation is used to improve the interpretability of the factors.
• Orthogonal rotation (Varimax) is commonly used in factor analysis.
• Oblique rotation (Promax) is used when the factors are expected to be correlated.
• The Kaiser criterion is a rule of thumb used to determine the number of factors to retain.
• Cattell's scree test involves looking for the point at which the eigenvalues level off.
• Exploratory Factor Analysis (EFA) is used to identify the underlying factors.
• Confirmatory Factor Analysis (CFA) is used to test a hypothesized factor structure. The number of factors to retain is not determined by the number of variables in the analysis. Factor analysis can be used for both exploratory and confirmatory purposes. The Kaiser criterion is not the only method used to determine the number of factors to retain.