Lecture 4 - EFA Flashcards
What is the primary purpose of Exploratory Factor Analysis (EFA)?
The primary purpose of EFA is to reduce a large set of observed variables into a smaller set of latent factors that can explain the observed correlations among the variables.
What are the key steps involved in conducting an EFA?
The key steps in conducting an EFA include checking assumptions (linearity, multicollinearity, factorability), deciding how many factors to extract, extracting factors, rotating factors for better interpretability, and interpreting the factor loadings.
What is Kaiser’s criterion and how is it used in EFA?
Kaiser’s criterion is a rule for determining the number of factors to extract in EFA. It suggests retaining factors with eigenvalues greater than 1, as these factors explain more variance than a single observed variable.
What is the purpose of rotating factors in EFA?
The purpose of rotating factors in EFA is to achieve a simpler and more interpretable factor structure by maximizing high loadings and minimizing low loadings for each factor.
What is the difference between orthogonal and oblique rotation?
Orthogonal rotation assumes that factors are uncorrelated, while oblique rotation allows for correlated factors. Examples of orthogonal rotation include Varimax, and examples of oblique rotation include Direct Oblimin.
What does the Scree plot show, and how is it used in EFA?
A Scree plot shows the eigenvalues of each extracted factor plotted against the factor number. It is used to determine the number of factors to retain by identifying the point where the plot levels off (the “elbow”).
How does Bartlett’s test of sphericity contribute to EFA?
Bartlett’s test of sphericity tests whether the correlation matrix is significantly different from an identity matrix. A significant result indicates that there are relationships among the variables, justifying the use of factor analysis.
What is the Kaiser-Meyer-Olkin (KMO) measure, and what does it indicate?
The KMO measure assesses the adequacy of sampling for EFA by measuring how well variables correlate with each other. Values above 0.60 are considered acceptable for factor analysis.
Describe Velicer’s Minimum Average Partial (MAP) test.
Velicer’s MAP test determines the number of factors to extract by calculating the average partial correlation for different numbers of factors and selecting the number that minimizes this average.
What are communalities in EFA, and why are they important?
Communalities represent the proportion of each variable’s variance that can be explained by the extracted factors. They are important because they indicate how well each variable fits into the factor model.
What are factor loadings and why are they important in EFA?
Factor loadings are the correlations between observed variables and the latent factors. They are important because they indicate the extent to which each variable is associated with a particular factor.
Explain the concept of communality in EFA.
Communality represents the proportion of a variable’s variance that is shared with other variables and can be explained by the extracted factors. High communalities indicate that the variable is well-represented by the factor solution.
What is the difference between Principal Component Analysis (PCA) and Exploratory Factor Analysis (EFA)?
PCA is a data reduction technique that transforms variables into a set of uncorrelated components, while EFA identifies underlying latent factors that explain the correlations among variables. PCA focuses on maximizing variance, while EFA focuses on uncovering the underlying structure.
How is the Determinant used to assess multicollinearity in EFA?
The Determinant of the correlation matrix is used to assess multicollinearity. A Determinant close to zero indicates high multicollinearity, which can affect the stability and interpretability of the factor solution.
Describe the purpose of the anti-image correlation matrix in EFA.
The anti-image correlation matrix is used to assess the adequacy of individual items for factor analysis. The diagonals of the anti-image correlation matrix provide the KMO values for each item, indicating how well each item correlates with other items.
