Which criterion is commonly used in factor analysis to decide how many factors to retain based on eigenvalues?

Which criterion is commonly used in factor analysis to decide how many factors to retain based on eigenvalues?

• A. Scree plot
• B. Kaiser's criterion
• C. Bartlett's test
• D. Parallel analysis

Answer: (B)

In factor analysis, the number of factors to keep is guided by the eigenvalues that come from the correlation (or covariance) matrix. An eigenvalue for a factor tells you how much of the total variance in the observed variables that factor explains. Kaiser's criterion says you retain only those factors with eigenvalues greater than one. The logic is that a factor should explain more variance than a single observed variable (which has variance 1 when data are standardized) to be considered worth keeping. So if a factor’s eigenvalue is above 1, it captures a meaningful amount of variance; if it’s below 1, it’s not worth retaining. This is a straightforward, widely used rule of thumb. Other methods, like the scree plot, involve visually inspecting where the eigenvalues start to level off (the elbow) to decide how many factors to keep; Bartlett’s test is about testing whether the correlation matrix differs from an identity matrix (not about how many factors to retain); and parallel analysis compares observed eigenvalues to those obtained from random data to determine the cutoff. Kaiser's criterion remains a simple, commonly taught criterion for deciding the number of factors.

In factor analysis, the number of factors to keep is guided by the eigenvalues that come from the correlation (or covariance) matrix. An eigenvalue for a factor tells you how much of the total variance in the observed variables that factor explains. Kaiser's criterion says you retain only those factors with eigenvalues greater than one. The logic is that a factor should explain more variance than a single observed variable (which has variance 1 when data are standardized) to be considered worth keeping. So if a factor’s eigenvalue is above 1, it captures a meaningful amount of variance; if it’s below 1, it’s not worth retaining.

This is a straightforward, widely used rule of thumb. Other methods, like the scree plot, involve visually inspecting where the eigenvalues start to level off (the elbow) to decide how many factors to keep; Bartlett’s test is about testing whether the correlation matrix differs from an identity matrix (not about how many factors to retain); and parallel analysis compares observed eigenvalues to those obtained from random data to determine the cutoff. Kaiser's criterion remains a simple, commonly taught criterion for deciding the number of factors.