Kaiser's rule

TL;DR

A heuristic used in factor analysis to decide how many factors to keep by counting eigenvalues greater than 1.
Eigenvalues measure the amount of variance explained by each factor; factors with eigenvalues ≤ 1 are treated as not significant.
Commonly applied when reducing large, complex data sets to their underlying factors.

Definition

Kaiser’s rule (also called the Kaiser criterion) states that the number of factors that can be extracted from a data set is equal to the number of eigenvalues greater than 1.

Explanation

Kaiser’s rule is applied in factor analysis, a statistical method for identifying underlying structure in large or complex data sets. For each potential factor, compute its eigenvalue, which represents the amount of variance explained by that factor. According to the rule, retain factors whose eigenvalues are greater than 1 and discard factors whose eigenvalues are less than 1.

Examples

Consumer behavior example

A company collects data on factors such as age, income, education level, and purchasing history to understand drivers of consumer purchasing decisions. Using factor analysis, they calculate the eigenvalues for each factor. If the eigenvalues for age, income, and education level are all greater than 1, but the eigenvalue for purchasing history is less than 1, then age, income, and education level are considered significant factors and purchasing history is not.

Psychological data example

A researcher studies personality using data on agreeableness, openness, conscientiousness, and neuroticism. After factor analysis, the researcher calculates eigenvalues for each factor. If the eigenvalues for agreeableness, openness, and conscientiousness are all greater than 1, but the eigenvalue for neuroticism is less than 1, then agreeableness, openness, and conscientiousness are considered significant factors and neuroticism is not.

Factor analysis
Eigenvalues