Concept Architecture
Concept
Theoretically, Kaiser Criterion is a decision rule used in exploratory factor analysis and principal component analysis to determine the number of factors or components to retain. It is founded on eigenvalue decomposition of the correlation matrix and is based on the principle that a retained factor should explain at least as much variance as an individual standardised variable. The criterion exists to provide a simple, objective rule for factor retention during dimensionality reduction.
Mathematically, the Kaiser Criterion evaluates the eigenvalues obtained from the correlation matrix of the observed variables. Factors with eigenvalues greater than one are retained, whereas those with eigenvalues less than one are discarded. An eigenvalue greater than one indicates that the factor explains more variance than a single standardised variable. Although widely used, the criterion is generally interpreted alongside other methods because it may overestimate or underestimate the true number of factors.
In practice, the Kaiser Criterion is applied immediately after factor extraction and before factor rotation. Analysts compare each eigenvalue with the threshold of one and retain only those satisfying the criterion. In health economics, the method is commonly used during the development and validation of patient-reported outcome measures, health-related quality-of-life instruments and other multivariate measurement scales.
Purpose
Used to determine the number of factors or principal components to retain by identifying those explaining more variance than an individual standardised variable.
Mathematical Formulae
Primary Formula
Retain factor j if:
?? > 1
where:
- ?? = eigenvalue of factor j
Supporting Formulae
Total variance explained:
TVE = (????? ?? / p) ? 100%
where:
- k = number of retained factors
- p = number of observed variables
For a correlation matrix:
????? ?? = p
Related Mathematical Methods
- Exploratory Factor Analysis
- Principal Component Analysis
- Eigenvalue Analysis
- Scree Plot
- Parallel Analysis
- Factor Rotation
- Communality
Example
A health-related quality-of-life questionnaire contains eight observed variables.
Eigenvalues obtained from exploratory factor analysis are:
3.84, 1.76, 1.21, 0.88, 0.62, 0.39, 0.20, 0.10
Applying the Kaiser Criterion:
- Factor 1: 3.84 > 1 ? Retain
- Factor 2: 1.76 > 1 ? Retain
- Factor 3: 1.21 > 1 ? Retain
- Factor 4: 0.88 < 1 ? Do not retain
Three factors are retained.
The percentage of variance explained is:
TVE = (3.84 + 1.76 + 1.21) / 8 ? 100%
TVE = 85.1%
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| IF | =IF(B2>1,"Retain","Discard") | Applies the Kaiser Criterion to each extracted factor. |
| SUM | =SUM(B2:B4) | Calculates the total retained eigenvalue. |
| COUNTIF | =COUNTIF(B2:B9,">1") | Counts the number of retained factors. |
| SUM | =SUM(B2:B4)/SUM(B2:B9)*100 | Calculates the percentage of total variance explained by retained factors. |
VBA (Optional)
Automate evaluation of eigenvalues using the Kaiser Criterion and generate a retained-factor summary with cumulative variance explained.
Sources
- Kaiser HF. The Application of Electronic Computers to Factor Analysis. Educational and Psychological Measurement. 1960.
- Kaiser HF. A Second Generation Little Jiffy. Psychometrika. 1970.
- Hair JF, Black WC, Babin BJ, Anderson RE. Multivariate Data Analysis.
- Fabrigar LR, Wegener DT. Exploratory Factor Analysis.
- Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation.
Related Concepts (2)
Library
Publications
1
Statistical Analysis of Cost-Effectiveness Data — Willan & Briggs, 1st Edition ed., 2006 (John Wiley & Sons)
A synthesis of statistical methods for analysing cost-effectiveness data, including net-benefit regression, confidence intervals for the ICER, cost-effectiveness acceptability curves, and covariate adjustment. Part of the Wiley Statistics in Practice series.
BookView source →
Frequently Asked Questions (6)
What is the Kaiser criterion?
A factor analysis rule retaining only factors with an eigenvalue greater than one, since these explain more variance than a single original variable.
Source: Kaiser 1960
How does the Kaiser criterion decide how many factors to keep?
The Kaiser criterion decides how many factors to retain in a factor analysis by keeping only those with an eigenvalue greater than one. The reasoning is that a factor with an eigenvalue below one explains less variance than a single original variable would on its own, so it is not worth keeping. Simple to apply, the rule is nonetheless criticised for retaining too many factors, which is why it is often weighed against a scree plot. Keeping factors that outperform a lone variable is its rule. Kline (2015) describes this criterion.
Source: Kline 2015
Why does the Kaiser criterion use an eigenvalue of one?
The Kaiser criterion uses one as the cut-off because, when factor analysis is based on the correlation matrix of standardised variables, each original variable contributes a variance of one, so an eigenvalue of one corresponds to the amount of variance in a single variable. A factor with an eigenvalue above one therefore accounts for more variance than a lone variable and is judged worth keeping. So the Kaiser criterion sets the threshold at one because that is the variance of a single standardised variable, making a factor retained only if it explains more than any individual variable would, which gives the rule its rationale.
Source: Kaiser 1960
What are the limitations of the Kaiser criterion?
The limitations of the Kaiser criterion include that it can retain too many factors, especially with many variables, and sometimes too few, since the cut-off of one is somewhat arbitrary and applied to sample eigenvalues that carry uncertainty; and that it ignores interpretability and the pattern of eigenvalues. So the Kaiser criterion is used with caution and alongside other approaches, since mechanically retaining every factor above one can over- or under-extract, which is why it is combined with methods such as the scree plot and parallel analysis and with judgement about whether the retained factors are meaningful and interpretable.
Source: Kaiser 1960
How does the Kaiser criterion relate to the scree plot?
The Kaiser criterion and the scree plot are two common approaches to deciding the number of factors: the Kaiser criterion retains factors with eigenvalues above one, while the scree plot displays the eigenvalues in order and looks for the point where they level off, retaining factors before the bend. They can suggest different numbers. So the Kaiser criterion and the scree plot are complementary rules based on the eigenvalues, one using a fixed threshold and the other the shape of the eigenvalue sequence, and because they may disagree, they are often examined together, along with interpretability, to reach a sensible decision on the number of factors to retain.
Source: Kaiser 1958
When is the Kaiser criterion used?
The Kaiser criterion is used in exploratory factor analysis and principal components analysis to make an initial decision about how many factors or components to retain, offering a quick, objective rule based on the eigenvalues. So the Kaiser criterion is used as a starting point for choosing the number of factors, valued for its simplicity, though it is not relied upon alone, since it can misjudge the number, which is why it is applied together with other criteria such as scree plots and parallel analysis and with attention to whether the resulting factors are interpretable and replicable, rather than as a definitive rule.
Source: Kaiser 1960
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 17 Dec 2025
Content version: 1.0.0
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