# A rationale and test for the number of factors in factor analysis

@article{Horn1965ARA, title={A rationale and test for the number of factors in factor analysis}, author={John Louis Horn}, journal={Psychometrika}, year={1965}, volume={30}, pages={179-185} }

It is suggested that if Guttman's latent-root-one lower bound estimate for the rank of a correlation matrix is accepted as a psychometric upper bound, following the proofs and arguments of Kaiser and Dickman, then the rank for a sample matrix should be estimated by subtracting out the component in the latent roots which can be attributed to sampling error, and least-squares “capitalization” on this error, in the calculation of the correlations and the roots. A procedure based on the generation…

## 6,021 Citations

On the Likelihood Ratio Test for the Number of Factors in Exploratory Factor Analysis

- Mathematics
- 2007

In the exploratory factor analysis, when the number of factors exceeds the true number of factors, the likelihood ratio test statistic no longer follows the chi-square distribution due to a problem…

Evaluating a proposed modification of the Guttman rule for determining the number of factors in an exploratory factor analysis

- Geology
- 2014

Exploratory factor analysis (EFA) is a widely used statistical method in which researchers attempt to ascertain the number and nature of latent factors that explain their observed variables. When…

Note On a Criterion for the Number of Common Factors

- Mathematics
- 1969

LINN (1968) has published the results of a, Monte Carlo approach to the number of factors problem involving the use of random normal deviates as additional variables in correlational matrices from…

Parallel Analysis Criteria: Revised Equations for Estimating the Latent Roots of Random Data Correlation Matrices

- Mathematics
- 1989

Regression equations may be used for estimating givenvalues to serve as parallel analysis criteria for determining the number of factors to retain. The accuracy of the first givenvalue's estimate…

Testing the number of required dimensions in exploratory factor analysis

- Computer Science
- 2017

Simulations implementing 144 sets of parameters, including correlated factors and presence of a doublet factor, show that all four NESTs largely outperform CD, the standard Parallel Analysis, the Mean Average Partial method and even the maximum likelihood approach, in identifying the correct number of common factors.

Some simple structure significance tests for exploratory component analysis with market survey data

- Business
- 1994

A simple structure criterion is suggested as a general framework for choosing the number of factors and for interpreting the rotated factor structure matrix and the results show the importance of increasing the information yield from exploratory factor analysis.

Determining the Number of Factors in High-Dimensional Generalized Latent Factor Models

- Computer ScienceBiometrika
- 2021

An information criterion to determine the number of factors in generalized latent factor models is proposed and an error bound is established for the parameter estimates, which plays an important role in establishing the consistency of the proposed information criterion.

A Comparison of Ten Methods for Determining the Number of Factors in Exploratory Factor Analysis

- Psychology
- 2013

Datalogix The effectiveness of 10 methods for estimating the number of factors were compared. These methods were the minimum average partial procedure, the likelihood ratio test, the Akaike…

Effects of Cross-loadings on Determining the Number of Factors to Retain

- Business
- 2020

ABSTRACT In exploratory factor analysis (EFA), cross-loadings frequently occur in empirical research, but its effects on determining the number of factors to retain are seldom known. In this paper,…

Estimating confidence intervals for eigenvalues in exploratory factor analysis

- BusinessBehavior research methods
- 2010

Two methods of estimating CIs for eigenvalues are demonstrated: one based on the mathematical properties of the central limit theorem, and the other based on bootstrapping.

## References

SHOWING 1-8 OF 8 REFERENCES

Some necessary conditions for common-factor analysis

- Mathematics
- 1954

LetR be any correlation matrix of ordern, with unity as each main diagonal element. Common-factor analysis, in the Spearman-Thurstone sense, seeks a diagonal matrixU2 such thatG = R − U2 is Gramian…

The Application of Electronic Computers to Factor Analysis

- Computer Science
- 1960

A survey of available computer programs for factor analytic computations and a analysis of the problems of the application of computers to factor analysis.

The advanced theory of statistics (Vols. I and II). London~ Eng

- The advanced theory of statistics (Vols. I and II). London~ Eng
- 1958

Advanced statistical methods in biornetric research Original manuscript received 1

- Advanced statistical methods in biornetric research Original manuscript received 1
- 1952