Abstract
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 of random variables is given for estimating the component which needs to be subtracted.
Keywords
Guttman scaleMathematicsStatisticsMathematical proofRank (graph theory)Covariance matrixLatent variableComponent (thermodynamics)Upper and lower boundsMatrix (chemical analysis)Factor analysisSampling (signal processing)EconometricsApplied mathematicsCombinatoricsComputer scienceMathematical analysis
Affiliated Institutions
Related Publications
Some Necessary Conditions for Common-Factor Analysis
Let R be any correlation matrix of order n , with unity as each main diagonal element. Common-factor analysis, in the Spearman-Thurstone sense, seeks a diagonal matrix U 2 such ...
ON THE INTERNAL CONSISTENCY RELIABILITY OF FACTORS
On the assumption that principle component scores are to be computed by what is known as the direct solution (in contrast to estimation procedures), the weighted internal consis...
A Series of Lower Bounds to the Reliability of a Test
Two well-known lower bounds to the reliability in classical test theory, Guttman’s λ 2 and Cronbach’s coefficient alpha, are shown to be terms of an infinite series of lower bou...
Stopping Rules in Principal Components Analysis: A Comparison of Heuristical and Statistical Approaches
Approaches to determining the number of components to interpret from principal components analysis were compared. Heuristic procedures included: retaining components with eigenv...
Asymptotic Theory for Principal Component Analysis
Abstract : The asymptotic distribution of the characteristic roots and (normalized) vectors of a sample covariance matrix is given when the observations are from a multivariate ...
Publication Info
- Year
- 1965
- Type
- article
- Volume
- 30
- Issue
- 2
- Pages
- 179-185
- Citations
- 8259
- Access
- Closed
External Links
Social Impact
Altmetric
PlumX Metrics
Social media, news, blog, policy document mentions
Citation Metrics
8259
OpenAlex
Cite This
John L. Horn
(1965).
A Rationale and Test for the Number of Factors in Factor Analysis.
Psychometrika
, 30
(2)
, 179-185.
https://doi.org/10.1007/bf02289447
Identifiers
- DOI
- 10.1007/bf02289447