### Abstract

Original language | English |
---|---|

Pages (from-to) | 161-172 |

Number of pages | 12 |

Journal | Psychometrika. Vol 67(1) |

Volume | 67 |

Issue number | 1 |

DOIs | |

Publication status | Published - Mar 2002 |

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### Keywords

- indeterminacy
- factor scores
- Confirmatory factor analysis
- exploratory factor analysis
- distance between factors

### Cite this

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*Psychometrika. Vol 67(1)*, vol. 67, no. 1, pp. 161-172. https://doi.org/10.1007/BF02294714

**On the construction of all factors of the model for factor analysis.** / Krijnen, Wim P.

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - On the construction of all factors of the model for factor analysis.

AU - Krijnen, Wim P

PY - 2002/3

Y1 - 2002/3

N2 - A construction method is given for all factors that satisfy the assumptions of the model for factor analysis, including partially determined factors where certain error variances are zero. Various criteria for the seriousness of indeterminacy are related. It is shown that B. F. Green's (1976) conjecture holds: For a linear factor predictor the mean squared error of prediction is constant over all possible factors. A simple and general geometric interpretation of factor indeterminacy is given on the basis of the distance between multiple factors. It is illustrated that variable elimination can have a large effect on the seriousness of factor indeterminacy. A simulation study reveals that if the mean square error of factor prediction equals .5, then two thirds of the persons are "correctly" selected by the best linear factor predictor. (PsycINFO Database Record (c) 2009 APA, all rights reserved)

AB - A construction method is given for all factors that satisfy the assumptions of the model for factor analysis, including partially determined factors where certain error variances are zero. Various criteria for the seriousness of indeterminacy are related. It is shown that B. F. Green's (1976) conjecture holds: For a linear factor predictor the mean squared error of prediction is constant over all possible factors. A simple and general geometric interpretation of factor indeterminacy is given on the basis of the distance between multiple factors. It is illustrated that variable elimination can have a large effect on the seriousness of factor indeterminacy. A simulation study reveals that if the mean square error of factor prediction equals .5, then two thirds of the persons are "correctly" selected by the best linear factor predictor. (PsycINFO Database Record (c) 2009 APA, all rights reserved)

KW - indeterminacy

KW - factor scores

KW - Confirmatory factor analysis

KW - exploratory factor analysis

KW - distance between factors

U2 - 10.1007/BF02294714

DO - 10.1007/BF02294714

M3 - Article

VL - 67

SP - 161

EP - 172

JO - Psychometrika. Vol 67(1)

JF - Psychometrika. Vol 67(1)

SN - 0033-3123

IS - 1

ER -