### Abstract

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

Pages (from-to) | 311-326 |

Journal | The British journal of mathematical and statistical psychology |

Volume | 57 |

Issue number | Pt 2 |

DOIs | |

Publication status | Published - 2004 |

### Keywords

- statistics
- models, theoretical
- psychology

### Cite this

}

*The British journal of mathematical and statistical psychology*, vol. 57, no. Pt 2, pp. 311-326. https://doi.org/10.1348/0007110042307140

**Convergence in mean square of factor predictors.** / Krijnen, Wim P.

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

TY - JOUR

T1 - Convergence in mean square of factor predictors.

AU - Krijnen, Wim P

PY - 2004

Y1 - 2004

N2 - Sufficient conditions for mean square convergence of factor predictors in common factor analysis are given by Guttman, by Williams, and by Schneeweiss and Mathes. These conditions do not hold for confirmatory factor analysis or when an error variance equals zero (Heywood cases). Two sufficient conditions are given for the three basic factor predictors and a predictor from rotated principal components analysis to converge to the factors of the model for confirmatory factor analysis, including Heywood cases. For certain model specifications the conditions are necessary. The conditions are sufficient for the existence of a unique true factor. A geometric interpretation is given for factor indeterminacy and mean square convergence of best linear factor prediction.

AB - Sufficient conditions for mean square convergence of factor predictors in common factor analysis are given by Guttman, by Williams, and by Schneeweiss and Mathes. These conditions do not hold for confirmatory factor analysis or when an error variance equals zero (Heywood cases). Two sufficient conditions are given for the three basic factor predictors and a predictor from rotated principal components analysis to converge to the factors of the model for confirmatory factor analysis, including Heywood cases. For certain model specifications the conditions are necessary. The conditions are sufficient for the existence of a unique true factor. A geometric interpretation is given for factor indeterminacy and mean square convergence of best linear factor prediction.

KW - statistics

KW - models, theoretical

KW - psychology

KW - psychologie

KW - statistiek

U2 - 10.1348/0007110042307140

DO - 10.1348/0007110042307140

M3 - Article

VL - 57

SP - 311

EP - 326

JO - The British journal of mathematical and statistical psychology

JF - The British journal of mathematical and statistical psychology

SN - 0007-1102

IS - Pt 2

ER -