### Abstract

Psychological research often deals with psychological constructs that cannot be directly measured. Thus independent variables of regression analysis for an observable dependent variable are sometimes latent variables (factors) that are defined independently of the dependent variable. In this study we pointed out the problem associated with the use of factor analysis for the combined set of dependent variable and independent variables in such a cases; that is, the derived factors are different from those originally intended, and the true regression parameters cannot be reproduced. We proposed a stagewise estimation method to solve the problem. This method estimates parameters of measurement equation in the first stage, and then estimates parameters of structural equation in the second stage. Our proposed method enables calculation of standard errors of estimators using Bootstrapping method. Numerical studies showed that the proposed method improves the estimation efficiency over the conventional methods, and provides estimates which are robust with respect to misspecification of model.

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

Pages (from-to) | 218-226 |

Number of pages | 9 |

Journal | Shinrigaku Kenkyu |

Volume | 74 |

Issue number | 3 |

Publication status | Published - 2003 Aug |

Externally published | Yes |

### Fingerprint

### Keywords

- Consistency of stagewise estimation
- Factor analysis
- Factorial invariance
- Robustness
- Structural equation modeling

### ASJC Scopus subject areas

- Psychology(all)

### Cite this

**Stagewise estimation for regression analysis when independent variables are latent variables.** / Hoshino, Takahiro.

Research output: Contribution to journal › Article

*Shinrigaku Kenkyu*, vol. 74, no. 3, pp. 218-226.

}

TY - JOUR

T1 - Stagewise estimation for regression analysis when independent variables are latent variables

AU - Hoshino, Takahiro

PY - 2003/8

Y1 - 2003/8

N2 - Psychological research often deals with psychological constructs that cannot be directly measured. Thus independent variables of regression analysis for an observable dependent variable are sometimes latent variables (factors) that are defined independently of the dependent variable. In this study we pointed out the problem associated with the use of factor analysis for the combined set of dependent variable and independent variables in such a cases; that is, the derived factors are different from those originally intended, and the true regression parameters cannot be reproduced. We proposed a stagewise estimation method to solve the problem. This method estimates parameters of measurement equation in the first stage, and then estimates parameters of structural equation in the second stage. Our proposed method enables calculation of standard errors of estimators using Bootstrapping method. Numerical studies showed that the proposed method improves the estimation efficiency over the conventional methods, and provides estimates which are robust with respect to misspecification of model.

AB - Psychological research often deals with psychological constructs that cannot be directly measured. Thus independent variables of regression analysis for an observable dependent variable are sometimes latent variables (factors) that are defined independently of the dependent variable. In this study we pointed out the problem associated with the use of factor analysis for the combined set of dependent variable and independent variables in such a cases; that is, the derived factors are different from those originally intended, and the true regression parameters cannot be reproduced. We proposed a stagewise estimation method to solve the problem. This method estimates parameters of measurement equation in the first stage, and then estimates parameters of structural equation in the second stage. Our proposed method enables calculation of standard errors of estimators using Bootstrapping method. Numerical studies showed that the proposed method improves the estimation efficiency over the conventional methods, and provides estimates which are robust with respect to misspecification of model.

KW - Consistency of stagewise estimation

KW - Factor analysis

KW - Factorial invariance

KW - Robustness

KW - Structural equation modeling

UR - http://www.scopus.com/inward/record.url?scp=38849198997&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38849198997&partnerID=8YFLogxK

M3 - Article

C2 - 14584252

AN - SCOPUS:38849198997

VL - 74

SP - 218

EP - 226

JO - Shinrigaku Kenkyu

JF - Shinrigaku Kenkyu

SN - 0021-5236

IS - 3

ER -