### Abstract

One of the problems with structural equation modeling (SEM) is that the estimation of measurement equation is not separated from the estimation of structural equation. The main aim of this study was to propose a new method to overcome that problem by using ability parameters estimated by item response theory (IRT) as data. According to IRT, the error variance of measurement equation can be easily computed as the reciprocal of the information function. By using the estimates of the error variance, we can fix all parameters in measurement equation and can separate the estimation of structural equation from that of measurement equation. This method also allows us to estimate relations among factor scores with improved precision, because the errors of estimating factor scores are taken into account. The article concludes with a simulation result for verifying the efficacy of this method and an actual numerical.

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

Pages (from-to) | 381-388 |

Number of pages | 8 |

Journal | Shinrigaku Kenkyu |

Volume | 75 |

Issue number | 5 |

Publication status | Published - 2004 Dec |

### Keywords

- Covariance structure
- Factor score
- Item response theory
- Structural equation modeling
- Test data

### ASJC Scopus subject areas

- Psychology(all)

### Cite this

**Structural equation modeling using ability parameters : Analysis in the situation where item parameters have been estimated by item response theory.** / Murohashi, Hiroto; Toyoda, Hideki.

Research output: Contribution to journal › Article

*Shinrigaku Kenkyu*, vol. 75, no. 5, pp. 381-388.

}

TY - JOUR

T1 - Structural equation modeling using ability parameters

T2 - Analysis in the situation where item parameters have been estimated by item response theory

AU - Murohashi, Hiroto

AU - Toyoda, Hideki

PY - 2004/12

Y1 - 2004/12

N2 - One of the problems with structural equation modeling (SEM) is that the estimation of measurement equation is not separated from the estimation of structural equation. The main aim of this study was to propose a new method to overcome that problem by using ability parameters estimated by item response theory (IRT) as data. According to IRT, the error variance of measurement equation can be easily computed as the reciprocal of the information function. By using the estimates of the error variance, we can fix all parameters in measurement equation and can separate the estimation of structural equation from that of measurement equation. This method also allows us to estimate relations among factor scores with improved precision, because the errors of estimating factor scores are taken into account. The article concludes with a simulation result for verifying the efficacy of this method and an actual numerical.

AB - One of the problems with structural equation modeling (SEM) is that the estimation of measurement equation is not separated from the estimation of structural equation. The main aim of this study was to propose a new method to overcome that problem by using ability parameters estimated by item response theory (IRT) as data. According to IRT, the error variance of measurement equation can be easily computed as the reciprocal of the information function. By using the estimates of the error variance, we can fix all parameters in measurement equation and can separate the estimation of structural equation from that of measurement equation. This method also allows us to estimate relations among factor scores with improved precision, because the errors of estimating factor scores are taken into account. The article concludes with a simulation result for verifying the efficacy of this method and an actual numerical.

KW - Covariance structure

KW - Factor score

KW - Item response theory

KW - Structural equation modeling

KW - Test data

UR - http://www.scopus.com/inward/record.url?scp=15744394845&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=15744394845&partnerID=8YFLogxK

M3 - Article

C2 - 15747560

AN - SCOPUS:15744394845

VL - 75

SP - 381

EP - 388

JO - Shinrigaku Kenkyu

JF - Shinrigaku Kenkyu

SN - 0021-5236

IS - 5

ER -