Structural equation modeling using ability parameters: Analysis in the situation where item parameters have been estimated by item response theory

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.