A non-iterative approach to estimating parameters in a linear structural equation model

The research described herein was motivated by a study of the relationship between the performance of students in senior high schools and at universities in China. A special linear structural equation model is established, in which some parameters are known and both the responses and the covariables are measured with errors. To explore the relationship between the true responses and latent covariables and to estimate the parameters, we suggest a non-iterative estimation approach that can account for the external dependence between the true responses and latent covariables. This approach can also deal with the collinearity problem because the use of dimension-reduction techniques can remove redundant variables. Combining further with the information that some of parameters are given, we can perform estimation for the other unknown parameters. An easily implemented algorithm is provided. A simulation is carried out to provide evidence of the performance of the approach and to compare it with existing methods. The approach is applied to the education example for illustration, and it can be readily extended to more general models.