Parameter Estimation of Structural Equation Models Using Latent Variable Scores

Structural Equation Modeling has two problems : (1) the form of the structural part aRects the estimates of the measurement part and (2) when continuous and discrete variables are mixed, simultaneous estimates are difficult to obtain. To avoid these problems, many researchers use some type of stepwise estimation procedure involving estimated latent variable scores. This paper shows this type of estimation to be biased, proposes a modified estimation method using estimated latent variable scores, and demonstrates consistency for the new method. Simulation studies illustrate that existing methods are biased even when sample sizes are large while the proposed method results in the parameter estimates close to the true values with relatively small sample sizes. The proposed method (1) is easy to apply even when the model contains different levels of measurement, (2) rarely yields improper solutions, (3) prevents the structural part from affecting the measurement part, and (4) is able to estimate the structural part without raw data.