Comparisons among several consistent estimators of structural equation models

Abstract

With the advent of consistent partial least squares (PLSc), an interest has surged in comparing the quality of various estimation methods in structural equation models. Of particular interest are, beside PLSc, Bentler’s non-iterative confirmatory factor analysis, Hagglund’s instrumental variable (IV) estimation method, and Ihara–Kano’s non-iterative uniqueness estimation method. All of these methods yield consistent estimates of parameters in measurement models (factor loadings and unique variances), but require additional steps to estimate parameters in structural models [covariances among latent variables (LVs) and path coefficients]. These additional steps typically involve calculating LV scores, either correlating them or applying regression analysis, and correcting possible “biases” incurred by the use of LV scores as proxies of true LVs. In this paper, we conduct a Monte Carlo study to evaluate parameter recovery capabilities of the above LV extraction methods in conjunction with subsequent LV score construction and bias correction methods. We also compare these methods against more conventional estimation methods, such as the full least squares and maximum likelihood methods, that estimate parameters in both measurement and structural models simultaneously. In addition, we examine three methods of estimating standard errors (SEs) of estimated parameters from a single data set, the bootstrap method, ordinary least squares regression, and the inverse Hessian method. The SEs are important in assessing the reliability of parameter estimates and in testing their significance. It was found that Hagglund’s method used to extract one LV at a time from each block of observed variables, combined with Croon’s bias correction method, worked best in both parameter recovery and resistance to improper solutions, and that the bootstrap method provided the most accurate estimates of SEs.