Maximum likelihood estimation of linear structural relationship model parameters assuming the slope is known

Abstract

A number of statistical techniques have been proposed by many authors to estimate the parameters in a linear structural relationship model, but only few papers discuss the precision of these estimators. In this study, we derive the maximum likelihood estimate (MLE) of the parameters by assuming the slope parameter β is known. β is estimated separately by a nonparametric method and is assumed to be known when other parameters are estimated by an MLE. We obtain closed-form estimates of parameters as well as the variance-covariance matrix. Using a simulation study and a real-world example we show that the estimated values of the parameters are unbiased and consistent.