A maximum likelihood estimator for composite models

Structural equation modeling (SEM) is a popular and widely applied method that predominantly models latent variables by means of common factor models. Yet, in recent years, the composite model has gained increasing research attention. In contrast to common factor models, approaches to estimate composite models are limited. We contribute a full-information maximum likelihood (ML) estimator for composite models. We present the general composite model including its model-implied variance-covariance matrix and derive a full-information ML approach to estimate the parameters of composite models. Moreover, a test is provided to assess the overall fit of composite models. To demonstrate the performance of the ML estimator and to compare it to its closest contender, i.e., partial least squares path modeling (PLS-PM), in finite samples, a Monte Carlo simulation is conducted. The Monte Carlo simulation reveals that, overall, the ML estimator performs well and is similar to PLS-PM in finite samples. Hence, under the considered conditions, the proposed estimator is a valid alternative with known superior statistical properties.