David Kreiberg

Automatica 156 Doi: https://doi.org/10.1016/j.automatica.2023.111187

Over the years, errors-in-variables (EIV) system identification has attracted considerable research interest. Among the many proposed approaches for identifying EIV models is confirmatory factor analysis (CFA), here referred to as EIV-CFA. This study extends previous research by presenting a EIV-CFA modeling framework that allows for colored output noise. Considerable attention is paid to the theoretical aspects of the minimum distance (MD) estimator. The finite sample performance of the MD estimator is briefly evaluated using simulation. The results suggest that model parameters are well estimated.

Structural Equation Modeling Doi: https://doi.org/10.1080/10705511.2022.2076093

This study presents a separable nonlinear least squares (SNLLS) implementation of the minimum distance (MD) estimator employing a fixed-weight matrix for estimating structural equation models (SEMs). In contrast to the standard implementation of the MD estimator, in which the complete set of parameters is estimated using nonlinear optimization, the SNLLS implementation allows a subset of parameters to be estimated using (linear) least squares (LS). The SNLLS implementation possesses a number of benefits, such as faster convergence, better performance in ill-conditioned estimation problems, and fewer required starting values. The present work demonstrates that SNLLS, when applied to SEM estimation problems, significantly reduces the estimation time. Reduced estimation time makes SNLLS particularly useful in applications involving some form of resampling, such as simulation and bootstrapping.

Structural Equation Modeling Doi: https://doi.org/10.1080/10705511.2020.1835484

This paper presents a numerically more efficient implementation of the quadratic form minimum distance (MD) estimator with a fixed weight matrix for confirmatory factor analysis (CFA) models. In structural equation modeling (SEM) computer software, such as EQS, lavaan, LISREL and Mplus, various MD estimators are available to the user. Standard procedures for implementing MD estimators involve a one-step approach applying non-linear optimization techniques. Our implementation differs from the standard approach by utilizing a two-step estimation procedure. In the first step, only a subset of the parameters are estimated using non-linear optimization. In the second step, the remaining parameters are obtained using numerically efficient linear least squares (LLS) methods. Through examples, it is demonstrated that the proposed implementation of MD estimators may be considerably faster than what the standard implementation offer. The proposed procedure will be of particular interest in computationally intensive applications such as simulation, bootstrapping, and other procedures involving re-sampling.

Automatica 66 p. 218-230 Doi: https://doi.org/10.1016/j.automatica.2015.12.007

Automatica 50(10) p. 2597-2605 Doi: https://doi.org/10.1016/j.automatica.2014.08.020