Convergence rate in structural equation models - analysis of estimation methods and implications in the number of observations

Abstract

Structural Equation Modeling (SEM) is used to analyze the causal relationships between observable and unobservable variables. Among the assumptions considered, but not essential, for the application of the SEM are the presence of multivariate normality between the data, and the need for a large number of observations, in order to obtain the variances and covariances between the variables. It is not always possible to have access to a sufficiently large number of observations to enable the calculation of parameters, and the convergence of the iterative algorithm is one of the problems in obtaining the results. This work investigates the convergence of iterative algorithms, which minimize the variation of parameters, through a stipulated convergence rate, using the Maximum Likelihood (ML) and Generalized Least Squares (GLS) estimation methods on structural equation models using confirmatory factor analysis (CFA) and regression models. Convergences were evaluated in relation to the number of observations, in order to obtain a minimum quantity sufficient for a convergence rate above 50%. The calculations were performed in the statistical environment R^® version 3.4.4, and the results obtained showed a convergence rate above 50% for models estimated by GLS, even with the data showing lack of multivariate normality, kurtosis and accentuated asymmetry. Thus, it was possible to define a minimum number of observations necessary for an adequate convergence of the iterative algorithms in obtaining the necessary parameters.