Scale validation conducting confirmatory factor analysis: a monte carlo simulation study with LISREL

Abstract

When psychologists are going to test their theoretical models (at the time of planning the research study), several questions may arise regarding the quality and potential accuracy of the estimation of Confirmatory Factor Analysis (CFA) models under certain applied conditions. For example, one question is the minimum sample size (N) and/or the number of indicators per factor (p/k) that is needed to estimate the CFA models properly. Many of these questions can be answered through simulation studies, because the magnitudes of the population factor loadings (λik) are known in advance. Monte Carlo simulation uses random sampling and statistical modeling to estimate mathematical functions, and is a key tool for studying analytically intractable problems (Harrison, 2010). It is quite frequent to find in the literature simulation studies that use CFA to fit measurement models. However, there is a lack of technical information in the published research to replicate this type of studies, probably due to length limitations. Furthermore, researchers and scholars must often go to numerous and technically complex sources of information to understand the laborious simulation and estimation process. In this paper we present complete technical information to conduct Monte Carlo simulation CFA-studies with PRELIS and LISREL programs. The LISREL program, apart from being one of the most used (and validated) software programs, is historically linked to CFA (Brown, 2015). Although it is a commercial program, there is a free student version that allows performing all the simulation tools and the analysis techniques shown in this work. Through a simulation study, we have evaluated the necessary conditions to test the CFA models fit, so we have chosen population structures formed by a single common factor to design the simulation study and low-moderate population factor loadings. It should be noted that these types of studies generate a considerable volume of information, even when using a simple unifactorial model. This approach was adopted for this study for ease of understanding the principles. Included, however, are the PRELIS and LISREL syntax examples for multidimensional factor structures. In the Supplementary Material (https://figshare.com/s/18eb0e998150d39bc952) we have attached both the simulated data and the CFA results (parameter estimates, standard errors and goodness-of-fit measures).