Likelihood and pls estimators for structural equation modeling: An assessment of sample size, skewness and model misspecification effects

This chapter aims to contribute to a better understanding of partial least squares (PLS) and maximum likelihood (ML) estimators’ properties, through the comparison and evaluation of these estimation methods for structural equation models with latent variables based on customer satisfaction data. Although PLS is a well-established tool to estimate structural equation models, more work is still needed in order to better understand its properties and relative merits when compared to likelihood methods. Despite the controversy over these two estimation techniques, their complexity makes any analytical comparison very difficult to be made. Therefore, it constitutes a fertile ground for conducting simulation studies. This chapter continues the research of Vilares et al. [Comparison of likelihood and PLS estimators for structural equation modelling: a simulation with customer satisfaction data. In: Vinzi, W.E., Chin, W.W., Henseler, J., Wang, H. (eds.) Handbook of Partial Least Squares. Concepts, Methods and Applications, pp. 289–307. Springer Handbooks of Computational Statistics, Springer (2010)], which has compared PLS and ML estimators using Monte Carlo simulation within three different frameworks (symmetric data, skewed data and formative blocks). It also continues to generate the data according to the ECSI (European Customer Satisfaction Index) model with the assumption that the coefficients of the structural and measurement models are known. This new chapter introduces the effect of sample size and includes two different simulations. The first one is conducted in a context of both symmetric data and skewed response data. This simulation is conducted for the sample sizes n = 50, 100, 150, 250, 500, 1,000 and 2,000 and uses reflective blocks. A second simulation includes the presence of model misspecifications (omissions of an existent path) for a sample size of 250 observations and symmetric data. In all simulations the ability of each method to adequately estimate the inner model coefficients and indicator loadings is evaluated. The estimators are analysed in terms of bias and dispersion (standard deviation). Results have shown that overall PLS estimates are generally better than covariance-based estimates. This is particularly true when the data is asymmetric, when estimating the model for smaller sample sizes and for the inner model structure.