International Journal of Statistics and Probability; Vol. 10, No. 2; March 2021 ISSN 1927-7032 E-ISSN 1927-7040 Published by Canadian Center of Science and Education 138 Comparative Performance of Estimation Maximization Among Residual Estimators: A Structural Equation Modelling Perspective A. R. Abdul-Aziz 1 (PhD), Albert Luguterah 2 (PhD) & Bashiru I. I. Saeed 3 (PhD) 1 Department of Mathematics & Statistics, Kumasi Technical University, Kumasi, Ghana. 2 Department of Statistics, Faculty of Mathematical Sciences, C.K. Tedam University of Technology and Applied Sciences (CKT-UTAS), Navrongo, Ghana. 3 Department of Statistical Sciences, Tamale Technical University (TaTU), Tamale, Ghana. Correspondence: Abdul-Aziz A. R., Department of mathematics & Statistics, Kumasi Technical University, Kumasi, Ghana. E-mail: agbazorlic@gmail.com Received: Decmeber 14, 2020 Accepted: February 1, 2021 Online Published: February 25, 2021 doi:10.5539/ijsp.v10n2p138 URL: https://doi.org/10.5539/ijsp.v10n2p138 Abstract As the concept of methodology has advanced, varied methods of estimating residuals have been developed including regression method, Bartlett’s method and Anderson-Rubin’s method. The study utilized estimation maximization approach together with other methods of estimating residuals under the structural equation model. The results showed that the strength of the existing methods in structural equation modelling are the weaknesses of the estimation maximization method, and vice versa. It was, therefore, found that from the comparative model fit information that the Bartlett’s based method gave better residual parameter estimates compared to the Regression based and the Anderson Rubin based methods. However, the estimation maximization method gave better residual parameter estimates than the other three existing methods; the Regression, Bartlett’s and the Anderson Rubin based methods. Keywords: estimation maximization, estimators, structural equation modelling, maximum likelihood 1. Introduction Structural equation models (SEM) have been successfully utilised in different research areas, including educational studies (Miranda & Russell, 2011; Saçkes, 2014), clinical psychology (Little, 2013; Löfholm et al., 2014), developmental psychology (Geiser et al., 2010), organizational studies (Binnewies et al., 2010; Kiersch & Byrne, 2015; Mahlke et al., 2016), and Multi-Trait Multi-Method (MTMM) analysis (Carretero-Dios et al., 2011). Observed variables in SEM research are most frequently not weighed on a continuous but rather on a discrete scale (i.e., categorical dependent variables), imposing additional challenges for the estimation process. Varied methods utilized in SEM to estimate estimators could be viewed based on Maximum Likelihood (ML) covariance method as well as component-based approach such as Partial Least Squares (PLS) and Generalized Structured Component Analysis (GSCA). The frequentist approach (such as ML, PLS, GSCA) and the Bayesian method such as Markov Chain Monte Carlo (MCMC) are other methods used in SEM. Methods such as the covariance based were developed for modelling, evaluating as well as validating. On the other hand, the component-based methods were meant to achieve how to compute and predict (Tenenhaus, 2008). In simple sense, the main difference is that covariance based was designed to test models while the component-based methods were meant to provide succinct meaning to variances as well as predict (Hulland et al., 2010; Tenenhaus, 2008). Meanwhile the frequentist technique usually identifies values of parameters which are due to measured data whereas the Bayesian methods look at estimate obtained from a parameter which are theoretical depictions of relations that rely on measured data. Again, adding to the varied reasons and dimensions of ML, PLS, GSCA, as well as MCMC usually varies in terms of how robust they appear due to different data scenarios. This is attributable, but not limited, to the size of the sample, variables considered, misspecifying the model as well as the kind of measurement-manifest observation link. Inference and deductions made from outcomes of modelling generally rely on the methods adopted and implemented in SEM. It remains though to point out whether hypothetical model normally presents correct information based on an application of a study or simulated study that has the capacity to shed light on the effect of misspecified parameter among methodologies of estimations (Asparouhov & Muthén, 2010; Hwang, et al., 2010). Moreover, the degree upon