Adjusting Structural Equation Modelling Of Spiritual Coping Scale: Use Of The Sattora-Bentler Method As An Alternative To Maximum Likelihood Estimation

Abstract

Background: Structural equation modelling (SEM) is a multivariate analysis method used to investigate direct and indirect effects among several observed or latent variables. In psychology and social sciences, data are often collected through questionnaires or inventories that commonly include Likert scale questions. Multivariate normal distribution is an essential assumption that often does not hold for this kind of data. Through an experiment on spiritual coping, our study aimed to illustrate key problems associated with using the common maximum likelihood (ML) method, and to assess a way for dealing with structural equation models when variables are in categorical form and don’t exhibit a normal and continuous distribution. Methods:Data regarding measurement of spiritual coping and its predictors collected through a questionnaire were analysed. A structural model was developed and specified for spiritual coping. The model was fitted and investigated to assess common fit indices and Sattora-bentler estimators for small samples and non-normal Likert scale data. Data analysis and modelling was done using the EQS statistical software package. Results:It was found that fit indices and parameters encountered underestimation problems when using common ML estimator method. The robust SB-χ method showed the model to have a better fit to the data ((S-B 2 )/ df) = 1.82, CFI = 0.94)). Conclusion:Structural equation modelling using a robust SB-estimator is an appropriate method for analysing complex Likert scale measurements, especially with a small sample size, specifically regarding the spiritual coping scale and similar metrics. INTRODUCTION Nearly everyone working in research fields of psychology and neuropsychiatric diseases is acquainted with the Likerttype scale. The Likert scale was invented by a psychologist called Likert Rensis . Although general applicability of Likert scales has been often questioned, this type of measurement remains an extremely popular methodology in the fields of psychology, public health and nursing research. In fact, it is so widely used in scaling responses in surveys that it is sometimes used interchangeably with rating scales, even though the two are not synonymous. Analysis of data measured on Likert scales is another issue requiring special notation. A variable measured using Likert type questions exists on an ordinal scalegenerally one limited to a few levels. This poses the question of whether we can safely apply statistical methods that rely on assumptions of normality. The issue gets even more problematic when the sample size is small and a complex model needs to be developed to assess a latent variable representative of a health-related phenomenon. Structural equation modelling (SEM) is a statistical methodology that takes a confirmatory (i.e. hypothesistesting) approach to the analysis of a structural theory bearing on some phenomenon. Typically, this theory represents “causal” processes that generate observations on multiple variables. Review of SEM applications during the past 15 years (in psychological research, at least) reveals most measurements to be based on Likert scaled data with estimation of parameters done using maximum likelihood (ML) procedures. When the number of categories is large and the data approximate a normal distribution, failure to address the Adjusting Structural Equation Modelling Of Spiritual Coping Scale: Use Of The Sattora-Bentler Method As An Alternative To Maximum Likelihood Estimation 2 of 7 ordinal form of the data is likely to have negligible consequences; however, this may not be the case in many studies. In psychology and other social sciences, data are often collected through questionnaireswhich use a Likert scale. Multivariate normality is an essential assumption that may not hold for this kind of data. In an experiment on assessing spiritual coping, the aim of our study was to illustrate the problems of using the common maximum likelihood (ML) method, and to assess a way for dealing with structural equation models when variables are in categorical form and don’t follow a normal and continuous distribution. MATERIAL AND METHODS The study population where the data come from contained 120 adolescents in State Welfare Organizations of Tehran database. Data was derived from institutionalized orphan adolescents between 14-20 years of age enrolled in nineteen protector centres of Tehran. A structural model was developed and specified for spiritual coping. The developed scale was called “Institutionalized adolescents spiritual coping scale”. The structural statistical model was fitted and investigated using common fit indices of ML, and Sattora-bentler estimators for small samples and non-normal Likert scale data. SATTORA-BENTLER METHOD () ML methods produce parameter estimators to ensure that observed sample probability is maximized. This method assumes that observed variables have multi-normal distribution. The likelihood function will be: