The Effect of Weighting Data on the Goodness of Fit Indicators of the Six Sigma Structural Equation Modeling

Abstract

The main core of Structural Equation Modeling (SEM) is the parameter estimation process. This process implies a variance-covariance matrix Σ that is close as possible to the sample variance-covariance matrix of data input (S). The six Sigma survey uses ordinal (rank) values from 1 to 5. There are several weighted correlation coefficients that overcome the problems of assigning equal weights to each rank and provide a locally most powerful rank test. This paper extends the SEM estimation method by adding the ordinal weighted techniques to enhance the goodness of fit indicators.  A two data sets of the Six Sigma model with different statistics properties are used to investigate this idea.   The weight 1.3 enhances the goodness of fit indicators with data set that has a negative skewness, and the weight 0.7 enhances the goodness of fit indicators with data set that has a positive skewness through treating the top-rankings.