A hybrid transformation approach for common scaling on various type Likert scales in Bayesian structural equation modeling

Almost all scientists benefit from using questionnaire forms in performing statistical analysis. In most cases, these forms consist of mixed-type scales. To analyze such scales is inconvenient because of the measurement differences, and this problem remains unsolved. In many studies, analysis of mixed-type scales is limited based on the score points of the factors. This study proposes an alternative approach to combine mixed-type scale data using linear transformation functions. Using this approach, it is possible to transform mixed data to the same scale, with the main benefit of allowing the analysis of the mixed data. It also makes it possible to interpret among different types of scales. We show that this transformation approach minimizes the loss of information between the original scale structure and the transformed data. To show the usefulness of our approach, we consider Bayesian structural equation modeling (SEM) within the threshold value approach. Application studies demonstrate that our transformation performs well, especially in the presence of non normality. The transformation approach also gains an advantage with respect to timing costs and the simplicity of the models.