Scoring ordianl variables for constructing composite indicators

In order to provide composite indicators of latent variables, for example of customer satisfaction, it is opportune to identify the structure of the latent variable, in terms of the assignment of items to the subscales defining the latent variable. Adopting the reflective model, the impact of four different methods of scoring ordinal variables on the identification of the true structure of latent variables is investigated. A simulation study composed of 5 steps is conducted: (1) simulation of population data with continuous variables measuring a two-dimensional latent variable with known structure; (2) extraction of a number of random samples; (3) discretization of the continuous variables according to different distributional forms; (4) quantification of the ordinal variables obtained in step (3) according to different methods; (5) construction of composite indicators and verification of the correct assignment of variables to subscales by the multiple group method and the factor analysis. Results show that the considered scoring methods have similar performances in assigning items to subscales, and that, when the latent variable is multinormal, the distributional form of the observed ordinal variables is not determinant in suggesting the best scoring method to use.