Generalizations of the polychoric correlation approach for analyzing survey data

Nowadays surveys are common data source for empirical research in marketing, social sciences, and official statistic. Such studies often focus on correlation analysis. Survey questions typically have answer scales and collect ordered-categorical data. For this type of data a great way to measure association is to estimate polychoric correlation coefficient. It standardly assumes bivariate normal distribution of underlying (latent) variables inferred from ordered-categorical variables. However, that is empirically implausible. In this paper we propose generalizations of the polychoric correlation approach to improve its flexibility. For this purpose bivariate Student and generalized lambda distributions are used. We have performed a simulation studies demonstrating benefits of proposed generalizations. Using the Russia Longitudinal Monitoring Survey data the distributional assumptions are tested. The chi-square goodness of fit test revealed that proposed generalizations allow to increase the number of cases in which the data are consistent with distributional assumptions.