Similarity-based model for ordered categorical data

In a large variety of applications, the data for a variable we wish to explain are ordered and categorical. In this paper, we present a new similarity-based model for the scenario and investigate its properties. We establish that the process is ψ-mixing and strictly stationary and derive the explicit form of the autocorrelation function in some special cases. Consistency and asymptotic normality of the maximum likelihood estimator of the model’s parameters are proven. A simulation study supports our findings. The results are applied to the Netflix data set, comprised of a survey on users’ grading of movies.