Generating Correlated Ordinal Categorical Random Samples

Abstract

Ordinal categorical random variables are common in many studies. In different context it is important to appropriately define and simulate from such ordinal categorical random variables with a desired pattern of the correlation structure. This is an important problem in longitudinal studies as well as analyzing clustered data involving ordinal categorical responses. The present paper deals with the theoretical presentation and the construction of multivarite ordinal categorical random variables with some desired patterns of correlation structure. Algorithms for generating samples for the AR-type correlation with particular illustration of AR(1) and AR(2), and equicorrelation are discussed using some urn models. Some key words: Longitudinal autocorrelation; Equicarrelation model; Ordinal categorical random variable; Urn model.