If the Gaussian Process model includes categorical predictors, the Gaussian correlation structure is used for the correlation structure. The elements of the R matrix are defined as follows:

There is a τ parameter for each combination of levels of a categorical variable, with τij corresponding to the unique combination formed by the observed levels of subject i and subject j. Thus, the covariance element, rij, depends on the combination of levels of the categorical predictors obtained from the ith and jth observations. For more information, see Qian et al. (2008).