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Publication date: 04/21/2023

Image shown hereStatistical Details for Models with Categorical Predictors

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:

Equation shown here

where

K = # of continuous predictors

P = # of categorical predictors

θk = theta parameter for the kth continuous predictor

xik = the value of the kth continuous predictor for subject i

xjk = the value of the kth continuous predictor for subject j

Equation shown here = the correlation between the observed level of predictor p for subject i and the observed level of predictor p for subject j

There is a τ parameter for each combination of levels of a categorical variable, where τij corresponds 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. See Qian et al. (2012).

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