| The motivation of the present work comes from experimental questions in the visual sciences in which ordered bivariate observations are considered. The questions of methodological interest are related to the covariance structure among the ordered observations, the corresponding induced-ordered observations and additional covariates. For example, the study of the association between the duration of treatment and a concomitant visual outcome (e.g., the visual acuity) in the eye, which is selected according to the ordered (within-subject) primary outcome (e.g., the intra ocular pressure), requires the derivation of the covariance structure among the ordered observations, the induced ordered observations, and a covariate. In this work, the necessary covariance structures between order and induced order observations are obtained under certain (e.g., permutation symmetric) conditions related to the original dependence structure of the primary vector of observations, the concomitant vector, and a covariate. |
