Symmetrically dependent models arising in visual assessment data

Given data from bilateral visual assessments on N subjects at k occasions, we consider inference for contralateral correlations (C) between fellow eyes and lateral correlations (L) among p different assessments of the same eye. Under permutation symmetric dependence structure between observations from fellow eyes and among observations from the same eye, we obtain maximum likelihood estimates of L, C, and L-C. Based on the large-sample estimates of the corresponding covariance structures, we test the hypothesis that the association between fellow eyes is constant across time and the hypothesis that lateral and contralateral associations between any two occasions are the same.