Abstract:
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Optometric variables such as visual acuity, waveforms and gaze position are measured in ordered categorical scales. They involve multiple variables that are measured multiple times on each subject. The usual mean- and covariance-based inferences are not appropriate for such dataset. We present general nonparametric methods for multivariate repeated measure data in factorial design. Treatment effects are characterized in terms of functionals of distribution functions with the sole assumption of nondegenerate marginal distributions. This model accommodates binary, categorical, discrete and continuous data in a unified manner. Hypotheses are formulated in terms of meaningful nonparametric measures of treatment effects. Wald-type statistic is proposed and its asymptotic properties are investigated. The theory can also be used to construct confidence intervals for the treatment effects. Simulations are conducted to show the finite-sample performance of the proposed methods in comparison with other parametric, nonparametric methods. Data from a study of infantile nystagmus syndrome(INS) investigating the interaction effect between patients’ mental load and gaze position will be analyzed.
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