Two-stage Circular-circular Regression with Rounding Error: An Application to Cataract Surgery Data
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In many real-life scenarios, the response and the covariate are circular in nature. In statistical literature, circular-circular regression models and estimation of associated parameters have been discussed and illustrated with various real-life applications. In this paper, data arising from post-operative monitoring of cataract patients is considered where measurements on the angular response and the covariate are rounded. However, there are no models to deal with rounded measurements on response as well as a covariate in the literature. The Möbius transformation based is developed for such data. We propose Bayesian estimation of the model parameters using the MCMC algorithm. Simulation results show the superiority of the performance of the proposed method over existing models. The method is applied to analyse a real dataset on astigmatism due to SICS, Snare and Conventional Phacoemulsification types of cataract surgery and the result would help effective decision making during post-operative care.
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