Quantile regression and REML approach for robust regression of clustered data . - Estoy, May Ann S. (University of the Philippines, 2016)
We proposed two procedure in the estimation of a linear mixed model. Quantile regression and REML are imbedded into the backfitting (QRB) to estimate fixed and random effects in linear mixed model. We further introduce bootstrap in the imbedded quantile regression and REML in backfitting (BootQRB) algorithm. To assess the performance of the proposed methods, the simulation cover a wide range of scenarios including outliers and specification errors. Both QRB and BootQRB are robust to misspecification errors, with high predictive ability and small standard errors (narrow LCI) across all quantiles compared to ordinary least squares and ordinary quantile regression. The proposed estimation methods are also robust to outliers, as exhibited in the estimates of quantiles near the tails of the distribution).