Additional file 1 of A two-phase procedure for non-normal quantitative trait genetic association study ZhangWei LiHuiyun LiZhaohai LiQizhai 2016 The derivations of ρ R , ρ A and ρ D under the null hypothesis. Consistent estimators of ρ R , ρ A and ρ D under the null hypothesis. Additional simulation results for the model selection procedure. Simulation results for the error term following the generalized extreme distribution. Simulation results for the error term following the centralized t distribution. Simulation results for the model with covariates. Additional p-value results of the SNPs in gene DNAH9 for the associated with Anti-CCP Measure. (PDF 179 kb)