Fig. 1

Simulations results for bias, coverage probability and standard error for both \( \hat{\beta_1} \) and \( \hat{\mathrm{RR}} \). Panel (a) and (b) plot the simulation results for \( \hat{\beta_1} \) and panel (c) and (d) plot the simulation results for \( \hat{\mathrm{RR}} \), when errors are normally (or logistically) distributed with mean (or location) 0 and standard deviation (or scale) 1, and α₁ = 0,−0.15, and −0.3. Dashed lines are 0, 0.95 and 1 for Bias, Coverage probability and Ratio: Mean/Empirical standard error (SE) respectively, which correspond to no bias, 95% coverage probability and mean and empirical SEs are the same. Normal and logistic linear models mean linear model with the error terms assumed to have normal and logistic distribution respectively