Figure 3.

(a) The comparison between the efficiency augmented and bias adjusted estimators for binary outcomes when $\left({\gamma }_0,\kappa \right)=\left(\mathrm{0,4}\right)$. Here the median of $\mid {\widehat{\theta }}_{\text{aug}}-{\widehat{\theta }}_{\text{adj}}|/{\text{esd}}_{\text{adj}}$ over 5000 simulations is 0.02 with ${\text{esd}}_{\text{adj}}$ being the empirical standard deviation of ${\widehat{\theta }}_{\text{adj}}$ over 5000 simulations. (b) The comparison between the efficiency augmented and bias adjusted estimators for binary outcomes when $\left({\gamma }_0,\kappa \right)=\left(\mathrm{1,4}\right)$. Here the median of $\left|{\widehat{\theta }}_{\text{aug}}-{\widehat{\theta }}_{\text{adj}}\right|/{\text{esd}}_{\text{adj}}$ over 5000 simulations is 0.02 with ${\text{esd}}_{\text{adj}}$ being the empirical standard deviation of ${\widehat{\theta }}_{\text{adj}}$ over 5000 simulations.