The estimate of <i>β</i>₁ (or β˜1) and its standard error for data simulated under ZINB when <b><i>ϕ</i></b>_<b>c</b> = <b>20%</b> and <b>γ</b>_<b>1</b> = <b>0.4</b>.

<p>The figure displays box-plots of estimates and their standard errors for the covariate effect on the log-odds of structural zeros for ZIP and ZINB method and on the log-odds of zeros for hurdle models from 1000 replications when <i>γ</i>₁ = 0.4. For each box of the boxplots, the center line represents the median, the bottom line represents the 25th percentiles and the top line represents the 75th percentiles. The whiskers of the boxplots show 1.5 interquartile range (IQR) below the 25th percentiles and 1.5 IQR above the 75th percentiles, and outliers are represented by small circles. Panels <b>(A1)</b>, <b>(C1)</b> and <b>(E1)</b> show the estimates of <i>β</i>₁ for consonant, neutral and dissonant effect case, respectively. The horizontal line in these panels represents the true value of <i>β</i>₁, which is −0.349 in <b>(A1)</b>, 0 in <b>(C1)</b> and 0.287 in <b>(E1)</b>. Panels <b>(A2)</b>, <b>(C2)</b> and <b>(E2)</b> show the estimates of <math><mrow><msub><mi>β</mi><mo>˜</mo><mn>1</mn></msub></mrow></math> for consonant, neutral and dissonant effect case, respectively. The horizontal line in these panels represents the true value of <math><mrow><msub><mi>β</mi><mo>˜</mo><mn>1</mn></msub></mrow></math>, which is −0.420 in <b>(A2)</b>, −0.240 in <b>(C2)</b> and −0.070 in <b>(E2)</b>. The bias, standard deviation (SD), and root mean square error (RMSE) of the estimates are shown above the box-plot for each method. Panel <b>(B1)</b>, <b>(D1)</b> and <b>(F1)</b> show the SEs of the estimates for <i>β</i>₁, and panel <b>(B2)</b>, <b>(D2)</b> and <b>(F2)</b> show the SEs of the estimates for <math><mrow><msub><mi>β</mi><mo>˜</mo><mn>1</mn></msub></mrow></math>. The mean and standard deviation (SD) of the standard error (SE) estimations are shown above the box-plot for each method.