Vuong’s test for the presence of zero inflation
| Vuong z-statistic | Model comparison | P value | |
| Raw | −4.982125 | model2>model1 | <0.001*** |
| Akaike information criterion-corrected | 4.978704 | model2>model1 | <0.001*** |
| Bayesian information criterion-corrected | −4.968557 | model2>model1 | <0.001*** |
***p<0.001.