# Interpreting ZINB - inflation model non-significant

I have a zero-inflated negative binomial model to a dataset (n = 47) with a over-dispersed dependent variable (mean = 6.70, sd = 17.68). The DV counts the number of fatalities in protest events, so the 0 value can be a result of the non-existence of protest, or of the lack of fatalities during the protests.

Thus, I estimate a ZINB model with the formula y ~ x1 + x2 + x3 + x4 | x1 + x2 + x3 + x5 + x6, and an offset.

The results in the inflation model show that no predictors are statistically significant (some of them are significant in the count model). Yet, a Vuong test between the ZINB model and a negative binomial (GLM with link negbin) model, with either all variables or only those in the count model, shows that the ZINB model is superior to the NB models. Neither the Log(theta) coefficient in the count part of the ZINB model or the (Intercept) in the inflation part are significant.

I don't understand this. If the inflation model is no significant, shouldn't a "plain" negative binomial model be better, or at least, indistinguishable? Is the ZINB model really a better fit?

PD. There are no important correlations between predictors that could alter significance values.