I am trying to estimate a zero-inflated negative binomial model with 11 predictor variables and the number of reported crimes as a response variable. The model seems to work OK, but I’m uncertain on how to interpret the results. Below is my model and the results:

`#estimate zero-inflated NB model zinf.nbi <- zeroinfl(CRIME ~ VAR1 + VAR2 + VAR3 + VAR4 + VAR5 + VAR6 + VAR7 + VAR8 + VAR9 + VAR10 + VAR 11, data = mydata, dist = "negbin") summary(zinf.nbi) > summary(zinf.nbi) Call: zeroinfl(formula = CRIME ~ VAR1 + VAR2 + VAR3 + VAR4 + VAR5 + VAR6 + VAR7 + VAR8 + VAR9 + VAR10 + VAR 11, data = mydata, dist = "negbin") Pearson residuals: Min 1Q Median 3Q Max -0.47719 -0.17583 -0.08080 -0.02709 26.99868 Count model coefficients (negbin with log link): Estimate Std. Error z value Pr(>|z|) (Intercept) -2.682578 0.269317 -9.961 < 2e-16 *** VAR1 1.436770 0.249026 5.770 7.95e-09 *** VAR2 -0.648535 0.268608 -2.414 0.015760 * VAR3 -0.130107 0.239543 -0.543 0.587029 VAR4 -0.008985 0.267949 -0.034 0.973249 VAR5 -0.807941 0.269470 -2.998 0.002715 ** VAR6 -1.396990 0.396299 -3.525 0.000423 *** VAR7 0.314514 0.113696 2.766 0.005670 ** VAR8 -1.959792 0.207233 -9.457 < 2e-16 *** VAR9 0.711452 0.338171 2.104 0.035394 * VAR10 -0.013628 0.132889 -0.103 0.918316 VAR11 0.092719 0.034799 2.664 0.007712 ** Log(theta) -1.429807 0.103981 -13.751 < 2e-16 *** Zero-inflation model coefficients (binomial with logit link): Estimate Std. Error z value Pr(>|z|) (Intercept) 1.14267 0.46786 2.442 0.014593 * VAR1 1.13108 0.51718 2.187 0.028742 * VAR2 -0.68871 0.33832 -2.036 0.041781 * VAR3 0.16412 0.37019 0.443 0.657527 VAR4 0.57907 0.42818 1.352 0.176241 VAR5 0.83822 0.40451 2.072 0.038247 * VAR6 0.02991 0.73117 0.041 0.967368 VAR7 0.01186 0.19025 0.062 0.950282 VAR8 -1.33618 0.39677 -3.368 0.000758 *** VAR9 1.40246 0.39349 3.564 0.000365 *** VAR10 -0.14713 0.22707 -0.648 0.517000 VAR11 -2.71317 0.64939 -4.178 2.94e-05 *** --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Theta = 0.2394 Number of iterations in BFGS optimization: 42 Log-likelihood: -2649 on 25 Df`

As far as I understand, the first block (the count component) is a summary of the full model and can be interpreted as a standard negative binomial model. The second block (the zero component), on the other hand, predicts whether or not the outcome is a certain zero. Now, what I would like to know is:

a) How do I interpret the second block of the model in relation to the first block? As you can see in the results, some variables are significant in both the first and the second block.

b) Which block should I present in my final results? The first block or the second block?

**Answer**

a) Here https://rpubs.com/kaz_yos/pscl-2 is a nice example of how to interpret the results of a ZINB model.

b) Obviusly you have to present both blocks.

Note:

ZINB regression model two separate processes so they produce two sets of coefficients: one for the count part of the model and the other for the logistic part of the model.

A common way of interpreting logistic regression models is to exponentiate the coefficients, which places the coefficients in an odds-ratio scale. With zero-inflated models the logistic part of the model predicts non-occurrence of the outcome.

Here you can fins another example https://stats.idre.ucla.edu/other/dae/.

**Attribution***Source : Link , Question Author : m.ras , Answer Author : Ferran Paüls Vergés*