# Interpret zero-inflated negative binomial regression

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?