# Interpretation of a zero-inflated poisson model

I have the following data

str(data)
'data.frame':   768 obs. of  5 variables:
$$PIANTA : chr "C-1-R1-1" "C-1-R1-1" "C-1-R1-2" "C-1-R1-2" ...$$ Trattamento: Factor w/ 4 levels "Controllo","Lidar",..: 1 1 1 1 1 1 1 1 1 1 ...
$$Blocco : Factor w/ 2 levels "1","2": 1 1 1 1 1 1 1 1 1 1 ...$$ Replica    : chr  "R1" "R1" "R1" "R1" ...
\$ Risposta   : num  0 1 0 1 0 3 2 3 2 4 ...


I have a total of 768 observations. I would like to test whether the treatment (Trattamento) has a significant effect with respect to my response variable (Risposta). The response variable is numeric (ranging from 0 to 9) and assumes the value 0 for more than 400 observations. This is my frequency table:

   data counts
1     0    478
2     1    107
3     2     89
4     3     50
5     4     21
6     5     13
7     6      3
8     7      5
9     8      1
10    9      1


Therefore I opted to use a zero-inflated poisson model using the following R code:

model1 <- zeroinfl(Risposta ~ Trattamento | Trattamento, data = data, count.dist = "poisson")

Call:
zeroinfl(formula = Risposta ~ Trattamento | Trattamento, data = data, count.dist = "poisson")

Pearson residuals:
Min      1Q  Median      3Q     Max
-0.8273 -0.6938 -0.4883  0.4219  6.2762

Count model coefficients (poisson with log link):
Estimate Std. Error z value Pr(>|z|)
(Intercept)          0.76103    0.07557  10.071   <2e-16 ***
TrattamentoLidar    -0.11973    0.13009  -0.920    0.357
TrattamentoRecupero -0.18094    0.14447  -1.252    0.210
TrattamentoStandard -0.19740    0.12201  -1.618    0.106

Zero-inflation model coefficients (binomial with logit link):
Estimate Std. Error z value Pr(>|z|)
(Intercept)          -0.3894     0.1778  -2.190 0.028523 *
TrattamentoLidar      0.9323     0.2518   3.703 0.000213 ***
TrattamentoRecupero   1.2351     0.2599   4.752 2.01e-06 ***
TrattamentoStandard   0.3500     0.2578   1.358 0.174542
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Number of iterations in BFGS optimization: 15
Log-likelihood: -939.4 on 8 Df


This is my intepretation:

• Count model coefficients: there is no statistically significant differences on count data among the different treatments
• Zero-inflation model coefficients: there are statistically significant differences on the probability of finding a zero for the treatments "Lidar" and "Recupero" respect to my intercept "control".

Is this interpretation correct? Am I missing something related to the goodness of using this model respect to the type of data I have?