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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?

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1 Answer 1

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Your interpretation is correct, but not very complete. Just as with OLS regression or any other test, we can say more than "significant" and "not significant". Also, I would say "with respect to the intercept (control)" but just "compared to the control group", but I think that's just semantics.

You haven't shown us any model diagnostics, so it's hard to say if this model is fitting well. But, just from your frequency table, there's not that much zero inflation -- there's certainly some -- but you do have some overdispersion. You might want to look at negative binomial instead of ZIP. Then you might not need zero inflation. To me, at least, that makes interpretation of results a bit more straightforward.

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  • $\begingroup$ thank you for the indications. Which kind of diagnostic tables might be suitable here? $\endgroup$
    – GiorgioS
    Commented Feb 9 at 11:50
  • 1
    $\begingroup$ See this thread for a discussion. $\endgroup$
    – Peter Flom
    Commented Feb 9 at 13:13

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