Dear R crew: 
 
I am sorry this question has been posted before, but I can't seem to solve
this problem yet. 
I have a simple dataset consisting of two variables: cestode intensity and
chick size (defined as CAPI). 
Intensity is a count and clearly overdispersed, with way too many zeroes. 
I'm interested in looking at the association between these two variables,
i.e. how well does chick size predict tape intensity?
 
Since I have a small sample size, I fit a zero inflated negat. Binomial (not
Poisson) model using the "pscl" package. 
 
I built tried two models and got the outputs below. 
 
> model <- zeroinfl(Int_Cesto ~ CAPI, dist = "negbin", EM = TRUE)
 
Call:
zeroinfl(formula = Int_Cesto ~ CAPI, dist = "negbin", EM = TRUE)
 
Count model coefficients (negbin with log link):
(Intercept)         CAPI  
   -2.99182      0.06817  
Theta = 0.4528 
 
Zero-inflation model coefficients (binomial with logit link):
(Intercept)         CAPI  
    12.1364      -0.1572  
 
> summary(model)
 
Call:
zeroinfl(formula = Int_Cesto ~ CAPI, dist = "negbin", EM = TRUE)
 
Pearson residuals:
     Min       1Q   Median       3Q      Max 
-0.62751 -0.38842 -0.21303 -0.06899  7.29566 
 
Count model coefficients (negbin with log link):
            Estimate Std. Error z value Pr(>|z|)  
(Intercept) -2.99182    3.39555  -0.881   0.3783  
CAPI         0.06817    0.04098   1.664   0.0962 .
Log(theta)  -0.79222    0.45031  -1.759   0.0785 .
 
Zero-inflation model coefficients (binomial with logit link):
            Estimate Std. Error z value Pr(>|z|)   
(Intercept) 12.13636    3.71918   3.263  0.00110 **
CAPI        -0.15720    0.04989  -3.151  0.00163 **
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
 
Theta = 0.4528 
Number of iterations in BFGS optimization: 1 
Log-likelihood: -140.2 on 5 Df
  
QUESTIONS
 
1. Is my model adequately specified?
 
2. CAPI is included in blocks 1 of output containing negative binomial
regression coefficients for CAPI, and is also included also in block 2
corresponding to the inflation model. Does this make sense?  
 
If I specify my model slightly differently, I get what I believe is more
reasonable results:
 
> model12 <- zeroinfl(Int_Cesto ~ 1|CAPI, dist = "negbin", EM = TRUE)
> model12
 
Call:
zeroinfl(formula = Int_Cesto ~ 1 | CAPI, dist = "negbin", EM = TRUE)
 
Count model coefficients (negbin with log link):
(Intercept)  
      2.692  
Theta = 0.4346 
 
Zero-inflation model coefficients (binomial with logit link):
(Intercept)         CAPI  
    13.2476      -0.1708  
 
> summary(model12)
 
Call:
zeroinfl(formula = Int_Cesto ~ 1 | CAPI, dist = "negbin", EM = TRUE)
 
Pearson residuals:
     Min       1Q   Median       3Q      Max 
-0.61616 -0.36902 -0.19466 -0.06666  4.85481 
 
Count model coefficients (negbin with log link):
            Estimate Std. Error z value Pr(>|z|)    
(Intercept)   2.6924     0.3031   8.883   <2e-16 ***
Log(theta)   -0.8334     0.4082  -2.042   0.0412 *  
 
Zero-inflation model coefficients (binomial with logit link):
            Estimate Std. Error z value Pr(>|z|)    
(Intercept) 13.24757    3.64531   3.634 0.000279 ***
CAPI        -0.17078    0.04921  -3.471 0.000519 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
 
Theta = 0.4346 
Number of iterations in BFGS optimization: 1 
Log-likelihood: -141.9 on 4 Df
 
QUESTION:
 
1.    Is this model specification and output more reasonable?
2.    CAPI appears only in the second block that corresponds to the
inflation model.
 
 
Thanks in advance!
Luciano      
 

 

 

 


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