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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