I am trying to fit a negative binomial GLM to fish catch data with month of the year (factor) as my explanatory variable. I have selected the month with the greatest number of catches as my reference level and fitted the model using the
glm.nb() function from the MASS package.
anova(model1) shows that the factor
month is significant and my pseudo $R^2$ is about 55%. The problem I have is that months with no catches at all have p-values greater than 0.05 (close to 1), even though I would expect them to be significantly lower than the reference level. Months with only very few catches are significant on the other hand. The output from the
predict() function makes sense, so I think the model should be fine.
Is there a problem with the likelihood test R uses, or am I fitting the wrong model to my data? From other posts I figured that I might have to use a likelihood ratio rather than Wald's test; any suggestions on how to do that in R?
Any help would be greatly appreciated. See model output below, the months with 0 catches are May and June:
Call: glm.nb(formula = NumCaught ~ factor(month) + offset(log(Effort_mins * Nhooks)), data = f[f$Area == "PW", ], init.theta = 1.181267049, link = log) Deviance Residuals: Min 1Q Median 3Q Max -1.8445 -0.7766 -0.2148 0.0000 1.5386 Coefficients: Estimate Std. Error z value Pr(>|z|) (Intercept) -2.647e+00 3.192e-01 -8.292 < 2e-16 *** factor(month)May -2.754e+01 1.024e+05 0.000 0.999785 factor(month)June -2.790e+01 3.122e+05 0.000 0.999929 factor(month)September -2.516e+00 6.516e-01 -3.861 0.000113 *** factor(month)December -1.112e-01 4.403e-01 -0.253 0.800543 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 (Dispersion parameter for Negative Binomial(1.1813) family taken to be 1) Null deviance: 80.420 on 45 degrees of freedom Residual deviance: 36.178 on 41 degrees of freedom AIC: 140.81 Number of Fisher Scoring iterations: 1 Theta: 1.181 Std. Err.: 0.525 2 x log-likelihood: -128.815