having constructed a glm we can pass them through an anova as such: anova(mnegbin1, mnegbin2, test = "Chisq") Likelihood ratio tests of Negative Binomial Models Response: count Model theta Resid. df 2 x log-lik. Test df LR stat. Pr(Chi) 1 origin + substrate + sample 18.46502 1232 -2459.886 2 substrate + sample 18.46502 1232 -2459.886 1 vs 2 0 -1.500666e-11 1 This gives us a comparison of the log likelihoods between the models, but can something similar be done for between residual deviances?: summary(mnegbin1) Null deviance: 5686.16 on 1304 degrees of freedom Residual deviance: 890.24 on 1232 degrees of freedom summary(mnegbin2) Null deviance: 5686.16 on 1304 degrees of freedom Residual deviance: 890.24 on 1232 degrees of freedom In this instance they are of course identical but does that actually tell us anything?