Briefly, my question is whether the results of a GLM (negative binomial) for a categorical variable should agree with the results of a non parametric test--in this case a kruskal-wallis test.
This question may be an artifact of my particular data set, but I'll attempt to explain. I am looking at fish counts with respect to a number of environmental variables. I have several independent variables, but for now I am interested in the interpretation of Biogenics (number of anemones like Metridium).
A negative binomial GLM suggests that with respect to the reference level 'Biogenics1', the intercepts of both Biogenics2 and Biogenics4 are significantly different. ( In this case the mean count of fish is smaller).
But! If I perform a Kruskal.Wallis test on the same data looking for differences in counts among the levels of Biogenics, there is an insignificant p.value. Maybe I'm all confused on the interpretation of these results (GLM vs kruskal.wallis), and how they should (or should not) relate to one another. Am I way off to think that a significant difference in negative binomial intercepts should translate to significant differences in the mean counts across the levels of a particular factor?
If the GLM is telling me there is a difference between the levels of Biogenics, but Kruskal Wallis says 'no, there is not', is this a problem?
glm.nb(formula = fish.counts ~ Bottom.Type + Lat + Slope + Depth_m + Biogenics + offset(log(area)), data = fish, maxit = 500, init.theta = 0.3167104931, link = log) Deviance Residuals: Min 1Q Median 3Q Max -1.5296 -0.7711 -0.4639 -0.2190 4.4543 Coefficients: Estimate Std. Error z value Pr(>|z|) (Intercept) 100.479364 8.357186 12.023 < 2e-16 *** Bottom.TypeHard 1.864022 0.273399 6.818 9.24e-12 *** Bottom.TypeMixed 0.606571 0.319242 1.900 0.057429 . Lat -2.831241 0.226682 -12.490 < 2e-16 *** Slope -0.037392 0.014754 -2.534 0.011266 * Depth_m -0.010358 0.004173 -2.482 0.013048 * Biogenics2 -1.170058 0.315571 -3.708 0.000209 *** Biogenics3 -0.400999 0.327457 -1.225 0.220732 Biogenics4 -0.753762 0.229439 -3.285 0.001019 ** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 (Dispersion parameter for Negative Binomial(0.3167) family taken to be 1) Null deviance: 936.30 on 702 degrees of freedom Residual deviance: 411.16 on 694 degrees of freedom AIC: 1503.6
kruskal.test(fish.counts ~ Biogenics, data = fish) --- Kruskal-Wallis rank sum test data: fish.counts by Biogenics Kruskal-Wallis chi-squared = 3.45, df = 3, p-value = 0.3273
P.S. I know no one likes 'here's my code, explain the results' types of questions, and so I'm not asking for the specifics of the GLM results, rather how to interpret these two statistical tests in light of each other.
P.SS A likelihood ratio test for the NB GLM suggests that the overal variable Biogenics improves the model fit, and should not be dropped