# Solved – Likelihood ratio test for poisson vs negative binomial GLM

I am trying to decide whether a poisson or negative binomial GLM is the better model for analysing my data. The models being:

``mal_NB <- glm.nb(own_stability ~ own_treatment +                           partner_treatment,                         data = compiled_mal_2, link = log) mal_poisson <- glm(own_stability ~ own_treatment +                      partner_treatment,                    family = poisson(link = "log"), data = compiled_mal_2) ``

I have two main questions, firstly, can I use a likelihood ratio test to compare the two (i.e. the `lrtest()` function in R. Secondly, how do I interpret the output (see below) of this test?

``> lrtest(mal_poisson, mal_NB) Likelihood ratio test  Model 1: own_stability ~ own_treatment + partner_treatment Model 2: own_stability ~ own_treatment + partner_treatment   #Df  LogLik Df  Chisq Pr(>Chisq)     1   5 -365.02                          2   6 -152.30  1 425.42  < 2.2e-16 *** --- Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 ``

** from the comments: Dispersion coefficients of both models are 0.83 or 1.34 and 16.37 or 15.81 (via two different methods) for negative binomial and poisson models, respectively. The AIC of poisson model = 740 and negative binomial model = 316 **

And residual plot for a poisson GLM, neither looks great (poisson maybe a little better) Contents

Check the documentation for the `countreg` R package here: https://cran.r-project.org/web/packages/pscl/vignettes/countreg.pdf as well as for rootograms: https://arxiv.org/pdf/1605.01311.pdf