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Which is better a Poisson or 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: 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?
Is the Poisson model nested in the negative binomial model?
Thus, the Poisson model is actually nested in the negative binomial model. We can then use a likelihood ratio test to compare these two and test this model assumption. To do this, we will run our model as a Poisson.
Why is the likelihood ratio test of Poisson non standard?
As a final detail: The likelihood ratio test of Poisson vs. NB is non-standard because the parameter theta = infinity is on the boundary of the parameter space. Therefore, the p-value from the chi-squared distribution has to be halved (similar to a one-sided test).
Which is the best negative binomial regression model?
The zinb model has two parts, a negative binomial count model and the logit model for predicting excess zeros, so you might want to review these Data Analysis Example pages, Negative Binomial Regression and Logit Regression. Since zinb has both a count model and a logit model, each of the two models should have good predictors.
What is the GOF test for negative binomial model?
The model estimates the dispersion parameter at about the value that we set for theta (i.e., 5) when generating random variates. The GOF test indicates that the negative binomial model fits the data.
How to fit a negative binomial regression in R?
It would appear that the negative binomial distribution would better approximate the distribution of the counts. To fit a negative binomial model in R we turn to the glm.nb () function in the MASS package (a package that comes installed with R). Again we only show part of the summary output:
What is the AIC of a negative binomial model?
** 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 **
How is deviance and likelihood ratio used in Poisson regression?
Deviance or Log Likelihood Ratio test for Poisson regression Both are goodness-of-fit test statistics which compare 2 models, where the larger model is the saturated model (which fits the data perfectly and explains all of the variability). Pearson and Likelihood Ratio Test Statistics
How to do likelihood ratio test for generalized linear models?
Computes the likelihood ratio test for the coefficients of a generalized linear model. an object that stores the results of glm fit of the model under the null hypothesis. an object that stores the results of glm fit of the model under the alternative hypothesis.
How to use a maximum likelihood estimator in GLM?
Using a “maximum likelihood” estimator … (i.e. modify the code above to maximize the likelihood of an intercept-only model) Are these estimates equal? Compute (and report) the log-likelihood, the number of parameters, AIC and BIC of the null model and of AIC, and BIC of the salinity logistic regression in the lab.