Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. It only takes a minute to sign up.
Sign up to join this community
I am looking for guidelines on how to interpret residual plots of glm models. Especially poisson, negative binomial, binomial models. What can we expect from these plots when the models are "correct"? (for example, we expect the variance to grow as the predicted value increases, for when dealing with a Poisson model)
I know the answers depend on the models. Any references (or general points to consider) will be helpful/appreciated.
I think this is one of the most challenging parts when doing regression analysis. I also struggle with most of the interpretations (in particular binomial diagnostics are crazy!).
I just stumbled on this post http://www.r-bloggers.com/model-validation-interpreting-residual-plots/ who also linked https://web.archive.org/web/20100202230711/http://statmaster.sdu.dk/courses/st111/module04/module.pdf
what helps me the most is to plot the residuals versus every predictive parameter included AND not included into the model. This means also the ones who were dropped beforehand for to multicolinearity reasons. For this boxplots, conditional scatterplots and normal scatterplots are great. this helps to spot possible errors
In "Forest Analytics with R" (UseR Series) are some good explanations how to interpret residuals for mixed effects models (and glms as well). Good read! https://www.springer.com/gp/book/9781441977618
Someday ago I thought about a website that could collect residual patterns which users can vote to be "ok" and to be "not ok". but I never found that website ;)
I would suggest the methods described in:
Buja, A., Cook, D. Hofmann, H., Lawrence, M. Lee, E.-K., Swayne, D.F and Wickham, H. (2009) Statistical Inference for exploratory data analysis and model diagnostics Phil. Trans. R. Soc. A 2009 367, 4361-4383 doi: 10.1098/rsta.2009.0120
There are a few different ideas, but they mostly come down to simulating data where you know what the true relationship is and that relationship is based on your analysis of the real data. Then you compare the diagnostics from your real data to the diagnostics of the simulated data sets. The vis.test function in the TeachingDemos package for R implements a variation of 1 of the suggestions in the paper. Read the whole paper (not just my very short summarization) for a better understanding.
This question is quite old, but I thought it would be useful to add that, since recently, you can use the DHARMa R package to transform the residuals of any GL(M)M into a standardized space. Once this is done, you can visually assess / test residual problems such as deviations from the distribution, residual dependency on a predictor, heteroskedasticity or autocorrelation in the normal way. See the package vignette for worked-through examples, also other questions on CV here and here.
