Solved – GLM model validation; Patterns in residuals ? – R

generalized linear modelrvalidation

I have attached an image obtained during my model validation. I fitted a negative binomial GLM to my data and I have 4 models possible with more or less the same residual plots.
I have been reading about GLM as it is the first time that I use this model and it seems that if there is no pattern in the residuals the model is fine. I have to admit that I cannot really decide if my residuals follow a pattern or not. Is there a test that I could use instead of the graph? If you think that there are patterns here what can I do?
I have tried Poisson and quasi poisson as well but there are clear patterns this time.
My response variable is a count variable and I have both categorical and continuous covariates.

Thank you very much for your help!

enter image description here

Best Answer

Here are two tests that you could use:

In the whiteness test, if the autocorrelation function of the residuals is within the confidence interval of the estimates, then it is considered a pass.

In the Independence test, the residuals should not depend on past inputs. The Durbin-Watson statistic is used in this test.

Related Solutions

Generalized Linear Model – Analyzing Residuals from GLM Model with Log Link Function

If you want to check the functional form, you would want to plot the partial residuals vs the predictor

resids = residuals(gl, type="partial")
plot(x, resids)

If the functional form of the predictor is correct, then the relationship between x and the partial residuals would appear linear. The plot does not look linear in your case. When fitting a glm with a log link for poisson data, one would assume that $log( E(y) ) = \beta_0 + \beta_x$ so that $E(y) = e^{\beta_0 + \beta_x}$. In your simulation, you have an additional term added to the poisson model which alters the mean variance relationship of the poisson model which assumes that $E(Y)=Var(Y)$. In your case, $E(Y) = Var(Y) + 10$. To check the mean variance relationship, you could plot the pearson residuals versus the fitted values. These residuals should have constant variance and mean 1 if the mean variance relationship is correctly specified.

plot( fitted(g1), residuals(g1, type="pearson"))

Solved – Interpret residual vs fitted values for negative binomial GLM

It is difficult to assess the fit of the negative binomial (or any other integer-valued GLM for that matter) with deviance residuals, because also a perfectly fitting NB model may exhibit inhomogeneous deviance residuals.

However, 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.

Best Answer

Related Solutions

Generalized Linear Model – Analyzing Residuals from GLM Model with Log Link Function

Solved – Interpret residual vs fitted values for negative binomial GLM

Related Question