Generalized Linear Model (GLM) is popular because it can deal with a wide range of data with different response variable types (such as binomial_, Poisson, or _multinomial).Comparing to the non-linear models, such as the neural networks or tree-based models, the linear models may not be that powerful in terms of prediction. But the easiness in interpretation makes it still attractive, especially when we need to understand how each of the predictors is influencing the outcome.The shortcomings of GLM are as obvious as its advantages. The linear relationship may not always hold and it is really sensitive to outliers. Therefore, it’s not wise to fit a GLM without diagnosing.In this post, I am going to briefly talk about how to diagnose a generalized linear model. The implementation will be shown in R codes.There are mainly two types of diagnostic methods. One is outliers detection, and the other one is model assumptions checking.

Residuals

Before diving into the diagnoses, we need to be familiar with several types of residuals because we will use them throughout the post. In the Gaussian linear model, the concept of residual is very straight forward which basically describes the difference between the predicted value (by the fitted model) and the data.

Response residuals

In the GLM, it is called “response” residuals, which is just a notation to be differentiated from other types of residuals.The variance of the response is no more constant in GLM, which leads us to make some modifications to the residuals.If we rescale the response residual by the standard error of the estimates, it becomes the Pearson residual.

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