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For GLM model, we have the linearity assumption that the transformed response variable (through) the link function) is linearly dependent on the variables. I'm checking this assumption using the Residuals vs Fitted plot (plot the Deviance residuals against the Transformed fitted value eta_i) and have the plot shown below.
I wonder if the plot below means that this linearity assumption is not valid?

enter image description here

gung - Reinstate Monica
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JaFranke
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    Take a look at the R DHARMa package - it's really hard to assess GLM assumptions using this kind of residual plot. https://cran.r-project.org/web/packages/DHARMa/vignettes/DHARMa.html – Alex J May 03 '23 at 22:57

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It is best not to use those plots for non-OLS regression models (cf.: Interpretation of plot (glm.model)). If you want a test of the assumption of linearity (on the transformed scale), you can add polynomial or spline terms beyond the linear term and test them as a set.

gung - Reinstate Monica
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