Conditional fixed effects for glme
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I have to reevalutae some old glme results of mine and I ran into a problem. I setup a simple model using the fitglme() function includeing only one fixed effect, a categorical variable indicating the experiment setup. (Similiar to the "supplier" variable in this expample : Fit a Generalized Linear Mixed-Effects Model - MATLAB & Simulink - MathWorks Switzerland). I only got the coefficents of two out of three possible values for the variable, same as in the example linked above. My question is why are the no estimates for the thrid option, supplier_A in case of the example?
Jeff Miller on 5 Aug 2022
I think this is the key sentence from the example page: "Specify the dummy variable encoding as 'effects', so the dummy variable coefficients sum to 0." This means that the estimate for supplier_A is whatever number is needed to make the estimates sum to zero across the three suppliers. It is not separately estimated, so it is not shown.
From the way these models are structured, it is pretty common for there to be only k-1 independent estimates for a variable that takes on k different values. For some models these estimates can be thought of as reflecting a change for each level of the variable relative to the overall mean across all levels. For other models, these estimates can be thought of as reflecting the change for each level of the variable relative to the one missing level. As you can see, a lot depends on the details of how the model is constructed.