How do I interpret/find the coefficient for an aliased factor?

Question

I've made a binomial model using the glm function in R as:

model <- glm(formula = ym ~ year + class, family = "binomial")

Where year is an integer and class is a factor with 4 levels (class = A, B, C, D). Which gave coefficients:

              Estimate Std. Error z value Pr(>|z|)  
(Intercept)  -12.0538   33.24887  -0.753   0.4512  
year          0.19302    0.01712   0.746   0.4558  
classB        0.19528    0.17428   1.293   0.1961  
classC        0.23886    0.15071   0.722   0.4701  
classD        0.35708    0.13439   1.913   0.0557 .

Ignoring the significance of variables, I'm trying to interpret the coefficients from the model before I go on to improve it. I believe the effect of each is logit(p) = intercept + classAx + classBx + classCx + classDx, where x = 1 only for the class the individual belongs to.

First, what is the coefficient for classA (which has been removed) here? is it -(0.19528+0.23886_0.35708), the negative sum of the other coefficients of class?

Second, while I understand year can be interpreted as an increase of year by one unit corresponds to an increase in logit(p) of 0.19302, for the classes would it simply be membership to class C increases logit(p) by 0.23886?

Answer 1

The coefficient for class A is 0. So if you want to get the logit value for an individual in class A for year X, the formula would read

$$ \widehat{\text{logit}}(p(A,X))= -12.0538+0+0.19302\cdot \text{year}. $$

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for the classes would it simply be membership to class C increases logit(p) by 0.23886?

Yes, compared to class A.