I am ruing a binomial logistic regression with a logit link function in R. My response is factorial [0/1] and I have two multilevel factorial predictors - let's call them a and b where a has 4 factor levels (a1,a2,a3,a4) and b has 9 factor levels(b1,b2...b9). Therefore:
mod <- glm(y~a+b, family=binomial(logit),data=pretend) summary(mod)
The model output would then show all the information about the model as well as the coefficients.
There is a factor level for both a and b missing (a1 and b1) from the summary output. I understand that it is fixed in the "intercept" of the model. I have read that if I want to remove the intercept term and see the estimates for those factor levels I can just add -1 or +0 to the model formula, i.e.:
mod2 <- glm(y~a+b-1, family=binomial(logit),data=pretend)
...OR... mod2 <- glm(y~a+b+0, family=binomial(logit),data=pretend) summary(mod2)
In the new model (mod2) the intercept term is then gone and variable a's factor-level a1 is given amongst the list of coefficients. But, variable b's factor-level b1 is still missing and given that there is no intercept term anymore, how can I interpret the odds-ratio for that factor level then?
Could someone please explain to me how to get the coefficient for b1 too and why this is happening?
Thank you.