Conditional logistic regression is a fixed effects model. If you're modeling the dependent variable $y$, a glm fixed effect model doesn't actually model $y$. Instead, the glm fixed effect models measure $y-mean(y)$ for a particular group. I think that this is not the case for a conditional logistic regression. The coefficients of the regression can be interpreted in the space of $y$. Is that correct?
My particular situation:
I am running a conditional logit with clogit in R, from the
survival package. Are the coefficients returned to be interpreted in the space of $y$, or in the space of something like $y-mean(y)$?
Normally the difference isn't very relevant; one would interpret the coefficient roughly the same either way. However, in my case one of the independent variables is fitted as a spline. Specifically, it is a restricted cubic spline, as calculated from
rcspline.eval in the Hmisc package.
clogit produces a coefficient for each knot of the spline, and in order to interpret the overall effect of the variable one needs to reconstruct the spline from the coefficients (using
rcspline.restate). I want to make sure that I should be looking at the shape of this spline in the range of $y$ (which in my case is 0-100) or in the range of something like $y-mean(y)$ (in this case, $mean(y)$ is the same for all groups: 50). If it is the case that the space is shifted this will be particularly weird for a spline, because presumably the knots should also be shifted somehow.