clogit in R: original variable or demeaned? 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.
 A: As nicely explained in this document:

The exponentiated conditional logistic regression coefficients have
  the same odds-ratio interpretation as ordinary logistic estimates.
Conditional logistic regression differs from ordinary logistic
  regression in that the data are divided into groups and, within each
  group, the observed probability of positive outcome is either
  predetermined due to the data construction (such as matched
  case–control)  or  in  part  determined  because  of  unobserved 
  differences  across  the  groups.  Thus,  the  likelihood  of  the 
  data depends  on  the  conditional  probabilities—the  probability  of
  the  observed  pattern  of  positive  and  negative  responses  within
  group  conditional  on  that  number  of  positive  outcomes  being 
  observed.  Terms  that  have  a  constant  within-group  effect  on 
  the unconditional  probabilities—such  as  intercepts  and  variables 
  that  do  not  vary—cancel  in  the  formation  of  these  conditional
  probabilities and so remain unestimated.

In other words, the difference between conditional logit and regular logit regressions comes from how you estimate the probability of a positive outcome for a given observation, not from how you interpret odds ratios (i.e. the exponentiated coefficients). In the conditional logit model, the estimated probability of observing y_i=1 for a given observation is conditional to the number of 1s that are observed in a given group.
If you are interested in the equations that show how this conditional probability works, a simple starting point is the Stata reference manual for clogit.
