At what level are covariates held constant in multiple logistic regression? I'm running a multiple logistic regression with several continuous and categorical covariates. I was wondering how to interpret the results of each covariate if the others are held constant. At what level are continuous control variables held? Are they held at their mean?
I believe that for categorical control variables, the reference category is the level at which it is held. What if I want to hold it to another level, such as one coded, 1 or 2?     
 A: Coding really doesn't matter, because when it comes down to it, regression coefficients are always based on slope, i.e., $\Delta y/\Delta x$.  Categorical factors are always broken down to either $k-1$ dummy indicators for each $k$-level factor (corner point coding, level-1's $\Delta y/\Delta x$ goes to constant term) or $k$ dummy indicator variables (sum-to-zero constraints, no constant term).  
Fundamental to regression is also the concept that $x$-predictors are not random variables, hence, the levels of every $x$-variable are supposed to be experimentally controlled values, which can in reality be set by e.g. a variometer.  For example, if age is a predictor, then the model will assume that at each age $18, 19, \ldots, 85+$ you enrolled experimental subjects for which $y$ was measured.  After all, this is what is done for each level of a categorical factor. 
Regarding inferential tests of hypotheses, once you have overcome coding issues, there is a series of partial $F$-tests, which can be employed to address your specific question.   
There is one caveat to tell students when learning regression, for e.g. serum plasma protein expression or mineral (element) concentrations, which is that, instead of thinking about a change in $y$ for a one-unit change in $x$, or concentration, for a significant positive slope the clinical interpretation is that subjects with greater $y$-values had greater $x$-values.
