Interpreting coefficients in a logistic regression model with a categorical variable having more than 2 levels There is quite some content online interpreting odds in a logistic model with a dichotomous predictor.  My problem is understanding coefficients when there are more than 2 levels for a categorical variable.  How do you define the odds then?
Data: 
X is a single categorical predictor with 4 levels: teenager, adult, mature, senior.
       Y: 1=smoking, 0=non smoking.

LR:  We use n-1 dummy variables.  
     I chose adult as the reference bin as it had the highest concentration. (ok??)

________ | Intercepts   | p
adult    |    -4.3801   | 0
teenager |    -0.32456  | 0
mature   |     1.45119  | 0
old      |    -0.9891   | 0

Interpreting the coefficients
Teenager: Teen is less likely to smoke (w.r.t adult?). In fact, a teen is 28% (exp-0.32456 -1) less likely to smoke THAN AN ADULT.  Is odds of teenager smoking always mentioned against the reference group?
Mature: Matures is more to smoke (w.r.t adult?). In fact, a mature is 326% more likely to smoke THAN AN ADULT.  Is odds of mature smoking always mentioned against the reference group? 
 A: If you write out the fitted model for the log odds of smoking
$$\log \frac{\Pr(Y=1)}{\Pr(Y=0)} = -4.380\,1 + -0.324\,56\ I_\mathrm{teen} + 1.451\,19 \ I_\mathrm{mature} + -0.989\,1\ I_\mathrm{old}$$
where the dummies are
$$I_\mathrm{teen}=\left\{
\begin{array}{l l} 0 & X\neq\mathrm{teenager}\\ 1& X=\mathrm{teenager}\\ \end{array}\right.$$ &c., you can confirm your calculations. Note though that "likely" is ambiguous—it might be taken as referring to probability—& you might prefer to say something like "the odds of a teenager's smoking are 28% lower than those of an adult's smoking" in a formal or didactic context.
A: It is important to understand that logistic regression parameters are only true locally. This means that the relative impact of each estimate will change depending on the value of your independent variables. Here is a paper that can helps explain things. 
A: if $y = F(\beta x) $ and $y\:  \epsilon\: (1,0) $ 
where $F(x) $ is a logit function then  $dy/dx_1 \neq dy/dx_2 $. This is because of the chain rule as $dy/dx = \frac{dy}{dF(x)}\frac{ dF(x)}{dx} $. If you look at a logit function  
You will see that the slope of x changes depending on where you are on the curve. In practice this means that you only interpret rank and sign in a logistic regression as the magnitude of the impact will depend on how you parameters and variables interact with the logit function
