In a multivariable logistic regression model, some continuous predictors are modeled using spline transformations to allow for nonlinear effects, while other continuous predictors are entered as simple linear terms. Can the predictors that remain linear still be interpreted in the usual way, that is, through odds ratios for a one-unit increase, even though other predictors in the same model are modeled with splines?
To be clear I'm not asking about the linear basis term within a spline expansion of the same predictor. I meant a model like:
$$ \text{logit}(P(Y=1)) = \beta_0 + \beta_1 x_1 + \beta_2 x_2 + f(x_3) $$
where $x_1$ and $x_2$ are entered linearly and $x3$ is modeled with a spline. My question is whether $\beta_1$ and $\beta_2$ can still be interpreted in the usual/simple way of presenting single odds ratio values.