# interpretation of model coefficient in logistic regression

In simple logistic regression, a common interpretation of the model coefficient $$\beta$$ is that a 'one-unit increase in the independent variable is associated with an increase of the log-odds ratio of the outcome variable by $$\beta$$'). This is already answered here.

What confused me is that the logit function is not linear with respect to $$x$$, so how can a one-unit increase in $$x$$ lead to a constant change in the log-odds ratio?

$$\ln\left({\frac{p}{1-p}}\right) = \mathbf{Xb}$$
where $$\mathbf{Xb}$$ is the linear predictor, $$\mathbf{X}$$ being the model matrix of explanatory variables and $$\mathbf{b}$$ the vector of coefficients. $$\ln\left({\frac{p}{1-p}}\right)$$ is the logit function (log of the odds).
Therefore every component of $$\mathbf{X}$$ (eg, an individual explanatory variable) is proportional to the log odds and so any change in one of them has a linear effect on it.