In my thesis I am using logistic regression models (either binomial or ordinal, depending on the type of the dependent variable) to analyse the association between environmental quality and socio-demographic characteristics.
The implementation in R was easy and I obtained reliable results. However, I am struggling with a rather simple problem: my supervisor asked me to also specify the regression models in a formula. What is the best way to do that for logistic regression?
Let's say my (simplified) regression models evaluates the influence of age, gender and income on whether a person rates the environmental quality as "good" or "bad". Would the following be the correct formula for the model to state in my thesis? Or is there any better was to state the model as a formula?
$$ P(\text{envquality = bad}) = \frac{1}{1+e^{-(\beta_0 + \beta_1 \cdot {\rm age} + \beta_2 \cdot {\rm gender} + \beta_2 \cdot {\rm income})}} $$
What does the formula for an ordinal logistic regression model look like?
R
code. I believe stats.stackexchange.com/q/89474/919 contains answers and some discussion. $\endgroup$