Let's assume we made a survey where participants had to evaluate us on a scale from 1 to 5. We want to analyse how different variables (let's say gender or age for instance) have an effect on the answers.
As we have discrete data, my first idea was to use a $\chi^2$-test for independence, however that would not reflect the "order" of the different answers (the test does not care about "3 is the midpoint between 2 and 4" and other similar relationships).
For that matter, I thought about fitting a linear regression model. Apart from that advantage, it is also easier to include multiple variables at the same time. However, I am worried that the discrete nature of the output makes regression unsuitable.
Finally, I considered working on our problem as a multinomial classification one, but we are back at the "ordering" issue.
What is the best way to attack this problem?