Can I have an Interaction term with ordinal variables in a multiple regression model? My dependent variable is corruption. I want to test the effect of press freedom and democracy on corruption. The measure for press freedom varies from 1-100 and the democracy variable is ordinal scaled from 1-7. Can I make an interaction term between press freedom and democracy?
 A: Yes you can. If $x_1$ is a continuous predictor modelled with a single linear term, & $z_1$, $z_2$ are dummies for a 3-level categorical predictor then the model without interaction for the response $Y$ is
$$\operatorname{E} Y = \alpha + \beta_1 x_1 + \gamma_1 z_1 + \gamma_2 z_2$$
For the 1st level of the categorical predictor $z_1=z_2=0$, &
$$\operatorname{E} Y = \alpha + \beta_1 x_1$$
For the 2nd level $z_1=1$ & $z_2=0$, &
$$\operatorname{E} Y = (\alpha + \gamma_1) + \beta_1 x_1$$
For the 3rd level $z_1=0$ & $z_2=1$, &
$$\operatorname{E} Y = (\alpha + \gamma_2) + \beta_1 x_1$$
So at each level of the categorical predictor the intercepts are different, but the slopes for $x_1$ are the same. If you include interaction terms the model is
$$\operatorname{E} Y = \alpha + \beta_1 x_1 + \gamma_1 z_1 + \gamma_2 z_2 + \delta_1 x_1 z_1 + \delta_2 x_1 z_2$$
For the 1st level of the categorical predictor $z_1=z_2=0$, &
$$\operatorname{E} Y = \alpha + \beta_1 x_1 $$
For the 2nd level $z_1=1$ & $z_2=0$, &
$$\operatorname{E} Y = (\alpha + \gamma_1) + (\beta_1 + \delta_1) x_1$$
For the 3rd level $z_1=0$ & $z_2=1$, &
$$\operatorname{E} Y = (\alpha + \gamma_2) + (\beta_1 + \delta_2) x_1$$
So at each level of the categorical predictor the intercepts & the slopes for $x_1$ are different.
