Categorical variables in survey

[Bright Tree]

It is more convenient for people to complete the survey if most questions are set with scale options, like income level can be categorized as low, middle, and high income level. But it may be inconvenient for later regression analysis? The variable now is not continuous.

reg expenditure income 

reg expenditure_scaled income_scaled

Could I get the reasonable results for these two kinds of variables or data? Thank you!

[Bright Tree]

For example, if the dependent variable is discrete ranged from 0 to 5, while one of independent variables is categorical, 0 ~2. Could I just use ols, like reg, 2sls, rather than tobit? Thank you!

[Phil Bromiley]

Strictly speaking, the dependent variable is ordinal so you should be using an ordinal logit. On the right-hand side, people often use such ordinal variables as continuous, or you can simply treat them as different categories. The 1st results in ologit y x and the second in ologit y i.x

[Bright Tree]

Dear Professor Bromiley, thank you so much for your helpful advice! I found there was endogeneity in my model.