When your dependent variable is not continuous, unbounded, and measured on 
an interval or ratio scale, linear models don’t fit. The data just will not meet the assumptions of linear models. But there’s good news, other models exist for many types of dependent variables.
Today I’m going to go into more detail about 6 common types of dependent variables that are either discrete, bounded, or measured on a nominal or ordinal scale and the tests that work for them instead. Some are all of these.
When the response variable for a regression model is categorical, linear models don’t work. Logistic regression is one type of model that does, and it’s relatively straightforward for binary responses.
When the response variable is not just categorical, but ordered categories, the model needs to be able to handle the multiple categories, and ideally, account for the ordering.
An easy-to-understand and common example is level of educational attainment. Depending on the population being studied, some response categories may include:
1 Less than high school
2 Some high school, but no degree
3 Attain GED
4 High school graduate
You can see how there are qualitative differences in these categories that wouldn’t be captured by years of education. You can also see that (more…)
The multinomial (a.k.a. polytomous) logistic regression model is a simple extension of the binomial logistic regression model. They are used when the dependent variable has more than two nominal (unordered) categories.
Dummy coding of independent variables is quite common. In multinomial logistic regression the dependent variable is dummy coded into multiple 1/0 variables. There is a variable for all categories but one, so if there are M categories, there will be M-1 dummy variables. All but one category has its own dummy variable. Each category’s dummy variable has a value of 1 for its category and a 0 for all others. One category, the reference category, doesn’t need its own dummy variable as it is uniquely identified by all the other variables being 0.
The multinomial logistic regression then estimates a separate binary logistic regression model for each of those dummy variables. The result is (more…)