Proportional Odds Model

Generalized Ordinal Logistic Regression for Ordered Response Variables

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 [Read more…] about Generalized Ordinal Logistic Regression for Ordered Response Variables

When Dependent Variables Are Not Fit for Linear Models, Now What?

by Karen Grace-Martin 28 Comments

When your dependent variable is not continuous, unbounded, and measured on an interval or ratio scale, your model will not meet the assumptions of linear models.

Today I’m going to go into more detail about 6 common types of dependent variables that are not continuous, unbounded, and measured on an interval or ratio scale and the tests that work instead.

Side note: the usual advice is to use nonparametric tests when normality [Read more…] about When Dependent Variables Are Not Fit for Linear Models, Now What?

Logistic Regression Models for Multinomial and Ordinal Variables

by Karen Grace-Martin 59 Comments

Multinomial Logistic Regression

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 [Read more…] about Logistic Regression Models for Multinomial and Ordinal Variables