How to Interpret an Ordinal Logistic Regression
In past blogs, we have discussed interpretation of binary logistic regressions, multinomial logistic regressions, and the more commonly used linear regressions. In this blog, we will discuss how to interpret the last common type of regression: ordinal logistic regression. It is important to note that, although there are other forms of regression out there, most of these are interpreted in the same way as the aforementioned types.
Although ordinal logistic regression involves some of the same steps of interpretation as the other methods, the interpretation of the individual predictors for ordinal regression can be a little tricky. If you haven’t read up on the other common regression interpretations, make sure to review them to stay caught up!
Like previous regressions, first check the model fitting information to ensure the overall regression is significant. You can also investigate the Nagelkerke pseudo R2, which you interpret similarly to other R2 statistics. Ordinal logistic regression differs in interpreting individual predictors. It shows how much each predictor moves the outcome closer to the next “jump up” or category increase.
The way you do this is in two steps. First, identify your thresholds’ estimates. You will have one for each possible increase in the outcome variable. For example, with low, medium, and high categories, you have two thresholds: low to medium and medium to high. Take note of these threshold estimates. You will be using them in comparison to the estimates for each significant predictor variable. For the significant variables, the variable’s estimate represents how much closer they get to a threshold.
Let’s look at an example where we assess students for College Readiness (an ordinal dependent variable), with MATH score and READING score as predictors. The dependent variable ranges from low, to medium, to high readiness. The threshold estimate assigned to low is 5, and the threshold assigned to medium is 10. Once a student hits a threshold of 5, they move to the medium group. Once they hit 10, they move to the high group. MATH score is the only significant predictor with an estimate of 2. This means each 1-point increase in MATH score moves students 2 points closer to the threshold.
So, a student with a math score of 3 is expected to be in the medium group because they tend to move 2 units closer to the threshold for each additional point in MATH (2 units closer to threshold for each MATH point * 3 MATH points = 6). Because 6 is greater than the threshold of 5, that student has broken into the medium category. If their MATH score were 3 units higher (i.e., 6), we would see the following happen: (2 units closer to threshold for each MATH point * 6 MATH points = 12). This would push them past the threshold of 10 into the high group.
You can interpret each significant predictor this way, and even consider how close they get to each threshold based on a combination of predictors, so if READING were also significant, the addition of their score in reading might also help push them past the next threshold even if their math score just barely missed pushing them past the jump.