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 have not already read up on the other common regression interpretations, make sure to give those a visit so you are caught up!
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Like the past regressions we have discussed, the first step is to check the model fitting information and make sure the overall regression is significant. You can also investigate the Nagelkerke pseudo R2, which is interpreted similarly to other R2 statistics. Where the ordinal logistic regression begins to depart from the others in terms of interpretation is when you look to the individual predictors. For an ordinal regression, what you are looking to understand is how much closer each predictor pushes the outcome toward the next “jump up,” or increase into the next category of the outcome. 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, if your outcome has a low, medium, and high category, you have two thresholds; one is for the increase from low to medium, and one is for the increase from 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 take a look at an example where students are assessed for College Readiness (an ordinal dependent variable) and our predictors are MATH score and READING score. 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. This means that once a student hits the threshold of 5, they jump to the medium group, and once they hit 10, they are in the high group. You might see that MATH score is the only significant predictor, and the estimate assigned to this predictor is 2. This means that each increase of 1 point on the MATH score (the estimate is always based on a 1 unit increase in the predictor) tends to push 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.