Ordinal variable in multiple linear regression model?

I am estimating the price of a car using past data (in other words, Predictive Multiple Linear Regression) and one of the variables is a rating from 1 to 4 of a particular guideline. How do I treat this variable? Should I treat it like an ordinary continuous variable like the other ratio scale variables in my model or should I omit this entirely? I checked a textbook for this matter and it suggested the use of logit/probit model which I haven't learnt yet in my uni's ongoing introductory econometrics course.

• It's often fine to treat ordinal predictors as continuous. A more general solution is to use polynomial contrasts. GAMs are another option.
– mkt
Apr 30 '21 at 14:52
• stats.stackexchange.com/a/206345/121522
– mkt
Apr 30 '21 at 14:53

You definitely don't need to use a logit/probit model. We use different "flavors" of regression analysis (OLS/linear regression, logit, tobit, negative binomial) based on the characteristics of the DEPENDENT variable. In your case you are analyzing price so normal multiple linear regression is still going to be just as appropriate regardless of what kinds of INDEPNDENT variables you include.

Now, the tough question: how do you deal with an ordinal independent variable. There is actually no obvious answer here. On one hand, treating "rating" as if it were a continuous ratio variable is obviously not ideal for a number of reasons. For example, you have no idea how "far apart" the points on the scale are. Maybe the substantive difference between a rating of 1 and 2 is way bigger than the difference between 4 and 5? So treating this variable as continuous may give you bad answers if you really want to know how having much a rating of 4 improves price compared to a rating of 3.

On the other hand, the fact that the scale is ordinal means that treating it as continuous won't give you TERRIBLE results. The coefficient will tell you how much moving up "one point" on the scale is related to price, which makes intuitive sense. If there really is a relationship with price then it should probably show us as significant if you treat the variable as continuous. This is in contrast to NOMINAL categorical variables, like "color": treating a variable like that as continuous will give you utter garbage results.

If you don't want to treat this variable as continuous, then you can either dichotomize it (into say "high rating vs low rating" although note that this will throw away potentially useful information) or create a set of dummy variables, leaving one category out as the omitted category - which is how we analyze nominal categorical variables.

See here for more on how to deal with categorical variables using "dummy coding:" https://stats.idre.ucla.edu/other/mult-pkg/faq/general/faqwhat-is-dummy-coding/

If you just want to use this model to figurer if rating "matters" at all, the treating it as continuous will probably do a OK job of answering that question. If you wanted to actually try and predict the price of cars with specific ratings, then I'd recommend treating it as categorical.

• Thank you for an elaborate answer :)! Could you elaborate a bit on the last point because I am actually building a predictive and not a causal regression model? Apr 30 '21 at 15:14
• This is a good answer, but I cringe at the suggestion to dichotomize the variable. That could be a reasonable approach, but won't typically be, IMO. Apr 30 '21 at 15:16
• I added a reference to another site that explains dummy coding and noted that dichotomization is potentially problematic because it throws away information (although for an assignment in an intro stats class it might be OK) Apr 30 '21 at 15:57