When can Ordinal Variables be treated as Interval Variables?

[fog37]

TL;DR

Understanding when ok to treat ordinal variables treated as interval variables

Hello,

Ordinal variables (see Likert scale) can be labelled using numbers and ranked by those numbers. However, the difference between category 2 and category 3 may not be exactly be the same as the difference between category 4 and 5. That said, I noticed that in social science ordinal variables are sometimes approximately treated as if they were numerical predictors if the ordinal variable has many levels...Is that a correct approach? What justifies that? I did some reading and found a variety of opinions on the topic...

Thanks

 

[Dale]

TL;DR Summary: Understanding when ok to treat ordinal variables treated as interval variables

What justifies that?

People did it previously in published papers. Doing it currently doesn’t sink a paper.

It isn’t a great justification. As you say, there are a variety of opinions on the topic. Including ones that are supportive of the practice.

So it will continue to be done for the time being. Most reviewers are statistically unsophisticated, and ordinal methods are less familiar and often less powerful.

 

[fog37]

People did it previously in published papers. Doing it currently doesn’t sink a paper.

It isn’t a great justification. As you say, there are a variety of opinions on the topic. Including ones that are supportive of the practice.

So it will continue to be done for the time being. Most reviewers are statistically unsophisticated, and ordinal methods are less familiar and often less powerful.

It seems to me that the issue is more serious if we treat a response/outcome variable that is ordinal as numerical and maybe less a serious issue if the ordinal variable is an independent variable and we treat it as an interval variable...

 

[statdad]

TL;DR Summary: Understanding when ok to treat ordinal variables treated as interval variables

Hello,

Ordinal variables (see Likert scale) can be labelled using numbers and ranked by those numbers. However, the difference between category 2 and category 3 may not be exactly be the same as the difference between category 4 and 5. That said, I noticed that in social science ordinal variables are sometimes approximately treated as if they were numerical predictors if the ordinal variable has many levels...Is that a correct approach? What justifies that? I did some reading and found a variety of opinions on the topic...

Thanks

"Is that a correct approach?"
No. The fact that something is [or has been] widely done does not make it valid.

 

[FactChecker]

IMO, there should be some subject-matter logic behind the relative numerical values in order to justify that approach. In the cases you refer to, you should base your evaluation on how well they justified the scaling. There may be very good reasons for unequal spacing, but there might not be. I would hope that any assignment of unequal spacing in a peer-reviewed publication was done for some subject-matter, logical reason.

 

[statdad]

Just a point: binning continuous data can be a very bad thing to do and you're losing information: care hast to be take even in the best of situations. Imagine a data set that is actually bimodal (or multimodal): a histogram with too few bins probably won't detect it. Using income data rounded to tens of thousands can hide evidence of inflation that would be detected from the raw values.

Frank Harrell has a very good illustration of problems at the following link.

https://discourse.datamethods.org/t/categorizing-continuous-variables/3402

 

[Dale]

binning continuous data can be a very bad thing to do and you're losing information: care hast to be take even in the best of situations. Imagine a data set that is actually bimodal (or multimodal): a histogram with too few bins probably won't detect it.

Binning can also produce a bimodal discrete distribution where the underlying continuous distribution is not bimodal.

However, very often with psychological data you are working with latent variables so you have no choice but to do an unknown binning on the unobservable latent scale.

 

[WWGD]

Binning can also produce a bimodal discrete distribution where the underlying continuous distribution is not bimodal.

However, very often with psychological data you are working with latent variables so you have no choice but to do an unknown binning on the unobservable latent scale.

There are methods too, for Latent variables, that assume observed data originate from a continuous,
iirc (wolg) normal variables. let me see if I can find refs.

 

[Dale]

There are methods too, for Latent variables, that assume observed data originate from a continuous,
iirc (wolg) normal variables. let me see if I can find refs.

Yes. I like the cumulative family with the logit or probit link in the brms package in R. With the probit link the latent variable is assumed to have a standard normal distribution.