Ordinal independent variable treated as continuous & marginal effects in ordinal logistic regression

[Archie Millar]

Hello,

I am an economics student doing an undergraduate empirical dissertation using data from the European Working Conditions Survey, where my DV is job satisfaction (ordinal, 4-point scale) and my two main predictor variables are recognition from employer (ordinal, 5-point likert scale: strongly disagree... strongly agree) and working from home (WFH).

The main issue I have is with my WFH variable. From the survey it is measured as follows: “during the last 12 months in your main paid job, how often you have worked in your own home?” 1=Daily; 2=Several times a week; 3=Several times a month; 4=Less often; 5=Never.

Due to the ordinal nature of my DV, I am conducting ordinal logistic regression, and of the two options for handling my ordinal predictors (treat as continuous or categorical), my supervisor advised that I treat them both as continuous. I am aware of the drawbacks of doing so (eg underlying assumption of equally spaced intervals), but have been told for purposes of undergrad dissertation, this is ok and in much existing literature, ordinal variables are treated as continuous in the same way.

My first question is when treating WFH as continuous, would I keep the original coding so it is just a continuous scale from 1 to 5, or is there a way to re-code it so it better approximates a continuous scale?

Secondly, I want to discuss marginal effects but this does not seem intuitive for my predictor variables that don't have an easily quantifiable "one-unit change".
For example if I had age as my continuous predictor variable, my interpretation would be "an increase in age by one year causes a beta change in the log-odds of reporting very satisfied with job."
But I am not sure of the equivalent of a one unit change in my WFH variable the way it is measured.
So how would I frame / quantify this marginal effect for my WFH variable? (and for that matter my recognition variable too?)

I would really appreciate any help/advice, thanks!

[Richard Williams]

This handout discusses different ways of treating ordinal independent variables:

https://www3.nd.edu/~rwilliam/xsoc73...ndependent.pdf

Or, better yet, if your library offers access to it,

https://methods.sagepub.com/foundati...dent-variables

If you are going to treat the variables as continuous, you can make yourself look at bit more impressive by doing formal tests of whether treating as continuous is legitimate.

[Archie Millar]

Richard Williams
Thank you for your response, I had actually seen parts of hat handout so reading it in full was very helpful.
And yes I was planning on doing Likelihood Ratio tests to check different specifications, but hadn't realised I could do it to compare categorical vs continuous treatment, so I will definitely do that, thank you.

On the other part of my question, if after those tests it is acceptable to use continuous treatment, how would you frame/quantify those marginal effects, like the equivalent of a one-unit change in the 'ordinal as continuous' variable?

Thanks very much.

[Marcel Schmelzer]

Richard Williams I have found your handout on ordinal independent variables very useful, thank you.

Do you have any advice on formally testing the legitimacy of treating an ordinal dependent variable as continuous?

[Richard Williams]

Richard Williams I have found your handout on ordinal independent variables very useful, thank you.

Do you have any advice on formally testing the legitimacy of treating an ordinal dependent variable as continuous?

With ordinal independent variables, there is something to be gained if you can legitimately treat them as continuous. The model is more parsimonious and the information about ordering is not discarded.

With ordinal dependent variables, I think you don't gain that much by treating them as continuous. It isn't that much harder to type ologit than it is to type regress. Interpretation is harder but marginal effects and adjusted predictions generally work just fine.

A lot of times you'll see people say they try ologit and regress and the conclusions were the same so they used regress. Perhaps, but I suspect what they really mine is that sign and significance were about the same, but that doesn't mean actual effects or predictions were the same.

This article makes the novel argument that it is actually better to use ordinal models with continuous outcomes!

https://onlinelibrary.wiley.com/doi/....1002/sim.7433

In short, I suspect nothing all that horrible happens if people use regress with an ordinal outcome, especially if the outcome has a lot of categories and categories seem equally spaced. But in most instances I figure you might just as well use an ordinal method.

[Marcel Schmelzer]

With ordinal independent variables, there is something to be gained if you can legitimately treat them as continuous. The model is more parsimonious and the information about ordering is not discarded.

With ordinal dependent variables, I think you don't gain that much by treating them as continuous. It isn't that much harder to type ologit than it is to type regress. Interpretation is harder but marginal effects and adjusted predictions generally work just fine.

A lot of times you'll see people say they try ologit and regress and the conclusions were the same so they used regress. Perhaps, but I suspect what they really mine is that sign and significance were about the same, but that doesn't mean actual effects or predictions were the same.

This article makes the novel argument that it is actually better to use ordinal models with continuous outcomes!

https://onlinelibrary.wiley.com/doi/....1002/sim.7433

In short, I suspect nothing all that horrible happens if people use regress with an ordinal outcome, especially if the outcome has a lot of categories and categories seem equally spaced. But in most instances I figure you might just as well use an ordinal method.

Thank you very much for your input!