relaxing the proportional odds assumption in ordinal logistic regression

[Nader Mehri]

I was wondering if it would be OK to relax the proportional odds assumption in ordinal logistic regression.by collapsing a 5-category ordinal variable into a 3-category variable (e.g., combining “Strongly Agree” and “Agree” into “Agree” and “Strongly Disagree” and “Disagree” into “Disagree”). @Richard Williams

[Erik Ruzek]

Nader,

I'm not sure how often Rich checks Statalist these days, but I can chime in with a bit of context. What you are talking about, collapsing the categories of a Likert item, is a different topic than the proportional odds assumption.

The latter deals with the association between an independent variable and the ordinal outcome, and whether that association is the same ("parallel") for the different cumulative logits. With an ordinal outcome having five responses, the cumulative logits are 1 vs. 2-5, 1,2 vs. 3-5, 1-3 vs. 4,5, and 1-4 vs. 5. The proportional odds assumption is that the odds ratios will be roughly equivalent (or parallel) across all those cumulative logit comparisons for a given predictor. This assumption can be easily relaxed to allow the odds ratios to differ across the cumulative logits. Rich's gologit2 command (search gologit2 in Stata) can be used to test the proportional odds assumption and relax the strict equality of the odds ratios as appropriate. See two of his relevant articles, here and here.

Reducing the number of categories from 5 to 3 for your outcome is another matter entirely. The cumulative logits are different for a three- and five-response option outcome, even if it is constructed from the same variable. There is little justification for reducing the variability unless you have cases where members of certain groups never choose a particular response option. Imagine that you have responses from males and females, and males never choose the "Strongly Agree" option. That might be a reason to recode all "Strongly Agree" responses to "Agree." But this is a slippery slope.

What is your justification for doing this?

[Mike Lacy]

My recollection is that the following book contains a careful treatment of such matters, among many other things:

Fullerton, Andrew S., and Jun Xu. Ordered regression models: Parallel, partial, and non-parallel alternatives. CRC Press, 2016.

I might be wrong and it might be that I'm thinking of some more recent article by one or the other of those authors.

[Leonardo Guizzetti]

I second Erik's comments, and also Mike's book recommendation.

I do not view collapsing your outcome variable to fewer levels as relating to the proportional odds assumption of the model at all. If anything, that places more restrictive assumptions on your estimated parameters because not only would be making proportional odds assumptions of the odds ratios, but that those estimated odds would be exact the same for the collapsed levels.

[Richard Williams]

Erik Ruzek I'm still here! Maybe when I retire in two years I'll be more diligent about checking in (or disappear completely).

Well, if you collapse an ordinal variable down to a dichotomy, you won't violate the proportional odds assumption. In fact you'll just use logistic regression. But you'll be throwing away information that way.

It isn't obvious to me that other collapses would help. I suppose it would be an empirical matter, e.g. maybe it would be good to combine A and SA if SA has hardly any cases.

[Nader Mehri]

Nader,

I'm not sure how often Rich checks Statalist these days, but I can chime in with a bit of context. What you are talking about, collapsing the categories of a Likert item, is a different topic than the proportional odds assumption.

The latter deals with the association between an independent variable and the ordinal outcome, and whether that association is the same ("parallel") for the different cumulative logits. With an ordinal outcome having five responses, the cumulative logits are 1 vs. 2-5, 1,2 vs. 3-5, 1-3 vs. 4,5, and 1-4 vs. 5. The proportional odds assumption is that the odds ratios will be roughly equivalent (or parallel) across all those cumulative logit comparisons for a given predictor. This assumption can be easily relaxed to allow the odds ratios to differ across the cumulative logits. Rich's gologit2 command (search gologit2 in Stata) can be used to test the proportional odds assumption and relax the strict equality of the odds ratios as appropriate. See two of his relevant articles, here and here.

Reducing the number of categories from 5 to 3 for your outcome is another matter entirely. The cumulative logits are different for a three- and five-response option outcome, even if it is constructed from the same variable. There is little justification for reducing the variability unless you have cases where members of certain groups never choose a particular response option. Imagine that you have responses from males and females, and males never choose the "Strongly Agree" option. That might be a reason to recode all "Strongly Agree" responses to "Agree." But this is a slippery slope.

What is your justification for doing this?

Thank you everyone for your valuable input. I believe there are several compelling reasons to consider collapsing the categories of Likert items in the context of ordered logistic regression analysis:

1. Conceptual Similarity: In many research contexts, the distinctions between "Strongly Disagree" (SD) and "Disagree" (D), as well as between "Strongly Agree" (SA) and "Agree" (A), are minimal. These adjacent categories often represent similar sentiments, which can justify their combination for a more streamlined analysis.
2. Simplification of Interpretation: Collapsing the Likert scale can greatly enhance the intuitiveness of interpreting results in the context of ordered regression. For example, explaining the coefficient for a combined category (like grouping SA with A) is much simpler than detailing separate coefficients for each original category, especially to an audience with limited statistical expertise. This approach helps to demystify the results, making them more accessible and less like we are obscuring details behind statistical complexity.
3. Manual Imposition of Constraints: By collapsing categories, we effectively impose a constraint that aligns with the parallel cumulative logits assumption. This manual adjustment ensures that the model reflects a consistent effect across these grouped categories, simplifying both the model structure and the interpretation of its parameters.

In summary, collapsing categories can be a practical approach to enhance clarity and interpretability in our analyses, provided that it is justified by the conceptual similarities among the responses and the needs of our audience.

[Richard Williams]

1. You lose information when you collapse. Agree may have a lower bound of very slight agreement, SA may have an upper bound of fanatical agreement. If you just have Agree then Agreement might range from very slight agreement to fanatical agreement. Having Agree and Strongly Agree gives you a better feel for how intensely people feel and what the upper and lower bounds are in a person’s answer, and the additional information can help you more precisely measure the values of coefficients.

2. I don’t understand your argument. Whether an ordinal variable has 2, 3, 5, or 17 categories, there will be one coefficient for each independent variable. The number of cut points will vary, but who pays attentions to cut points?

3. How does collapsing to 3 categories guarantee proportional odds is met? In any specific case this might happen to be empirically true, but I see no reason it always has to be true.

Your first 2 arguments might be more valid with mlogit than ologit. With mlogit, the number of parameters can get overwhelming.

But, if you are convinced that collapsing is good, you might as well consider collapsing down to 2 categories. If empirically it seems justified, then your interpretation tasks will be even easier.

Don’t get me wrong. Sometimes I do think collapsing categories can be good. The Ns for some categories may be far too small for the information in them to be very useful. Categories like “Hardly ever” and “Never” may be too similar to bother separating them.

But, I wouldn”t start off by thinking that collapsing is a good idea or that it will automatically solve problems I have.