Ordinal logistic regression query

[Marcel Schmelzer]

I have two survey items, both are measured on an ordinal scale. However, the difference between the two is more interesting than the value of each one.

Is it valid to use the ologit command using the difference between the two items as the dependent variable?

[Mike Lacy]

If you truly regard these as ordinal, the difference variable would just be <, =, or >. There are circumstances where that kind of response variable is useful; I've done it myself. However, considering standard literature deprecating change scores in analogous situations with continuous responses, what about using -meologit-, with both variables treated as nested within respondent?

[Marcel Schmelzer]

Thank you Mike for your useful reply. I apologise if my post was not clear - I think your response may be on the assumption of a single item being measured at two time points.

My issue is having two distinct survey questions measured at the same time. It's difficult to explain the background of the study concisely, but the responses lack meaningful interpretation in isolation, and can only be understood in relation to each other.

[Mike Lacy]

If the situation doesn't involve time, it can always (?) be thought of as involving measures repeated across *context.* (For example, the responses could be "How do you rate Product1, and how do you rate Product2.) So, whether the difference is time or context, you can create a difference variable and leave the data in the wide layout and analyze it with -ologit-, which might be desirable. Or, you could could reshape to long layout, with a separate observation for each individual's response in each context, treat the separate responses as nested within person, and use -meologit-. Is there some reason why this doesn't make sense for your situation?

[Marcel Schmelzer]

Thank you for your response, I really appreciate your input. Apologies if I am spelling out the obvious/asking basic questions, but I just want to make sure I have understood correctly.

To take your example, imagine I am interested in estimating the impact of an advertising campaign on relative product rankings (with x a treatment variable indicating exposure to the campaign).

If using ologit:

ologit y x

Would y need to be a difference variable of the form you previously mentioned (i.e. </>/=)? Or could it be a difference variable indicating the number of levels difference in the response?

If using meologit:

meologit y x || id:

In this case y would be the raw data for both items. What would be the advantages of such an approach? Is it precisely that it would take into account the number of levels differences in the response?

[Mike Lacy]

If you're using "y" as the "number of levels of difference," then you've more or less assumed that y is an interval level variable, so you might as well use a conventional regression or anova model rather than -ologit-. If you're an ordinal purist -- then you'd just make the difference variable "bigger, the same, smaller."

The reaon -meologit- or something like that might be preferred is that there is a longstanding literature opposing the use of difference scores in the case of continuous response variables based on issues of reliability. I'd presume that argument applies to ordinal responses as well. Not everyone agrees with that argument, however.

Your example about product ratings doesn't strike me as quite relevant here as it sounds like each respondent only gave a response under one condition, i.e., "exposed to advertising" or "not exposed." If that fits your actual situation, then difference scores or some form of a repeated-measures model would not be relevant, as there is no within-person difference.

[Marcel Schmelzer]

Thank you Mike. Yes, there are no repeated measures over time y1 and y2 are only measured once. Understood that ologit is probably the best approach. Just wanted to hopefully find an analysis that took into account the scale of the difference, not only the direction, but it seems like this may not be possible.