Sharing cutpoint parameters in several ordinal regressions for survey

I’m wondering what standard practice is when using a proportional odds model for many ordinal response questions in a survey. Does it make sense for the cutpoint parameters (or intercepts) to be the same for all questions of a similar type?

For example, suppose we have two questions about how much a respondent likes ice cream and another for cheese on a 5-point scale. If I fit two separate models I can’t easily compare the effect parameters since the underlying cutpoints might be different. If I share the cut points then I can make this comparison. I would assume that the latent continuous random variable would be binned similarly given the similarity of the questions.

Is this typically done?

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What is almost always done is that each response variable gets its full share of intercepts, i.e., if response variable Y has k distinct values then the ordinal model for Y will have k-1 intercepts. You can still compare effects across different response variables with different ordered categories because the \beta's, e.g., log odds ratios, are relative effects that are (mainly) independent of Y categories.

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