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I am trying to analyse how people respond to the question: "It is all right for a couple to live together without intending to get married?" The data is in the form of a Likert scale. I want to analyse if age, gender and religious status affect this. What form of regression should I use - multinomial logistic regression or ordered logistic regression?

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Since you mention the data are on a likert scale (from good to bad or something similar), the data would be ordinal. For example:

"It is alright for a couple to live together without intending to get married?"
1. Totally alright
2. Alright
3. Neutral
4. Not alright
5. Totally not alright

Hence, using ordered logistic regression preserves more information than using multinomial logistic regression, which essentially considers the data nominal (i.e. no order). The latter would be more appropriate for a survey with answers like: yes, no, no opinion, since these categories have no logical order to them.

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