Fit mult-option data with Multinomial distributuion or normal distribution?

Questions
1

Dear Bayesian model experts,

Assuming one has data with 20 categories, multinomial distribution, or normal distribution, which one is more suitable to this dataset？ Thank you very much.

Best,

2

I think you should provide a bit more details, are the 20 categories your predictor? Then you should choose a distribution as likelihood that fits the type of data you have (Normal is a fine choice if the observation is unbounded). If instead you have observed 20 categories then you should use multinomial distribution as likelihood (i.e., a multinomial regression)

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3

Thank you for your response. I think the condition is the latter one, 20 categories are the observed data. However, I think normal needs less parameter than multinomial distribution and therefore I speculate when the dataset is not very large, the normal distribution has less possibility to over fit? I am a psychology student and I read some papers that require participants to do some trial-by-trial questionnaires. However, different papers choose different distributions. For example, in this paper, participants indicated their happiness after each decision, and the author modeled this happiness data by putting a utility function into a normal regression model, so they choose normal distribution as likelihood. On the contrary, this paper choose a multinomial distribution. I am a little confused about which distribution is more suitable in this condition, cause both papers are published in relatively good journals. Thank you very much. BTW, thank you for responding to me. I am always a big fan of you, cause you have done plenty of jobs in Pymc3 community.

4

Glad to help, I think what you are looking for is actually ordinal regression, see eg Estimating Monotonic Effects with brms and some discussion in make ordinal regression great again · Discussion #5066 · pymc-devs/pymc · GitHub

You can see some more example in Rethinking chapter 11 (resources/Chp_11.ipynb at master · pymc-devs/resources · GitHub)

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5

Thank you very much. Really appreciate it, it indeed solves my problem!