Ordinal regression

[NathanielF]

Example Notebook using Ordinal Regression Model

Related to this issue: #277

Notebook is a work in progress. Just experimenting with different model specifications on fake data with known properties.
Current plan is fit and explain the regression model with a discussion of the priors over the cut points and evaluating different implications of the model specification. Rough plan is to then apply the techniques to examples in Agresti's book on categorical data analysis.

• Notebook follows style guide https://docs.pymc.io/en/latest/contributing/jupyter_style.html
• PR description contains a link to the relevant issue:
  • a tracker one for existing notebooks (tracker issues have the "tracker id" label)
  • or a proposal one for new notebooks
• Check the notebook is not excluded from any pre-commit check: https://github.com/pymc-devs/pymc-examples/blob/main/.pre-commit-config.yaml

Helpful links

• https://github.com/pymc-devs/pymc-examples/blob/main/CONTRIBUTING.md

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[NathanielF]

Marking this one as ready for a pull request because I think i have the bones of what I want... but not quite the structure. I also know @drbenvincent has thoughts on this one too. So opening it up for feeback or pushback, suggestions

Broad structure at the moment is

1. Open with scenario of employee rating system to motivate the view of a latent sentiment and explicit rating.
2. Generate fake data and visualise it. Explain the nature of the regression model
3. Run a variety of models
4. Plot outcomes
5. Use Krushcke's movie data set to compound the importance of modelling ordinal data properly
6. Conclude

[drbenvincent]

Great stuff. Reviewing this and the other notebook is definitely on my list 🙂

[drbenvincent]

I hope to have time to review this Friday or Monday. Feel free to ping me if I violate that 🫠

[NathanielF]

Giving this one a nudge @drbenvincent

[drbenvincent]

Thanks for the reminder. A bunch of house move things get finished today, so should have capacity for this very soon :)

[NathanielF]

Just giving another nudge here @drbenvincent. At this point i'm pretty happy with it.

[drbenvincent]

Sorry, taking a look now :)

[drbenvincent]

• In the intro, add wikipedia link to Likert scale page
• Could potentially add seed for RNG in the make_data function. But entirely optional
• Can we easily remove the Unnamed: 0 column in df?
• Where it says "brainchild of Dr Ben Vincent", add Adrian Seyboldt also. I can't quite remember how it came about, but it was some mix of both of us.
• Could add some alpha to the histogram plots
• Change "Normal V Uniform Priors" title to say "versus"
• Comparison to statsmodels is nice, but could have a short description to focus the reader to any salient points.
• Plot under heading "Interrogating the Model's Implications" is cool but could perhaps have a brief explanation.
• Update dates to June 2023 (sorry)

Very nice 👍

[NathanielF]

Made those changes. Think we're all good now. Thanks for the review!