Enforce positivity on sigmas in SEM model

[NathanielF]

Model Specification Improvement on SEM mediation model

Related to this issue: #782

• 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

---

📚 Documentation preview 📚: https://pymc-examples--783.org.readthedocs.build/en/783/

[review-notebook-app]

Check out this pull request on 

See visual diffs & provide feedback on Jupyter Notebooks.

---

Powered by ReviewNB

[NathanielF]

Tagging you @fonnesbeck as i think you reviewed the original. This is a small improvement to the final SEM mediation model in light of the issue raised on PyMC discourse.

I've also changed the prior on the variances from Inverse Gamma to Gamma to match the default in the Blavaan package.

[review-notebook-app]

View / edit / reply to this conversation on ReviewNB

fonnesbeck commented on 2025-04-04T14:58:54Z
----------------------------------------------------------------

typo: "...data IN psychometrics ..."

NathanielF commented on 2025-04-06T21:01:52Z
----------------------------------------------------------------

Thanks, fixed.

[review-notebook-app]

View / edit / reply to this conversation on ReviewNB

fonnesbeck commented on 2025-04-04T14:58:55Z
----------------------------------------------------------------

Perhaps briefly say where the notation comes from -- what is Ksi? An acronym?

NathanielF commented on 2025-04-06T21:03:12Z
----------------------------------------------------------------

I've added a note to clarify that the notation reflects the Levy and Mislevy book and additionally flagged that the greek notation versus Ksi distinguishes the latent factor draws from the other parameters.

[review-notebook-app]

View / edit / reply to this conversation on ReviewNB

fonnesbeck commented on 2025-04-04T14:58:56Z
----------------------------------------------------------------

If you are interested in making mu more compact:

lambdas = pm.math.concatenate([lambdas_1, lambdas_2])
ksi_cols = pm.math.stack([ksi[obs_idx, 0], ksi[obs_idx, 0], ksi[obs_idx, 0], 
                            ksi[obs_idx, 1], ksi[obs_idx, 1], ksi[obs_idx, 1]]).T
mu = pm.Deterministic("mu", tau + ksi_cols * lambdas) 

NathanielF commented on 2025-04-06T21:04:12Z
----------------------------------------------------------------

Decided to stick with the less compact notation.

[review-notebook-app]

View / edit / reply to this conversation on ReviewNB

fonnesbeck commented on 2025-04-04T14:58:57Z
----------------------------------------------------------------

"Same scale" meaning within an order of magnitude?

[review-notebook-app]

View / edit / reply to this conversation on ReviewNB

fonnesbeck commented on 2025-04-04T14:58:57Z
----------------------------------------------------------------

Add an energy plot as part of the convergence-checking workflow?

[review-notebook-app]

View / edit / reply to this conversation on ReviewNB

fonnesbeck commented on 2025-04-04T14:58:58Z
----------------------------------------------------------------

These are really nice. I wish this was the default behavior for plot_ppc.

NathanielF commented on 2025-04-06T21:04:43Z
----------------------------------------------------------------

I could look into adding this to arviz.

[review-notebook-app]

View / edit / reply to this conversation on ReviewNB

fonnesbeck commented on 2025-04-04T14:58:59Z
----------------------------------------------------------------

"in-apt"? Is this short for inappropriate?

NathanielF commented on 2025-04-06T21:05:02Z
----------------------------------------------------------------

Yes, just changed for inappropriate

[fonnesbeck]

LGTM. A couple of typos and comments that you are free to ignore.

[NathanielF]

Thanks @fonnesbeck will amend next week! Enjoy your weekend!

[NathanielF]

Thanks, fixed.

---

View entire conversation on ReviewNB

[NathanielF]

I've added a note to clarify that the notation reflects the Levy and Mislevy book and additionally flagged that the greek notation versus Ksi distinguishes the latent factor draws from the other parameters.

---

View entire conversation on ReviewNB

[NathanielF]

Decided to stick with the less compact notation.

---

View entire conversation on ReviewNB

[NathanielF]

I could look into adding this to arviz.

---

View entire conversation on ReviewNB

[NathanielF]

Yes, just changed for inappropriate

---

View entire conversation on ReviewNB

[NathanielF]

Updated with those changes there @fonnesbeck .

Would you be able to merge whenever is convenient, i don't have those permissions on this repo.

Thanks again!