Memo: Do country and car access jointly predict regular transit?

Research memorandum — country × car additive and interaction RFs

Research question: Do country of residence and car access (Q21) jointly—or as an interaction—predict regular public-transit use better than either alone?

Parent open question: transit_covariate_followups.qmd · Companions: country_predicts_transit.qmd · car_access_predicts_transit.qmd

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1 Answer, Response, + Summary of Results

On respondents with complete country + Q21 (n = 149), nested categorical Random Forests ((Breiman, 2001)) (seed=42) show clear synergy.

Short answer: Yes. Country + car AUC ≈ 0.699, beating car alone (0.631) and country alone (0.608). An explicit country × car interaction feature is similar but slightly weaker (0.683). Figure Figure 1 shows the AUC comparison.

Figure 1.. Country × car AUC comparison

1.1 Nested CV performance (common n = 149)

Table Table 1 reports the nested CV ROC-AUCs.

Table 1.. Country and car interaction predicting regular transit.

Model	ROC-AUC
Country + car (additive)	0.699
Country × car (interaction string)	0.683
Car access only (Q21)	0.631
Country only	0.608
Chance	0.500

1.2 Interpretation

1. Closes the follow-ups memo’s “country × car” open item: place and auto access are ****complementary****, not redundant.
   
2. Additive encoding is sufficient; a saturated interaction string does not buy more AUC in this sample.
   
3. Still far below full-cohort Q28 (≈0.762), so country×car is a mid-tier place/mobility bundle—not a rideshare substitute.

Sources: ca-personas followup-experiments --experiments country_car · outputs/followup_experiments/country_car/ · formal write-up docs/secondary_rq_followup_experiments.md

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2 What questions or uncertainties remain?

Would denser geography (metro area / transit agency coverage) interact with car access more sharply than coarse country labels?

References

Breiman, L. (2001). Random forests. Machine Learning, 45(1), 5–32. https://doi.org/10.1023/A:1010933404324