Causal framing and CausalPy Models 1 / 1b / 1c: results note

This note summarizes fixed-effects associational regressions in notebooks/causal_model.md, framed by minimal DAGs, alongside the main Bayesian hierarchical LE model (notebooks/bayesian_model.md). It compares standardized Gap_* slopes (and residualized Gap_*_resid in Model 1c) to the LE posterior from the Bayesian notebook.

Core point: These runs are regression implementations of minimal causal hypotheses, not fully identified causal estimates. The DAGs make structure explicit; the fitted lines are associational unless stronger identification is argued.

What we have done so far¶

notebooks/causal_model.md (same data pipeline for both):

• Panel: interim/panel_le.h5, Gap_* from utils.gap_predictor_columns, excluding Gap_MaternalDisorders and Gap_ConflictTerrorism.

• Outcome: LE_gap centered (global mean subtracted).

• Estimator: CausalPy LinearRegression (Normal priors on coefficients via PyMC).

• Model 1 + Model 1c (current notebook): country FE on LE_gap; no year FE. Model 1 uses globally z-scored raw Gap_*. Model 1c uses Gap_*_resid = Gap_* − mean(Gap_* | country) over all years, z-scored, then LE_gap ~ resid_* + country FE. Log: causal_model_le_with_covid_2023.txt. Figures: dag_model1_minimal.png, dag_model1c_country_causes_gaps.png, causalpy_le_linear_forest_model1_gap_betas.png, causalpy_le_linear_forest_model1c_resid_gap_betas.png.

• Model 1b (separate run, not in current notebook): country FE + year FE. Log: causal_model_le_1b_with_covid_2023.txt. Figures: dag_model1b_minimal.png, causalpy_le_linear_forest_model1b_gap_betas.png.

Planned: expanded DAG (Model 2); competing-risks DAG (Model 3). causalpy 0.8.x has no CausalModel export; DAGs use graphviz.Source + DOT.

Model 1 vs Model 1b (CausalPy only)¶

Design

Runs reviewed: Model 1 + 1c log 2026-04-10 (causal_model_le_with_covid_2023.txt); Model 1b log 2026-04-10 (causal_model_le_1b_with_covid_2023.txt).

Posterior means for standardized Gap_* (94% HDI in logs): Δ = Model 1b − Model 1.

Sources (checked against logs, 2026-04-10): Model 1 — notebooks/logs/causal_model_le_with_covid_2023.txt, block CAUSALPY — MODEL 1 (GLOBAL Z, COUNTRY FE), lines 75–87 (posterior means). Model 1b — notebooks/logs/causal_model_le_1b_with_covid_2023.txt, lines 77–89. R²: Model 1 unit_0_r2 line 127; Model 1b unit_0_r2 line 152.

Interpretation: Adding year fixed effects changes the estimand: slopes are closer to associations after netting out a shared time pattern in LE_gap (and implicitly co-moving gap structures). That is not the same regression as Model 1, so large moves—especially road traffic, childhood, chronic respiratory, and cardiovascular—are expected. In 1b, cardiovascular and diabetes posterior means are near zero and their 94% HDIs overlap zero (see log); childhood turns negative with an interval away from the Model 1 / Bayesian story. Homicide is stable across 1 and 1b (≈0.43). Do not read Model 1b as a “closer” or “better” causal fit than Model 1 without an explicit estimand; it is a different partialing-out of time.

On R²: Values are high because of dense FE and many predictors. Treat as in-sample flexibility, not validation of a causal story.

Model 1c (within-country deviations vs country mean)¶

Estimand: Model 1c estimates how deviations from a country’s long-run average cause-specific gap are associated with LE_gap, with the same country FE on the outcome as Model 1. (Outcome: LE_gap globally centered; country dummies absorb country-specific levels of LE_gap, so slopes on resid_* speak to within-country variation in gaps relative to each country’s mean.) This is not the same question as Model 1 (total association mixing between- and within-country signal) or Model 1b (within-year, cross-country contrasts after year FE).

Decomposition: Each Gap_* is split into a country-level component (the group mean) and a within-country deviation; the regression relates the deviation to LE_gap. resid_* is orthogonal to country by construction; country FE remain in the LE_gap equation (mostly shifting intercepts; slopes on resid_* ≈ a model without FE on X, with posteriors slightly stabilized).

Triangulation: three CausalPy specs¶

Together: Model 1 = broadest associational pattern; 1b answers what happens when time is netted out; 1c answers what happens when persistent country structure in gaps is netted out.

Log (same run as Model 1): notebooks/logs/causal_model_le_with_covid_2023.txt — 2026-04-10, CausalPy 0.8.0, 888 rows.

Posterior means (94% HDIs in log); Δ = Model 1 − Model 1c:

What the joint pattern implies¶

No sign changes, substantial shrinkage for many causes, and R² essentially unchanged is a strong diagnostic combination:

• Stable signs → Model 1 is picking up real cross-cause structure, not arbitrary sign noise.

• Shrinkage → Residualization is removing the between-country component of gaps cleanly; a large share of the Model 1 association for several major causes reflects persistent differences between countries rather than changes within countries over time—stronger than “a country-level component.”

• Unchanged R² is not trivial: LE_gap is explained as well when predictors are within-country deviations (plus country FE) as when they are global z-scored gaps. So the fit does not depend on between-country contrast in X to achieve the same in-sample R²; within-country variation in gaps still carries substantial signal for LE_gap, which supports the credibility of the within-country interpretation.

Key causes (posterior means)¶

Homicide (0.43 → 0.17): Model 1 mixes “countries with higher homicide gaps tend to have higher LE gaps” with within-country co-movement. After removing country-mean gaps, a positive association remains but smaller: within-country deviations still matter—credible and interpretable.

Road traffic (triangulation with 1b):

Year FE (1b) pull the coefficient down sharply (shared time trend in road safety); country-mean removal (1c) leaves a middle ground: within-country deviations in the road-traffic gap stay meaningfully associated with LE_gap. That aligns with the view that shared time trends in road safety reflect real (e.g. policy- and technology-driven) change not captured as pure confounding by year FE alone—and that 1c is the spec that preserves a within-country road signal without the over-correction that 1b can impose on this cause. (Still associational; not a causal identification proof.)

Chronic respiratory, neoplasms, suicide (large shrinkage): Posterior means move from 0.31 / 0.26 / 0.34 toward 0.10 / 0.049 / 0.11—consistent with smoking history, health systems, demographics, and other slow-moving, country-specific factors quantifying how much of Model 1 was between-country.

COVID (0.11 → 0.11): Unchanged at the mean. COVID’s variation is mostly temporal, not a long-run country characteristic of the gap—so the Model 1 slope is not driven by country means; a useful sanity check.

Cardiovascular and diabetes (still negative, smaller |β|): The “protective” (negative) association is partly country-level structure but not entirely—consistent with a competing-risks / composition reading.

Big picture¶

Model 1c shows that while much of the cross-cause pattern in Model 1 is driven by persistent differences between countries, a substantial within-country relationship remains for several important causes—notably road traffic, homicide, and suicide. That supports the interpretation that changes in these causes within countries over time are meaningfully associated with LE_gap in a principled decomposition, after removing long-run country-level structure in the gaps.

Comparing resid_* to Bayesian Gap_* posteriors below is not apples-to-apples (different predictors).

Comparison to the Bayesian LE model (not HALE)¶

Reference table: notebooks/tables/beta_coefficients_le_ihme_nomid_nogrw_y2023_covid.html — IHME, no Mid predictors, no year GRW (INCLUDE_YEAR_EFFECTS = False), cutoff 2023, COVID included. Posterior means below are from that export.

Structural difference: The Bayesian LE model uses random intercepts by country and does not include a year random walk in this reference run. Model 1b does include year FE. So Model 1 was closer in spirit to “country heterogeneity + shared slopes, no explicit year term” than 1b is. Comparing 1b to Bayesian mixes different time adjustment choices.

Model 1 vs Bayesian LE (posterior mean); Δ = CausalPy − Bayesian¶

What matched (Model 1): Same sign at posterior mean for all 13 gaps vs Bayesian (two negative: cardiovascular, diabetes); similar top-tier ranking (road traffic, homicide, suicide, chronic respiratory, neoplasms). HDI caveats still apply (e.g. childhood in Bayesian table has wide intervals). FE vs pooling: agreement between Model 1 and Bayesian supports that the headline cross-cause pattern is not solely an artifact of partial pooling in the hierarchical model.

Model 1b vs Bayesian LE (posterior mean); Δ = CausalPy − Bayesian¶

Takeaway: 1b still aligns with Bayesian on homicide and roughly on alcohol / COVID / neoplasms, but differs sharply on road traffic, childhood, chronic respiratory, and cardiovascular—consistent with year FE absorbing global time trends that overlap those cause structures. For Bayesian-aligned robustness of shared slopes without a year term in CausalPy, Model 1 is the cleaner apples-to-apples contrast; 1b answers a different question.

Main takeaway¶

• Model 1 is a useful robustness check against the Bayesian LE model: country FE + no year term, similar standardized mean pattern and signs vs hierarchical LE (with HDI scrutiny where needed).

• Model 1c is arguably the most informative of the three CausalPy specs: it implements the DAG and delivers a clean between-country vs within-country read on gaps. Key result: for several major causes, a substantial fraction of the Model 1 signal reflects persistent between-country differences not within-country dynamics; yet within-country associations remain for causes such as road traffic, homicide, and suicide. COVID unchanged at the mean sanity-checks that the Model 1 slope is not driven by country means. Road traffic triangulates 1 / 1b / 1c in a way that supports treating shared time in road safety as substantive and preserves a policy-relevant within-country signal under 1c—without claiming full causal identification.

• Model 1b is the two-way FE analogue (country + year); it changes gap slopes materially and answers a different estimand than 1 or 1c; tension between 1 and 1b is partly resolved by 1c (country structure vs time trends).

• All three CausalPy specs remain associational models framed by DAGs, not fully identified causal analyses.

• Quantitative decomposition and model-based counterfactual calculations (structural, model-implied sense) should still rely on bayesian_model.md for partial pooling, full posteriors, and existing workflows.

Files¶

Source: Institute for Health Metrics and Evaluation. Used with permission. All rights reserved.