{ "features": [ "log_gdp", "Schooling", "BMI", "Polio", "Diphtheria", "Hepatitis_B", "Measles", "Alcohol_consumption", "Thinness_ten_nineteen_years", "log_population" ], "excluded": [ "Infant_deaths", "Under_five_deaths", "Adult_mortality", "Incidents_HIV", "Country", "Region", "Year", "economy flags" ], "split": { "train": "2000\u20132010", "validation": "2011\u20132012", "refit": "2000\u20132012", "test": "2013\u20132015", "train_n": 1969, "validation_n": 358, "refit_n": 2327, "test_n": 537 }, "selection": "Lowest validation MAE, then refit on 2000\u20132012. Test metrics not used to select model or tune settings.", "selected_model": "Gradient boosting", "validation": [ { "model": "Mean baseline", "mae": 7.612585437408316, "rmse": 8.83455868395397, "r2": -0.07969972863613606 }, { "model": "Linear regression", "mae": 3.3309402920018485, "rmse": 4.346251808518563, "r2": 0.7386857813628882 }, { "model": "Ridge regression", "mae": 3.3278736079502114, "rmse": 4.343108093922957, "r2": 0.7390636702925513 }, { "model": "Random forest", "mae": 1.9479319401317075, "rmse": 2.948481967348806, "r2": 0.8797375008919432 }, { "model": "Gradient boosting", "mae": 1.8035616401843988, "rmse": 2.5867527223326063, "r2": 0.9074357893419686 } ], "test": [ { "model": "Mean baseline", "mae": 7.357159056625363, "rmse": 8.513937826508377, "r2": -0.1279395887276047 }, { "model": "Linear regression", "mae": 3.3275565348373357, "rmse": 4.220625401931086, "r2": 0.7228093939789315 }, { "model": "Ridge regression", "mae": 3.321980995903669, "rmse": 4.217061386215198, "r2": 0.7232773315340595 }, { "model": "Random forest", "mae": 2.0400028063919, "rmse": 2.8479649843797423, "r2": 0.8737898793645086 }, { "model": "Gradient boosting", "mae": 1.9920554468707692, "rmse": 2.7118878873312537, "r2": 0.8855625020796092 } ], "permutation_importance": [ { "feature": "log_gdp", "mae_increase": 2.788546331755846, "sd": 0.13754794452847116 }, { "feature": "Thinness_ten_nineteen_years", "mae_increase": 1.0504024294769716, "sd": 0.0708777521161217 }, { "feature": "log_population", "mae_increase": 0.8245241227247628, "sd": 0.05373365068426316 }, { "feature": "Alcohol_consumption", "mae_increase": 0.656265434828741, "sd": 0.0384501512298133 }, { "feature": "Schooling", "mae_increase": 0.5342428326723062, "sd": 0.03266813199360894 }, { "feature": "BMI", "mae_increase": 0.4991375558299876, "sd": 0.0756987626624163 }, { "feature": "Measles", "mae_increase": 0.42199618528904065, "sd": 0.053366564989530095 }, { "feature": "Polio", "mae_increase": 0.12096766496008189, "sd": 0.02711198476387222 }, { "feature": "Hepatitis_B", "mae_increase": 0.07294198335815559, "sd": 0.016094952105428266 }, { "feature": "Diphtheria", "mae_increase": 0.04705934079627861, "sd": 0.02474853617355609 } ], "geographic": { "model": "Gradient boosting", "mae": 2.3099051536328905, "rmse": 3.1708109463559815, "r2": 0.8905799869275218, "train_countries": 143, "test_countries": 36, "validation": [ { "model": "Mean baseline", "mae": 7.541943815878974, "rmse": 8.750813579755782, "r2": -0.0786615980405938 }, { "model": "Linear regression", "mae": 3.6474732398856853, "rmse": 4.633156228571248, "r2": 0.697627533350174 }, { "model": "Ridge regression", "mae": 3.641828578184303, "rmse": 4.630044239672027, "r2": 0.6980335907743391 }, { "model": "Random forest", "mae": 2.0588624267715643, "rmse": 3.0880516811307728, "r2": 0.8656748069735547 }, { "model": "Gradient boosting", "mae": 1.8181059437288245, "rmse": 2.6321878730943995, "r2": 0.9024062240983799 } ], "note": "Country holdout across all years. Model family selected on 2011\u20132012 using only the 143 training countries, then refit on all their years. 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