{"id":"W2290394383","doi":"10.1016/j.ejor.2016.02.036","title":"From partial derivatives of DEA frontiers to marginal products, marginal rates of substitution, and returns to scale","year":2016,"lang":"en","type":"article","venue":"European Journal of Operational Research","topic":"Efficiency Analysis Using DEA","field":"Decision Sciences","cited_by":10,"is_retracted":false,"has_abstract":false,"ca_institutions":"Université du Québec à Montréal","funders":"","keywords":"Data envelopment analysis; Returns to scale; Econometrics; Function (biology); Economics; Substitution (logic); Efficient frontier; Production–possibility frontier; Marginal cost; Transformation (genetics); Point (geometry); Production (economics); Scale (ratio); Parametric statistics; Constant (computer programming); Mathematical economics; Mathematics; Computer science; Mathematical optimization; Statistics; Microeconomics; Financial economics","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["metaresearch"],"consensus_categories":[],"category_scores_codex":[0.01522448,0.0001226692,0.0003797738,0.0009634779,0.000209565,0.0001879588,0.000930279,0.00002199107,0.0003219647],"category_scores_gemma":[0.01626979,0.00007304316,0.00008316425,0.00131754,0.0005997018,0.0005208872,0.0002449466,0.0002067428,0.00008332102],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00006229824,"about_ca_system_score_gemma":0.0005290121,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001699579,"about_ca_topic_score_gemma":0.000009069311,"domain_scores_codex":[0.9927533,0.002181042,0.001206392,0.0004084015,0.003168287,0.000282542],"domain_scores_gemma":[0.9925775,0.001121842,0.0003325932,0.0003663575,0.005308433,0.0002932856],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"bench_or_experimental","study_design_gemma":"observational","study_design_scores_codex":[0.002462822,0.000384513,0.09938453,0.00001489495,0.0001742949,0.0001060186,0.005336121,0.003161082,0.8128846,0.004178662,0.05447392,0.01743858],"study_design_scores_gemma":[0.001628787,0.001953531,0.6777208,0.0005478828,0.00004048974,0.00005720123,0.002227881,0.0005846099,0.2717897,0.002842451,0.04026382,0.000342878],"study_design_candidate":"bench_or_experimental","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9536099,0.000297373,0.03384048,0.01146454,0.0001695176,0.0001441398,0.00004700021,0.00000214331,0.0004249518],"genre_scores_gemma":[0.9758898,0.00002902178,0.02288202,0.00005425247,0.0003684165,0.000001127753,0.000001628633,0.00001127199,0.0007624446],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.5783362,"threshold_uncertainty_score":0.9920166,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1557870684248234,"score_gpt":0.4305235655144412,"score_spread":0.2747364970896178,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}