Statistical Methods

This section documents the mathematical foundations behind MORIE’s estimators. The methods are dataset-agnostic — they apply to any suitably-shaped tabular input, including the OTIS placement records, TPS incident feeds, CPADS survey data, and any other dataset that matches the estimator’s signature.

Quick reference

Each entry below names the estimator, the estimand it targets, and the Python function that produces it.

Causal estimators

  • run_propensity_ipw_analysis — IPW (Hájek), ATE

  • estimate_att — IPW (Hájek), ATT

  • estimate_atc — IPW (Hájek), ATC

  • estimate_aipw — AIPW (doubly robust), ATE

  • estimate_gate — GATE (AIPW per group)

  • estimate_cate — T-learner / S-learner, CATE (per unit)

  • estimate_late — 2SLS / Wald IV, LATE

  • estimate_ate — DML–PLR, ATE

  • estimate_irm — DML–IRM, heterogeneous ATE

  • estimate_pliv — DML–PLIV, LATE

  • estimate_ate_gcomputation — G-computation, ATE

  • run_ebac_selection_ipw_analysis — eBAC-IPW, selection-adjusted ATE

  • e_value — E-value sensitivity bound

  • sensitivity_rosenbaum — Rosenbaum bounds

Logistic / model comparison

  • run_weighted_logistic_analysis — weighted logistic, OR

  • compare_nested_logistic_models — nested-model LRT

Survey + descriptive statistics

  • morie.survey helpers — survey-weighted CIs and prevalence

  • horvitz_thompson_total — HT estimator, population total

  • hajek_mean — Hájek estimator, population mean

Power + Bayes

  • run_power_design_module — N required for a given design

  • Beta-binomial Bayes — posterior mean / CI (see morie.causal)

Psychometrics

  • crba — Cronbach’s α (internal consistency)

  • mcdo — McDonald’s ω (reliability)

  • kmo — KMO sampling adequacy

  • bart — Bartlett’s sphericity (factorability)

  • paran — Parallel analysis (factor retention)

  • crel — Composite reliability

  • ave — Average Variance Extracted (convergent validity)

OTIS-specific

  • rplace — Regional placement counts / proportions

  • astcmb — Alert-state combination encoding

  • volat — Regional volatility (movement metric)

  • otdml — DML IRM on correctional data, ATE / ATT