Statistics — Page 4
Explore statistical methods, their assumptions, interpretation and limitations.
Research field
Method family
Machine Learning-Augmented Sensitivity Analysis for Causality
Machine learning-augmented sensitivity analysis combines flexible ML estimators with formal robustness checks to assess how much unmeasured confounding would be required to overturn a causal finding. Rooted in Chernozhukov et al.'s double/d...
Machine Learning-Augmented Synthetic Control Method
The machine learning-augmented synthetic control method extends the classical synthetic control estimator by using penalized regression or other ML algorithms — such as lasso, ridge, or random forests — to construct the donor weights and to...
Machine learning-augmented causal impact analysis
Machine learning-augmented causal impact analysis combines quasi-experimental counterfactual reasoning with flexible ML prediction models to estimate the causal effect of an intervention on a time series outcome. Building on Brodersen et al...
Machine learning-augmented difference-in-differences
Machine learning-augmented DiD combines the classic difference-in-differences identification strategy with flexible ML estimators for nuisance functions — the propensity score and the outcome regression — to obtain valid causal estimates ev...
Machine learning-augmented doubly robust estimation
Machine learning-augmented doubly robust (ML-DR) estimation combines the classical doubly robust (AIPW) identification strategy with flexible machine learning models for the nuisance functions — the propensity score and the outcome regressi...
Machine learning-augmented event study design
Machine learning-augmented event study design combines the standard event study framework — which traces outcome dynamics around a treatment date — with ML-based methods such as double/debiased machine learning (DML) or regularized regressi...
Machine learning-augmented instrumental variables
Machine learning-augmented instrumental variables combines the causal identification power of classical IV with modern high-dimensional machine learning — using methods such as LASSO, random forests, or neural networks to select valid instr...
Machine learning-augmented propensity score weighting
Machine learning-augmented propensity score weighting (ML-PSW) replaces logistic regression with flexible ML algorithms — such as gradient boosting, LASSO, or random forests — to estimate the propensity score, then uses inverse probability...
Machine learning-augmented regression discontinuity design
Machine learning-augmented regression discontinuity design (ML-RDD) combines the sharp identification logic of classical RDD — exploiting a known assignment cutoff in a running variable — with flexible, data-adaptive ML methods for bandwidt...
Marginal structural model in education research
A marginal structural model (MSM) is a causal inference technique that uses inverse probability weighting to estimate the effect of a treatment or educational intervention that changes over time. Introduced by Robins, Hernán and Brumback (2...
Matching Estimator
The matching estimator identifies the causal effect of a treatment by pairing each treated unit with one or more untreated units that have similar observed characteristics. Formalised by Rubin (1973) and given rigorous large-sample theory b...
Matching Methods
Matching Methods are a family of causal-inference techniques beyond propensity-score matching that pair treated and control units with similar covariates so that a treatment effect can be read off the balanced sample. The family includes Co...
Mendelian Randomization
Mendelian randomization is a method for estimating causal effects of exposures on outcomes using genetic variants as instrumental variables. Introduced by George Davey Smith in the 1990s, it exploits Mendel's law of segregation to remove co...
Meta-Regression
Meta-regression is a statistical technique that extends conventional meta-analysis by regressing study-level effect sizes on one or more study characteristics (moderators) to explain between-study heterogeneity. Formalized by Thompson and H...
Moderation Analysis
Moderation analysis tests whether the effect of a predictor X on an outcome Y changes with the level of a third variable W, the moderator. It is estimated within a regression framework through an interaction term X×W, popularised by Aiken &...
Multi-period Coarsened Exact Matching
Multi-period Coarsened Exact Matching (multi-period CEM) extends the CEM framework of Iacus, King, and Porro to longitudinal data with multiple pre- and post-treatment periods. It bins continuous covariates into coarsened categories, matche...
Multi-period Counterfactual Impact Evaluation
Multi-period Counterfactual Impact Evaluation (CIE) estimates the causal effect of a policy or program by constructing what would have happened to treated units across multiple time periods had they not been treated. Unlike single-period ev...
Multi-period Difference-in-differences
Multi-period Difference-in-Differences extends the classic two-period DiD framework to settings where units adopt treatment at different points in time. Formalised by Callaway and Sant'Anna (2021) and Goodman-Bacon (2021), it decomposes the...
Multi-period Doubly Robust Estimation
Multi-period doubly robust (DR) estimation extends the classic doubly robust approach to longitudinal settings with multiple treatment periods and time points. It combines an outcome regression model and a propensity score model for each pe...
Multi-period Event Study Design
The multi-period event study design estimates causal treatment effects at each point in time relative to the treatment onset, using panel data with multiple pre- and post-treatment periods. By plotting the full path of treatment coefficient...
Multi-period Fuzzy Regression Discontinuity
Multi-period fuzzy regression discontinuity design estimates a local average treatment effect when a cutoff rule only partially determines treatment — that is, crossing the threshold raises the probability of treatment but does not guarante...
Multi-period Interrupted Time Series
Multi-period Interrupted Time Series (MITS) extends the classic ITS framework to settings where two or more interventions occur at known time points within the same series. By fitting a segmented regression with multiple breakpoints, MITS e...
Multi-period Inverse Probability Weighting
Multi-period Inverse Probability Weighting (IPW) estimates the causal effect of a treatment that varies across multiple time periods by reweighting observations according to the probability of receiving each period's treatment given past tr...
Multi-period Matching Estimator
The multi-period matching estimator extends the standard matching framework to settings with multiple time periods, pairing each treated unit to similar untreated units based on pre-treatment covariates or propensity scores, then using with...