Statistics — Page 65
Explore statistical methods, their assumptions, interpretation and limitations.
Research field
Method family
Spatial Bayesian Inference
Spatial Bayesian inference applies Bayesian hierarchical modeling to data indexed by geographic location. By placing structured spatial priors on location-specific random effects, the model borrows information from neighboring regions or ne...
Spatial Bayesian Model Averaging
Spatial Bayesian model averaging (spatial BMA) extends classical BMA to settings where observations are georeferenced and spatial dependence must be modelled. Rather than selecting a single spatial regression model — which spatial weight ma...
Spatial Bootstrap Simulation
Spatial bootstrap simulation is a resampling technique designed for spatially dependent data. By resampling contiguous spatial blocks rather than independent observations, it preserves the local autocorrelation structure of the data and yie...
Spatial Causal Impact Analysis
Spatial causal impact analysis estimates the causal effect of a spatially-targeted intervention — a policy, shock, or treatment applied to particular locations — while explicitly accounting for geographic spillovers between treated and untr...
Spatial Coarsened Exact Matching
Spatial Coarsened Exact Matching applies the Coarsened Exact Matching framework to study designs involving geographic units — neighbourhoods, census tracts, municipalities, or grid cells. Covariates are coarsened into discrete bins and unit...
Spatial Conflict Analysis
Spatial conflict analysis models armed conflict while taking geography seriously: conflict is not randomly scattered but clusters in space, and a place's risk depends on its neighbors. Building on georeferenced data and spatial-statistical...
Spatial Counterfactual Impact Evaluation
Spatial Counterfactual Impact Evaluation (SCIE) is a family of quasi-experimental methods that estimate the causal effect of geographically targeted policies — such as EU Cohesion Funds, enterprise zones, or place-based subsidies — by const...
Spatial Difference-in-Differences
Spatial Difference-in-Differences (Spatial DiD) extends the classical DiD estimator to settings where observations are geo-referenced and outcomes may be spatially autocorrelated or subject to spillover effects. Introduced by Delgado and Fl...
Spatial Doubly Robust Estimation
Spatial doubly robust estimation is a semiparametric causal inference method that combines propensity score weighting with outcome regression modeling — providing protection against misspecification of either component — while explicitly ac...
Spatial Durbin Model
The Spatial Durbin Model is a general spatial regression model that includes a spatial lag of both the dependent variable (ρWy) and the explanatory variables (WXθ). Introduced as the recommended starting point by LeSage and Pace (2009), it...
Spatial Entropy Balancing
Spatial entropy balancing extends standard entropy balancing to observational settings where units are embedded in geographic space, incorporating spatial structure into the reweighting process so that balance is achieved while respecting s...
Spatial Error Model
The Spatial Error Model, developed within Anselin's spatial econometrics framework (1988), is a regression model that assumes spatial dependence enters through the error term: the disturbances of neighbouring units are correlated. It is use...
Spatial Event Study Design
Spatial event study design estimates the dynamic causal effects of a geographically concentrated shock or policy by plotting how outcomes in affected locations evolve relative to unaffected locations across time periods, while explicitly ac...
Spatial Fuzzy Regression Discontinuity
Spatial Fuzzy Regression Discontinuity Design (Spatial Fuzzy RDD) estimates a local average treatment effect when a geographic boundary determines treatment eligibility but some units on either side of the boundary fail to comply with their...
Spatial Gibbs Sampling
Spatial Gibbs sampling applies the Gibbs sampler — a coordinate-wise Markov chain Monte Carlo algorithm — to models where observations are arranged in space and nearby locations are statistically dependent. By exploiting the conditional ind...
Spatial Instrumental Variables
Spatial Instrumental Variables (Spatial IV) is a causal inference method for settings where units — regions, firms, neighborhoods — are spatially interdependent, creating endogeneity that standard IV approaches ignore. It constructs instrum...
Spatial Interaction Model
Spatial interaction models predict the volume of flows — migrants, commuters, shoppers, trade, trips — between origins and destinations as a function of the size of each place and the distance or cost separating them. By analogy to Newton's...
Spatial Interrupted Time Series
Spatial Interrupted Time Series (Spatial ITS) extends the classic ITS design to settings where units are geo-referenced and outcomes in one location may spill over into or correlate with outcomes in neighbouring locations. It estimates the...
Spatial Inverse Probability Weighting
Spatial Inverse Probability Weighting extends the classical IPW estimator to settings where units are geo-referenced and spatial location is a confounding dimension. By incorporating geographic coordinates or spatial proximity into the prop...
Spatial Kalman Filter
The spatial Kalman filter applies classical Kalman filtering to spatio-temporal state-space models, treating a spatially distributed latent field as the hidden state that evolves over time. At each time step, the filter recursively predicts...
Spatial Lag Model
The Spatial Lag Model is an autoregressive regression that assumes spatial dependence in the dependent variable itself: the outcome values of neighbouring units enter the model as an explanatory term (ρWy). It was formalised in Anselin's Sp...
Spatial MCMC
Spatial MCMC applies Markov chain Monte Carlo sampling to Bayesian models that explicitly account for spatial dependence among observations. It draws posterior samples from models such as conditional autoregressive (CAR), simultaneous autor...
Spatial Marginal Structural Model
The Spatial Marginal Structural Model (Spatial MSM) extends the classical marginal structural model to settings where units are geographically distributed and spatial dependencies — such as neighborhood spillovers, clustering, and spatial c...
Spatial Matching Estimator
The Spatial Matching Estimator estimates causal treatment effects by pairing each treated geographic unit with one or more similar untreated units nearby, exploiting the assumption that units close in space share similar unobserved characte...