Statistics — Page 45
Explore statistical methods, their assumptions, interpretation and limitations.
Research field
Method family
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 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 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 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 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 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 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 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 Monte Carlo Simulation
Spatial Monte Carlo simulation applies random sampling methods to spatial problems, generating many stochastic realisations of a spatial process — such as a random field, point pattern, or network — to estimate distributional properties, pr...
Spatial Panel Model
The spatial panel model is a family of econometric models that adds spatial dependence to panel data (units observed over time). It combines fixed- or random-effects panel structure with spatial lag, spatial error, or spatial Durbin compone...
Spatial Propensity Score Weighting
Spatial propensity score weighting extends inverse probability of treatment weighting (IPTW) to settings where units are geographically located and treatment assignment may depend on spatial factors such as location, neighborhood characteri...
Spatial Regression
Spatial regression is a family of regression models that build geographic neighbourhood relationships directly into the model, introduced by Luc Anselin in his 1988 treatment of spatial econometrics. It splits into a spatial lag model, wher...
Spatial Regression of Crime
Spatial regression models explain crime rates across areal units — neighborhoods, census tracts, counties — while explicitly accounting for the fact that nearby places tend to have similar crime levels. Ordinary regression assumes each unit...
Spatial SAC Model
The Spatial Autoregressive Combined (SAC) model, also known as the SARAR model, simultaneously accounts for spatial dependence in both the dependent variable and the error term. Formalized by LeSage and Pace (2009), the SAC model combines t...
Spatial Variational Inference
Spatial variational inference is a scalable approximate Bayesian method that fits latent Gaussian or Gaussian-process models to georeferenced data by optimising a lower bound on the marginal likelihood. It replaces expensive MCMC sampling w...
Spearman Correlation
The Spearman rank correlation coefficient (ρ) is a nonparametric measure of the monotonic association between two variables. Introduced by Charles Spearman in 1904, it converts raw observations to ranks and measures how consistently one var...
Split-Plot Design
The split-plot design is a parametric experimental design that applies one factor to large whole plots and a second factor to subdivisions (sub-plots) within each whole plot. It was introduced by Frank Yates in 1935 to handle agricultural e...
Stable Population Theory
Stable Population Theory is a mathematical framework in demography that describes the age structure and growth dynamics of a closed population subject to constant age-specific fertility and mortality schedules over a long period. Foundation...
State Space Model
A state space model is a general time series framework that describes a series through unobserved (latent) state variables linked by a measurement equation and a transition equation, with the states estimated in real time by the Kalman filt...
Status Attainment Model
The status attainment model, introduced by Peter Blau and Otis Dudley Duncan in The American Occupational Structure (1967), is a recursive path model that explains an individual's occupational status from their social origins and intervenin...
Stepwise Regression
Stepwise regression is an automated variable selection procedure for multiple linear regression that adds or removes predictor variables one at a time according to a statistical criterion, typically the F-statistic or a p-value threshold. T...