Statistics — Page 3
Explore statistical methods, their assumptions, interpretation and limitations.
Research field
Method family
Local Moran's I
Local Moran's I, introduced by Luc Anselin in 1995, is a Local Indicator of Spatial Association (LISA) that decomposes global spatial autocorrelation into location-specific contributions. For every observation it produces a signed statistic...
Local Network-Based Spatial Analysis
Local Network-Based Spatial Analysis computes spatial statistics and network measures — such as accessibility, centrality, and density — within restricted local neighborhoods of a spatial network, revealing how connectivity and flow vary ac...
Local Ordinary Kriging
Local Ordinary Kriging (LOK) is a geostatistical interpolation method that estimates values at unsampled locations using only a spatially defined moving neighborhood of nearby observations. By restricting each prediction to a local data win...
Local Spatial Autocorrelation
Local Spatial Autocorrelation methods decompose global spatial clustering into location-specific statistics, revealing where in a study area significant clustering or dispersion occurs. Each observation receives its own association score an...
Local Spatial Durbin Model
The Local Spatial Durbin Model (Local SDM) extends the global Spatial Durbin Model by allowing regression coefficients to vary across geographic space. It combines the SDM's ability to capture both spatial lag of the dependent variable and...
Local Spatial Lag Model
The Local Spatial Lag Model extends the classical spatial lag model by allowing both the spatial autocorrelation parameter and the regression coefficients to vary across geographic locations. Instead of one global estimate of how neighborin...
Local Spatial Regression
Local Spatial Regression fits a separate regression model at each location in a study area, allowing regression coefficients to vary continuously across space. Rather than forcing one global slope on all observations, it reveals where and h...
Local Universal Kriging
Local Universal Kriging is a geostatistical interpolation method that combines a spatially varying deterministic trend with a stochastic residual, estimated using only nearby observations within a defined search neighborhood. It generalizes...
MGWR
Multiscale Geographically Weighted Regression, introduced by Fotheringham, Yang and Kang in 2017, is a spatial regression model that lets each coefficient vary across space at its own spatial scale. It generalises Geographically Weighted Re...
Moran's I
Moran's I is the standard global statistic for detecting spatial autocorrelation: whether nearby locations tend to share similar values. The index ranges from approximately −1 (perfect dispersion) through 0 (spatial randomness) to +1 (perfe...
Moran's I
Moran's I is a global statistic, introduced by Patrick Moran in 1950, that measures whether and how a continuous variable is spatially autocorrelated across mapped units. A positive value signals clustering of similar values, a negative val...
Multiscale Geographically Weighted Regression
Multiscale Geographically Weighted Regression (MGWR) is a local spatial regression framework that relaxes the single-bandwidth constraint of standard GWR by allowing each predictor to operate at its own spatial scale. Each coefficient surfa...
Multiscale Getis-Ord Gi*
Multiscale Getis-Ord Gi* extends the classic local hot spot statistic by computing Gi* z-scores across a range of spatial distance bands or neighborhood sizes. This reveals whether clusters of high or low values are scale-dependent — appear...
Multiscale Moran's I
Multiscale Moran's I extends the classic global Moran's I statistic by computing spatial autocorrelation across a series of distance lags or spatial scales. The resulting spatial correlogram reveals at which geographic scales clusters or di...
Multiscale Spatial Autocorrelation
Multiscale spatial autocorrelation extends classical spatial autocorrelation analysis by computing and comparing autocorrelation statistics (such as Moran's I) across a range of spatial scales simultaneously. This reveals at which geographi...
Network-Based Spatial Analysis
Network-based spatial analysis (NBSA) analyzes the distribution and interaction of spatial phenomena constrained to a network structure — such as roads, railways, or rivers — using network distance rather than straight-line (Euclidean) dist...
Ordinary Kriging
Ordinary Kriging (OK) is the standard geostatistical method for interpolating a continuous spatial variable at unsampled locations. It derives optimal, unbiased weights from the spatial covariance structure of the data, making it the Best L...
Panel Geary's C
Panel Geary's C extends the classic Geary contiguity ratio to panel datasets, measuring spatial autocorrelation across georeferenced units (regions, cities, countries) observed over multiple time periods. It detects whether neighboring unit...
Panel Geographically Weighted Regression
Panel Geographically Weighted Regression (Panel GWR) extends the standard GWR framework to panel data, allowing regression coefficients to vary both across geographic locations and over time. It captures spatially non-stationary relationshi...
Panel Hot Spot Analysis
Panel Hot Spot Analysis applies hot spot detection — typically via the Getis-Ord Gi* statistic — repeatedly across multiple time periods on the same spatial units, enabling researchers to track where clusters of high or low values persist,...
Panel Kernel Density Estimation
Panel Kernel Density Estimation (Panel KDE) extends the standard kernel density estimator to panel (longitudinal) data, estimating smooth density surfaces for spatial or attribute variables observed across multiple units and time periods. I...
Panel Kriging
Panel Kriging is a geostatistical interpolation method that combines kriging's spatial prediction framework with a panel (longitudinal) data structure. It estimates unknown values at unobserved locations and times by borrowing strength from...
Panel Local Indicators of Spatial Association
Panel Local Indicators of Spatial Association extends Anselin's LISA statistics — most commonly Local Moran's I — to panel datasets, identifying spatial clusters and outliers at each location across multiple time periods. By applying local...
Panel Multiscale Geographically Weighted Regression
Panel MGWR extends Multiscale Geographically Weighted Regression to repeated-observations (panel) data, allowing each predictor to operate at its own spatial bandwidth while controlling for unit-specific or time-specific fixed effects. It i...