An overview of the Modeling Spatial Relationships toolset

The Modeling Spatial Relationships toolset contains tools for exploring and quantifying data relationships.

In addition to analyzing spatial patterns, GIS analysis can be used to examine or quantify relationships among features. Use the Modeling Spatial Relationships tools to construct spatial weights matrices or model spatial relationships using various analysis techniques including regression, forest-based approaches, and maximum entropy methods.

Tool	Description
Bivariate Spatial Association (Lee's L)	Calculates the spatial association between two continuous variables using the Lee's L statistic.
Causal Inference Analysis	Estimates the causal effect of a continuous exposure variable on a continuous outcome variable by approximating a randomized experiment and controlling for confounding variables.
Colocation Analysis	Measures local patterns of spatial association, or colocation, between two categories of point features using the colocation quotient statistic.
Exploratory Regression	Evaluates all possible combinations of the input candidate explanatory variables, looking for OLS models that best explain the dependent variable within the context of user-specified criteria.
Forest-based and Boosted Classification and Regression	Creates models and generates predictions using one of two supervised machine learning methods: an adaptation of the random forest algorithm developed by Leo Breiman and Adele Cutler or the Extreme Gradient Boosting (XGBoost) algorithm developed by Tianqi Chen and Carlos Guestrin. Predictions can be performed for both categorical variables (classification) and continuous variables (regression). Explanatory variables can take the form of fields in the attribute table of the training features, raster datasets, and distance features used to calculate proximity values for use as additional variables. In addition to validation of model performance based on the training data, predictions can be made to either features or a prediction raster.
Generalized Linear Regression (GLR)	Performs generalized linear regression (GLR) to generate predictions or to model a dependent variable in terms of its relationship to a set of explanatory variables. This tool can be used to fit continuous (OLS), binary (logistic), and count (Poisson) models.
Generate Network Spatial Weights	Constructs a spatial weights matrix file (.swm) using a network dataset, defining spatial relationships in terms of the underlying network structure.
Generate Spatial Weights Matrix	Generates a spatial weights matrix file (.swm) to represent the spatial relationships among features in a dataset.
Geographically Weighted Regression (GWR)	Performs Geographically Weighted Regression (GWR), a local form of linear regression used to model spatially varying relationships.
Local Bivariate Relationships	Analyzes two variables for statistically significant relationships using local entropy. Each feature is classified into one of six categories based on the type of relationship. The output can be used to visualize areas where the variables are related and explore how their relationship changes across the study area.
Multiscale Geographically Weighted Regression (MGWR)	Performs Multiscale Geographically Weighted Regression (MGWR), which is a local form of linear regression that models spatially varying relationships.
Ordinary Least Squares (OLS)	Performs global Ordinary Least Squares (OLS) linear regression to generate predictions or to model a dependent variable in terms of its relationships to a set of explanatory variables.
Predict Using Spatial Statistics Model File	Predicts continuous or categorical values using a trained spatial statistics model (.ssm file).
Presence-only Prediction	Models the presence of a phenomenon given known presence locations and explanatory variables using a maximum entropy approach (MaxEnt). The tool provides output features and rasters that include the probability of presence and can be applied to problems in which only presence is known and absence is not known.
Spatial Association Between Zones	Measures the degree of spatial association between two regionalizations of the same study area in which each regionalization is composed of a set of categories, called zones. The association between the regionalizations is determined by the area overlap between zones of each regionalization. The association is highest when each zone of one regionalization closely corresponds to a zone of the other regionalization. Similarly, spatial association is lowest when the zones of one regionalization have large overlap with many different zones of the other regionalization. The primary output of the tool is a global measure of spatial association between the categorical variables: a single number ranging from 0 (no correspondence) to 1 (perfect spatial alignment of zones). Optionally, this global association can be calculated and visualized for specific zones of either regionalization or for specific combinations of zones between regionalizations.