Beyond analyzing spatial patterns, GIS analysis can be used to examine or quantify relationships among features. The Modeling Spatial Relationships tools construct spatial weights matrices or model spatial relationships using regression analyses.

The Generate Spatial Weights Matrix and Generate Network Spatial Weights tools construct spatial weights matrix files that measure how features in a dataset relate to each other in space. A spatial weights matrix is a representation of the spatial structure of your data: the spatial relationships that exist among the features in your dataset.

True spatial statistics integrate information about space and spatial relationships into their mathematics. Some of the tools in the Spatial Statistics toolbox that accept a spatial weights matrix file are Spatial Autocorrelation (Global Moran's I), Cluster and Outlier Analysis (Anselin Local Moran's I), Hot Spot Analysis (Getis-Ord Gi*), and Colocation Analysis.

The regression tools provided in the Spatial Statistics toolbox model relationships among data variables associated with geographic features, allowing you to make predictions for unknown values or to better understand key factors influencing a variable you are trying to model. The Generalized Linear Regression and Geographically Weighted Regression tools allow you to verify relationships and to measure how strong those relationships are. Exploratory Regression allows you to examine a large number of Ordinary Least Squares (OLS) models quickly, summarize variable relationships, and determine if any combination of candidate explanatory variables satisfies all of the requirements of the OLS method. The Local Bivariate Relationships tool allows you to explore and determine if there are relationships between two variables in your map.

The Colocation Analysis tool measures the degree of spatial association between two point patterns, while the Forest-based Classification and Regression tool creates models and generates predictions using unsupervised learning methods for both categorical and continuous data and can use variables from rasters or distance features as well.

Tool | Description |
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Measures local patterns of spatial association, or colocation, between two categories of point features using the colocation quotient statistic. | |

The Exploratory Regression tool 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. | |

Creates models and generates predictions using an adaptation of Leo Breiman's random forest algorithm, which is a supervised machine learning method. 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. | |

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. | |

Constructs a spatial weights matrix file (.swm) using a network dataset, defining spatial relationships in terms of the underlying network structure. | |

Constructs a spatial weights matrix (.swm) file to represent the spatial relationships among features in a dataset. | |

Performs Geographically Weighted Regression (GWR), a local form of linear regression used to model spatially varying 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. | |

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. |