# Spatial Regression

## Definition

Spatial regression is a statistical technique used to establish relationships and associations between different spatial entities. It goes a step further than traditional regression analysis by accounting for spatial dependence and spatial heterogeneity, two distinct characteristics commonly observed in spatial data. These consistencies are notably absent from classical statistical models like OLS (Ordinary Least Squares), which assume that data are independently and identically distributed (i.i.d). By contrast, spatial regression models acknowledge and incorporate the spatial autocorrelation that exists among neighboring spatial units.

## What is Spatial Regression?

Spatial regression is a form of regression analysis used in spatial econometrics, specifically tailor-made for geographic or spatial data. It allows for modeling of data where the observations are correlated because of their relative physical locations (referred to as spatial autocorrelation) or where the structure of the variable of interest is not spatially homogeneous (referred to as spatial heterogeneity). The motivation behind using spatial regression is to avoid specification errors and generate unbiased and efficient estimators when dealing with spatial data.

There are multiple types of spatial regression models including Spatial Lag Model (SLM), Spatial Error Model (SEM), and Spatial Durbin Model (SDM), each with particular uses and assumptions. These models differ mainly in how they incorporate spatial effects, whether through the dependent variable, the error terms, or both.

## FAQs

### What is the purpose of using spatial regression?

The primary purpose of using spatial regression is to correctly model and analyze the data exhibiting spatial dependence or spatial heterogeneity. Ordinary regression models can produce misleading results when used on spatial data, which could lead to inaccurate conclusions or predictions.

### What is spatial autocorrelation in the context of spatial regression?

Spatial autocorrelation in the context of spatial regression refers to the phenomenon where the value of one unit is not independent of the values of its neighbors. In other words, nearby observations tend to be more alike than distant observations. This violates a key assumption of traditional regression models, which expect observations to be independent, leading to the necessity of spatial regression.

### What is spatial heterogeneity and how does it impact the spatial regression?

Spatial heterogeneity refers to the variation of a variable across space. It can cause a problem because traditional regression analysis assumes a constant relationship across space (homogeneity). Spatial heterogeneity could lead to unstable and unreliable estimates when using conventional regression techniques. Therefore, spatial regression is useful to appropriately model and capture such heterogeneity.

### What is the difference between Spatial Lag Model and Spatial Error Model?

The Spatial Lag Model (SLM) addresses spatial autocorrelation by incorporating the spatial lags of dependent variables into the model. It assumes that a given region's values depend on neighboring regions' values. On the contrary, the Spatial Error Model (SEM) includes spatial autocorrelation in the error term. It assumes that the error of one unit may be influenced by errors of neighboring units. The choice between the two depends on the specifics of the data and the research question at hand.