Spatial regression models
Spatial error model (SEM) assumes that spatial autoregressive process occurs only in the error term and neither in response variable and predictor variables. It is due to omitted (unobserved) spatially correlated variables, or the boundaries of spatial regions not coinciding with actual behavior units. SEM assumes that there are spatial variations between response variable and error, independent variable and error, among omitted variables not considered in the model. But there is not spatial variation between X and Y in the model. The spatial error model is used mainly to obtain more efficient estimators. For, example, tree height at one location is not only a function of DBH, but also affected by those unobserved variables at neighboring locations.
Spatial lag model (SLE) indicates that the Yi depends one its j neighbors in addition to Xi. SLM assumes there are variations between Y and error, Y and X. There is no spatial variation between X and error. SLM is suitable for those cases when there are structural spatial interactions among tree heights and spatial competition is emphasized.
SDM indicates that Yi depends on both the response variable and DBH of its surrounding trees in addition to Xi. The spatial variations exist in Y and X, Y and error, X and error. The SDM seems closer to the reality of the relationships among trees in forest stands.
Spatial lag model (SLE) indicates that the Yi depends one its j neighbors in addition to Xi. SLM assumes there are variations between Y and error, Y and X. There is no spatial variation between X and error. SLM is suitable for those cases when there are structural spatial interactions among tree heights and spatial competition is emphasized.
SDM indicates that Yi depends on both the response variable and DBH of its surrounding trees in addition to Xi. The spatial variations exist in Y and X, Y and error, X and error. The SDM seems closer to the reality of the relationships among trees in forest stands.
