Localizing general models based on local indices of spatial association

A general regression model for large areas may have poor statistical properties for smaller sub-regions. In this study, we test the local indicators of spatial association (LISA) in the selection of localization areas of a general regression model. We present four different LISAs: Moran’s I _i , Geary’s c _i , G _i , and G _i *. These indices show if there is a cluster of similar values in the data (Moran’s I _i and Geary’s c _i ) or if there is a cluster of positive or negative values (G _i and G _i *). The material is NFI9 (9th National Forest Inventory) sample tree (Pinus sylvestris) data from Southern Finland. LISAs were calculated from the residuals of a form height regression model, which was fitted to the original data. We detected statistically significant clustering of similar values with both global indices Moran’s I and Geary’s c. This means that local indices may show statistically significant clustering of similar values only because the surrounding of an observation happens to have high values. Therefore we use G _i *-index in selection of sub-areas. We tested the localization in three sub-areas: (1) one where the G _i *-index was positive, (2) one where the index was negative, and (3) one where the index was both positive and negative and zero. In particular, localization removed the local bias of the global model. The effect of localization on variances was minor. The effect of localization on residuals in Areas 1 and 2 correspond to a level correction of the global model. The G _i *-index (and G _i -index) seem to be useful for selecting localization areas, even though there is still need for future studies.