Localized Autocorrelation Diagnostic Statistic (LADS) for Sociological Models

Regression models in sociology, because they are often based on data sets with a surfeit of variables and an underlying connectivity pattern, permit the use of unique diagnostic techniques. This article elaborates on the localized autocorrelation diagnostic statistic, LADS, which determines the probability that in a model with N cases, a connected set of size C or more among the E most extreme, same-signed residuals occurred by chance. LADS can suggest variables to be included in a model and can be applied to time-series, geographic, group (i.e., cliques, blocks, clusters, and different values on a nominal variable), and network data. Exact formulas for LADS for time-series and grouped data, as well as principles for the robustness of LADS under global autocorrelation, are introduced, and a general algorithm for all data sets of connected cases is presented. Examples demonstrate how LADS can suggest new variables and improve the overall fit of models.