LM tests for functional form and spatial error correlation form and spatial error correlation

This article derives Lagrangian multiplier (LM) tests to jointly test for functional form and spatial error correlation. In particular, this article tests for linear and log-linear models with no spatial error dependence against a more general Box-Cox model with spatial error correlation. Conditional LM tests and modified Rao score tests that guard against local misspecification are also derived. These tests are easy to implement and are illustrated using Anselin's crime data. The performance of these tests is also compared using Monte Carlo experiments.