Increasingly survey data is being used in regression analysis. If disturbance correlation arising from block and/or subblock random effects is ignored, it can lead to inefficient regression estimates and predictions as well as misleading inferences. This paper addresses the problem of testing for subblock effects in the presence of block effects in a three-stage sampling regression model. Point optimal invariant (POI) and one-sided and two-sided Lagrange multiplier (LM) tests are constructed. An empirical comparison of the sizes and powers of two versions of the POI tests and the two LM tests is reported. It reveals that the true size of the one-sided LM test is about one-half of its nominal size and that the two-sided LM test lacks power. The POI tests are found to have extremely desirable small-sample properties.