Does number of level-2 units in multilevel structural equation modeling matter?

Abstract

How to determine the number of level-2 units in multilevel structural equation modeling (MSEM) as a standard applied to nested or hierarchical data structure was still unknown. This research used Canada data in the large database “Programme for International Student Assessment 2003”(PISA 2003) to check the model-fit indexes and parameters stability in our proposed empirical example processed by MSEM under different numbers of level-2 units. Our proposed example model was first be handled to fit Canada data (26884 students, 948 schools), and then the stabilities of the estimated parameters in the example model under 120, 240, 360, 480, 600, 720, 840 level-2 units were compared. Level-1 units in each school less than10 students will be crossed out in advance. Besides, intraclass correlations of all variables were controlled in a specified range in different numbers of level-2 units. Finally, we found the ratio of the number of level-2 units relative to the number of estimated parameters of between-level in the multilevel model were 8: 1.