Rheological measurements on a model thixotropic suspension by Dullaert and Mewis [J. Non-Newtonian Fluid Mech. 139(1-2), 21-30 (2006); Rheol. Acta 45, 23-32 (2005)] are extended to include large amplitude oscillatory shear (LAOS) flow, shear flow reversal, and a novel unidirectional LAOS flow to provide an extended rheological data set for testing constitutive models. We use this extended data set to test a new structure-based model developed by improving the Delaware thixotropic model [A. Mujumdar et al., J. Non-Newtonian Fluid Mech. 102,157-178 (2002); A. J. Apostolidis et al., J. Rheol. 59, 275-298 (2015)]. Model parameters are determined from steady, small amplitude oscillatory, and step shear rate tests. Holding those parameters fixed, model predictions are compared to LAOS experiments. Similar comparisons are made for three contemporary models from the literature. Two of these models use a scalar internal structural parameter and include the modified Jeffreys model proposed by de Souza Mendes and Thompson [Rheol. Acta 52, 673-694 (2013)]. The third model is based on fluidity additivity [F. Bautista et al., J. Non-Newtonian Fluid Mech. 80, 93-113 (1999)]. A common weakness in all models is shown to be the use of scalar order parameters that cannot account for the reversal of flow directionality inherent in LAOS flow. This is further illustrated by comparison with flow reversal and unidirectional LAOS experiments. (C) 2016 The Society of Rheology.