Thixotropic materials belong to the important class of time dependent, evolving, and aging systems. Their characteristics are currently understood through rheological measurements of steady and step shear wherein the steady states reached at large deformations and the transition from one steady state to another are monitored. Small deformation protocols are not well explored for such systems. This is contrary to the common approach of probing equilibrium state and small perturbations from the equilibrium state initially by focusing on linear viscoelasticity. This work addresses the question of how to understand thixotropic materials by focusing on both the small and large deformations. A model suspension of fumed silica in polyisobutylene/paraffin oil is characterized using steady shear, transient shear, and oscillatory shear rheology. The physical processes occurring due to structural changes during each of the tests are interpreted from the corresponding response. Several structural kinetics and elastoplastic/viscoelastic phenomenological models are evaluated, and a novel combination of models is proposed to obtain the description of the responses to various tests. The advantage of this strategy is highlighted in terms of possible difference in the mechanisms at small and large deformations. Kramers-Kronig relations are used to examine the experimental and simulated dataset obtained from oscillatory shear to identify possible violation of linearity or time independence. We demonstrate that the analysis of the oscillatory response using Kramers-Kronig relations leads to important insights about these systems. © 2020 Author(s).