Context effects are phenomena of multiattribute, multialternative decision-making that contradict normative models of preference. Numerous computational models have been created to explain these effects, communicated through the estimation of model parameters. Historically, parameters have been estimated by fitting these models to choice response data alone. In other contexts, such as those conventionally studied in perceptual decision-making, the times associated with choice responses have proven effective in improving understanding and testing competing theoretical accounts of various experimental manipulations. Here, we explore the advantages of incorporating response time distributions into the inference procedure, using the most recent model of context effects–the multiattribute linear ballistic accumulator (MLBA) model–as a case study. First, we establish in a simulation study that incorporating response time data in the inference procedure does indeed produce more constrained estimates of the model parameters, and the extent of this constraint is modulated by the number of observations within the data. Second, we generalize our results beyond the MLBA model by using likelihood-free techniques to estimate model parameters. Finally, we investigate parameter differences when choice or choice response time data are used to fit the MLBA model by fitting different model variants to real data from a perceptual decision-making experiment with context effects. Based on likelihood-free and likelihood-based estimations of both simulated and real data, we conclude that response time measures offer an important source of constraint for models of context effects. (PsycINFO Database Record (c) 2019 APA, all rights reserved)