<p>The reliability of parameter estimation is crucial in using computational models for choice data in decision-making tasks, especially so since the cognitive meaningful parameters within these models often are leveraged for further analysis. Typically, model-fitting involves using the model log-likelihood as the loss function to quantify discrepancies between model predictions and observed data. However, outlier data in choice datasets can bias parameter estimation when using log-likelihood. Alternative loss functions that are less sensitive to outliers are available. In this study, we compared a total of 3 such outlier-insensitive loss functions with the log-likelihood function in terms of parameter recovery. We compared their performance in both a reinforcement learning model in a learning paradigm and a hyperbolic model in an intertemporal choice paradigm, in both systematically varying the presence of outliers (ranging from no outliers to 25% of the data being outliers). Our parameter recovery results show that even a small proportion of outlier data can substantially impair parameter identification when using the log-likelihood function, especially for the choice consistency/explore–exploit trade-off parameter. In contrast, outlier-insensitive loss functions markedly improve the recovery of computational model parameters. Moreover, our power analysis further suggests that even a small proportion of outlier trials (e.g., 5%) can potentially undermine the statistical power to detect condition differences, underscoring the importance of accounting for outliers when using cognitive models as measurement tools. Based on our results, we recommend using the outlier-insensitive loss functions for non-hierarchical model estimation as it performed well across both the learning and the intertemporal choice paradigms and under varying degrees of outlier presence.</p>