The proposed research contributes to our understanding of incorporating heterogeneity in discrete choice models with respect to exogenous variables and decision rules. Specifically, the proposed latent segmentation based mixed models segment population to different classes with their own decision rules while also incorporating unobserved heterogeneity within the segment level models. In our analysis, we choose to consider both random utility and random regret theories. Further, instead of assuming the number of segments (as 2), we conduct an exhaustive exploration with multiple segments across the two decision rules. The model estimation is conducted using a stated preference data from 695 commuter cyclists compiled through a web-based survey. The probabilistic allocation of respondents to different segments indicates that female commuter cyclists are more utility oriented; however, the majority of the commuter cyclist's choice pattern is consistent with regret minimization mechanism. Overall, cyclists' route choice decisions are influenced by roadway attributes, cycling infrastructure availability, pollution exposure, and travel time. The analysis approach also allows us to investigate time based trade-offs across cyclists belonging to different classes. Interestingly, we observe that the trade-off values in regret and utility based segments for roadway attributes are similar in magnitude; but the values differ greatly for cycling infrastructure and pollution exposure attributes, particularly for maximum exposure levels.