In this research, statistical and deep learning models are applied to determine factors that affect motorcycle crash-injury severities. Four methodological challenges are considered: 1) imbalanced data (because fatal injuries are an exceedingly small portion of all resulting injury outcomes); 2) unobserved heterogeneity (because many unobserved factors will influence resulting injury severities); 3) quantification of variable effects; and 4) the possibility of temporally shifting relationships among variables. Convolutional neural networks and deep neural networks are the deep learning models considered, and random parameters logit models with heterogeneity in means and variances is the statistical model considered. Extensive experimentation indicated that data imbalance and unobserved heterogeneity could be best handled in deep learning models with a Bayesian deep neural network with a random generator and weighted loss function. With statistical modeling indicating significant shifts in model parameters over time, the data were segmented by year and both statistical and deep learning models were estimated. While techniques are available for deep learning to potentially handle data imbalance and unobserved heterogeneity, the quantification of variable effects and temporal shifts remains a challenge. For example, a comparison of variable effects show that the deep learning estimates of variable effects are generally inconsistent with the plausible values generated by the statistical models in terms of magnitudes and occasionally in terms of direction, indicating a need for improvements in deep-learning variable-effect extraction methods. The findings also show the need for future work to isolate the effect of complex temporal relationships which are currently imbedded in deep learning approaches, because the segmentation of data that has been used in statistical models to isolate temporal effects, and even the use of all data and defining new time-dependent variables, may not be a viable deep learning option due to the potential loss in predictive performance.