Driving at nighttime may make drivers more likely to be involved in fatal crashes. To investigate the temporal instability and age differences of contributors determining different injury severity levels in nighttime crashes, this paper estimates three groups of random parameters logit models with heterogeneity in the means and variances (young/middle-age/old groups). Nighttime single-vehicle crashes in this study are gathered over four years in California, from January 1, 2014, to December 31, 2017, provided by Highway Safety Information System, including single-vehicle crashes occurring under dark, dawn, and dusk lighting conditions. Simultaneously, to investigate the temporal instability and transferability of nighttime crash severity relating to drivers of different ages, three disaggregate groups are defined: young drivers (15–29 years old), middle-age drivers (30–49 years old), old drivers (over 49 years old). Three injury-severity categories are determined as outcome variables: severe injury, minor injury, and no injury, while multiple factors are investigated as explanatory variables, including driver characteristics, vehicle characteristics, roadway characteristics, environmental characteristics, crash characteristics, and temporal characteristics. Two series of likelihood ratio tests are undertaken to unveil the contributors determining nighttime crash injury severities varying among drivers of different ages over time. Besides, the current study also compares the differences between out-of-sample and within-sample predictions. The results indicate the unstable direction of predictions across different age groups over time and underscore the necessity to adequately accommodate the temporal instability and age differences in accident prediction. More studies can be conducted to accommodate the self-selectivity issue and the out-of-sample prediction differences between using the parametric models and non-parametric models.