With the growing demand for inter-city freight transport, proportion of trucks in the freeway traffic has been increasing in China and worldwide in the past decade. There have been serious safety concerns for the prevalence of truck in freeway traffic given its size and weight, and the interferences of unsafe maneuvers of trucks on other traffic. However, existing literatures mainly focus on the crash severity of truck-involved crashes only. It is rare that the effects of the presence of trucks (of various classes) on the crash severity of non-truck-involved crashes (i.e. not involving any truck) are studied. To account for the effect of unobserved heterogeneity, random parameters discrete outcome models have been deployed to model the crash severity. However, the possible correlations between random parameters are seldom considered. This study aims to investigate the role of the presence and prevalence of trucks of various classes on the severity of non-truck involved crashes, with which both the uncorrelated and correlated panel-level space–time-varying heterogeneities are considered. To account for possible temporal instability, the uncorrelated and correlated grouped random parameters binary logit models are established for each separate year, based on the comprehensive crash and traffic data of eight freeway segments in Shandong of China during the period from 2016 to 2019. 4,008 crashes are extracted and grouped with space (i.e. road segment)-time (i.e. time of the day) variations considered. Results indicate that the proposed correlated grouped random parameters model is superior to the uncorrelated grouped random parameters logit model in three out of the four years. Also, correlation in the heterogeneous effects between super-large truck volume and average speed is significant. Moreover, temporal instability is revealed for majority of the factors, to different extents, including the heterogenous ones and volumes of all truck types. Nevertheless, this study addresses and discusses the fundamental issues of the temporally unstable correlation in unobserved heterogeneity between possible factors in crash severity analysis.