Traffic　crash　risk　prediction　models　have　been　developed　to　investigate　crash　occurrence　mechanisms　and　analyze　the　effects　of　various　traffic　operation　factors,　data　on　which　are　collected　by　densely　deployed　detectors,　on　crash　risk.　However,　in　China,　freeway　detectors　are　widely　spaced　(the　spacing　is　usually　more　than　2　km)　and　the　road　geometries　vary　frequently,　especially　in　mountainous　areas.　Moreover,　many　freeway　sections　are　located　in　urban　areas　and　serve　commuting　functions.　Due　to　the　different　mechanisms　of　crash　occurrence　on　road　segments　with　different　geometric　design　features　and　traffic　operation　status,　it　is　necessary　to　consider　these　heterogeneities　in　crash　risk　prediction.　In　addition　to　considering　observable　heterogeneous　effects,　it　is　equally　important　to　consider　the　existence　of　unobserved　heterogeneities　among　crash　units.　This　study　focuses　on　the　effects　of　different　types　of　heterogeneities　on　crash　risk　for　segments　of　the　Yongtaiwen　Freeway　in　Zhejiang　Province,　China,　using　crash,　traffic　flow,　and　road　geometric　design　data.　Latent　class　analysis　(LCA),　latent　profile　analysis　(LPA),　and　a　combination　of　both　methods　are　respectively　used　to　classify　road　segments　into　subgroups　based　on　road　geometric　design　features,　the　traffic　operation　status,　and　a　combination　of　both.　The　results　reveal　that　the　binary　logit　model　considering　the　heterogeneous　effects　of　the　combination　of　road　geometric　design　features　and　the　traffic　operation　status　achieves　the　best　performance.　Furthermore,　binary　conditional　logit　models　and　grouped　random　parameter　logit　models　are　developed　to　analyze　the　unobserved　heterogeneity　among　crash　units,　and　the　results　show　that　the　latter　has　a　better　goodness　of　fit.　Finally,　a　paradigm　of　the　crash　risk　prediction　for　freeway　segments　with　widely-spaced　traffic　detectors　and　frequently-changing　geometric　features　is　provided　for　traffic　safety　management　departments.　©　2024　Elsevier　Ltd