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It is a dangerous behaviour for pedestrians and nonmotorized vehicles to cross intersections without waiting when they arrive at intersections during the red-light period. This paper investigates three typical signalized major-major intersections in the center of Beijing, by collecting and analyzing 1368 samples of pedestrians and nonmotorized vehicles. A random parameter logit model (RPLM) is established, with immediate red-light running (IRLR) behaviour as the dependent variable. The results show that the number of people waiting upon arrival, number of people crossing upon arrival, traffic mode, motor vehicle phase upon arrival, and speed change upon arrival have significant effects on IRLR behaviour. Accordingly, we suggest enforcing education administration on cyclists to reduce cyclists' IRLR behaviour. Thus, people's red-light running (RLR) behaviour will further decrease with fewer cyclists' IRLR behaviour. [ABSTRACT FROM AUTHOR]

• Ordered and unordered frameworks are used to investigate cyclists' RLR behaviors. • Heterogeneity in means and variances of random parameters are examined. • Threshold heterogeneity in the ordered frameworks is examined. • Differences in factors between risk-taking and opportunistic behaviors are analyzed. • Insights are vital for precise micro-simulation and practical traffic safety measures. This paper aims to empirically evaluate the ordered and unordered discrete outcome frameworks to approach riders' red-light running (RLR) decisions and compare the differences in influencing factors between riders' risk-taking and opportunistic RLR behaviors. A total of 2057 cyclist samples approaching the intersections during red signals were observed by video in Beijing, China. To better capture the unobserved heterogeneity, apart from the traditional models, three advanced models including the random thresholds random parameters hierarchical ordered logit (RTRPHOL) model, the random parameters logit model with heterogeneity in means and variances (RPLHMV) model, and the correlated random parameters logit model with heterogeneity in means (CRPLHM), are developed. Results show that: 1) the unordered framework statistically outperformed its ordered counterparts, and the RPLHMV and CRPLHM models are statistically better than others. 2) The female and e-bicycle indicators produce a heterogeneity-in-means effect, and the low-volume and left-side indicators produce a heterogeneity-in-variances effect. 3) e-bike riders and riders from the right side are more inclined to have risk-taking behavior than opportunistic behavior, and both RLR behaviors of cyclists are most susceptible to the number of violating individual indicator. Findings illustrate that multilayer unobserved heterogeneity should be adequately considered in developing precise micro-simulation and practical guidance in traffic safety. [ABSTRACT FROM AUTHOR]