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Injury severities in traffic accidents are usually recorded on ordinal scales, and statistical models have been applied to investigate the effects of driver factors, vehicle characteristics, road geometrics and environmental conditions on injury severity. The unknown parameters in the models are in general estimated assuming random sampling from the population. Traffic accident data however suffer from underreporting effects, especially for lower injury severities. As a result, traffic accident data can be regarded as outcome-based samples with unknown population shares of the injury severities. An outcome-based sample is overrepresented by accidents of higher severities. As a result, outcome-based samples result in biased parameters which skew our inferences on the effect of key safety variables such as safety belt usage. The pseudo-likelihood function for the case with unknown population shares, which is the …