 This study found that the logbinomial model can be biased when the link function is mis-specified, or when the response variable has a non-linear relationship with the predictor variables. When the response variable is truncated at the right tail, the bias increases as the proportion of truncated observations increases. In contrast, the robust Poisson model was unbiased regardless of the model mis-specification or the non-linearity of the response variable. Therefore, the robust Poisson model is preferred over the logbinomial model in situations where the link function is mis-specified, or the response variable has a non-linear relationship with the predictor variables. This article was authored by Wansi Chen, Lei Chen, Jia Xia Xia, and others.