Quantile regression is used to model the effects of covariates on the quantiles of the response variable of interest. This is in contrast to traditional regression modelling, which estimates the conditional mean of the response variable at certain values of the covariates. Despite its usefulness in addressing diverse research questions, quantile regression is mostly utilized for the continuous response setting, whereas the traditional quantile regression approaches cannot be directly applied when the response variable is discrete. Recently, taking a model-based approach to model the conditional quantiles for a discrete distribution has been proposed. This approach mostly considers the continuous counterpart of the generating distribution in performing the estimation. We explore some numerical approaches when taking this model-based approach, including evidence supporting the validity of the model-based method. Moreover, generalized linear models play a central role in this approach, while nonlinear least squares is shown to be a reliable method in computation. Additional data structures using this model-based approach will also be discussed.