qmodel: A command for fitting parametric quantile models

Abstract

In this article, we introduce the qmodel command, which fits parametric models for the conditional quantile function of an outcome variable given covariates. Ordinary quantile regression, implemented in the qreg command, is a popular, simple type of parametric quantile model. It is widely used but known to yield erratic estimates that often lead to uncertain inferences. Parametric quantile models overcome these limitations and extend modeling of conditional quantile functions beyond ordinary quantile regression. These models are flexible and efficient. qmodel can estimate virtually any possible linear or nonlinear parametric model because it allows the user to specify any combination of qmodel-specific built-in functions, standard mathematical and statistical functions, and substitutable expressions. We illustrate the potential of parametric quantile models and the use of the qmodel command and its postestimation commands through realand simulated-data examples that commonly arise in epidemiological and pharmacological research. In addition, this article may give insight into the close connection that exists between quantile functions and the true mathematical laws that generate data.