The receiver operating characteristic (ROC) curve is a currently well-developed statistical tool for characterizing accuracy of medical diagnostic tests. Recently, several authors suggest approaches referred to as ROC regression models in order to evaluate effects of factors influencing accuracy of diagnostics. Oe, Ochi, & Goto (2016) have presented an inference process of a ROC regression model based on Generalized Additive Model with penalized splines via REstricted Maximum Likelihood method. This approach focuses on smoothing continuous-type covariates, but in addition to continuous covariates (e.g. age, weight, etc), discrete covariates (e.g. sex, smoking, etc) often significantly effect on accuracy of diagnostics. On this article, we proposed an extended method so that we could model discrete and continuous covariates simultaneously. We provided the formulation and the inference procedure, and evaluated inference performance of this method through several simulations. In the simulation result, we found that both effect of discrete and continuous covariates on the ROC was appropriately estimated. Furthermore, we applied our method to the neonatal hearing impairment screening data and evaluated how some covariates effect on the ROC with auditory brainstem response (ABR) as a diagnostic valuable for hearing impairment. From the analysis results, it was suggested that sex and Transient Evoked Otoacoustic Emission (TEOAE) influenced on the ROC with ABR.