Compared with other methods for assessing brain function, EEG is relatively inexpensive, simple to administer, and non-invasive. Psychiatric researchers show considerable interest in determining whether EEG data, possibly in combination with other clinical characteristics, can be used to guide clinical practice: either in diagnosing psychiatric disorders or in selecting treatment. Challenges associated with using EEG data in this context include the high-dimensional and correlated nature of the data as well as issues related to data quality (i.e., EEG data of unacceptable quality may need to be discarded). We present two applications in which clinical and EEG data are used together in scalar-on-function prediction models (1) to distinguish healthy controls from those with major depressive disorder (MDD) and (2) to distinguish antidepressant responders from non-responders among those with MDD. In each case, some subjects have missing EEG data due to poor quality of the collected images. We discuss strategies for handling missing scalar and functional predictors in this context and consider implications of these strategies on the performance of the estimated prediction models.