Recent developments in mathematical modeling of electroencephalography (EEG) enable the tracking of otherwise-inaccessible neurophysiological parameters throughout sleep. Likewise, advancements in wearable electronics have enabled easy and affordable collection of sleep EEG at home. The convergence of these two advances, namely neurophysiological modeling for mobile sleep EEG, can boost preclinical and clinical assessments of sleep. However, this subject area has received limited attention in existing literature. To address this, we used an established model of the corticothalamic system to analyze EEG power spectra from five datasets, spanning from research-grade systems to at-home mobile EEG. In the present work, we compare the convergent and divergent features of the data and the estimated physiological model parameters. While data quality and characteristics differ considerably, key patterns consistent with previous theoretical and empirical work are observed. During the transition from lighter to deeper NREM, (1) exponent of the aperiodic ($1/f$) spectral component is increased, (2) bottom-up thalamocortical drive is reduced, (3) corticocortical connection strengths are increased. This effect is observed in healthy subjects but is interestingly absent when taking SSRI antidepressants, suggesting possible effects of ascending neuromodulation on corticothalamic oscillations. We further show a month-long increase in REM% in one mobile EEG subject, associated with boosted high-frequency activity in spectra and higher thalamothalamic gains in the model, pointing to possible changes of thalamic inhibition in REM parasomnias. Our results provide a proof-of-principle for the utility and feasibility of this physiological modeling-based approach to analyzing mobile EEG data, providing a mechanistic measure of brain physiology during sleep.