  Circadian rhythms influence multiple essential biological activities
including sleep, performance, and mood. The dim light melatonin onset (DLMO) is
the gold standard for measuring human circadian phase (i.e., timing). The
collection of DLMO is expensive and time-consuming since multiple saliva or
blood samples are required overnight in special conditions, and the samples
must then be assayed for melatonin. Recently, several computational approaches
have been designed for estimating DLMO. These methods collect daily sampled
data (e.g., sleep onset/offset times) or frequently sampled data (e.g., light
exposure/skin temperature/physical activity collected every minute) to train
learning models for estimating DLMO. One limitation of these studies is that
they only leverage one time-scale data. We propose a two-step framework for
estimating DLMO using data from both time scales. The first step summarizes
data from before the current day, while the second step combines this summary
with frequently sampled data of the current day. We evaluate three moving
average models that input sleep timing data as the first step and use recurrent
neural network models as the second step. The results using data from 207
undergraduates show that our two-step model with two time-scale features has
statistically significantly lower root-mean-square errors than models that use
either daily sampled data or frequently sampled data.
