  In this study, learning modalities offered by public schools across the
United States were investigated to track changes in the proportion of schools
offering fully in-person, hybrid and fully remote learning over time. Learning
modalities from 14,688 unique school districts from September 2020 to June 2021
were reported by Burbio, MCH Strategic Data, the American Enterprise
Institute's Return to Learn Tracker and individual state dashboards. A model
was needed to combine and deconflict these data to provide a more complete
description of modalities nationwide.
  A hidden Markov model (HMM) was used to infer the most likely learning
modality for each district on a weekly basis. This method yielded higher
spatiotemporal coverage than any individual data source and higher agreement
with three of the four data sources than any other single source. The model
output revealed that the percentage of districts offering fully in-person
learning rose from 40.3% in September 2020 to 54.7% in June of 2021 with
increases across 45 states and in both urban and rural districts. This type of
probabilistic model can serve as a tool for fusion of incomplete and
contradictory data sources in support of public health surveillance and
research efforts.
