Inferring school district learning modalities during the COVID-19 pandemic with a hidden Markov model

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.