Fig. 3: An illustration of the GAM used.

The model contains a time-varying function, f(t_i), of school attendance at each timepoint t_i for the ith school, and parameters of boil water notice, city-wide boil water notice, a method of instructional delivery in school and vulnerabilities. The notation, μ_i,ti, indicates the conditional mean for unexcused absence rates given all the confounding variables and school attendance. In the model, we include a host of census block-level demographic characteristics as follows: boil water notice/advisory, city-wide boil water notice/advisory, virtual, online or virtual, hybrid or virtual, percentage of individuals who identify as Black, Asian, Native American, Hispanic, or 2 or more races (BANHT), percentage of people with disability status, percentage of people older than 65 years, percentage of people younger than 18 years, percentage of people older than 65 years and living alone, percentage of people with limited English, percentage of households with no computer access, percentage of people living in a household under poverty and percentage of single-parent households. For a time-varying function f(·), we considered the cubic regression spline basis function to approximate a non-parametric function.⁷⁵ See Supplementary Section Statistical Analysis for the model specification, including the details on types of models and selection of roughness parameters and knot locations. All images are drawn using icons in Microsoft PowerPoint.