## 3 Machine Learning Models: Results and Interpretation
### Discussion of Results across the Regimes  
Why is GBM so effective at obtaining high accuracy, nearly almost better than the other methods, across the different regimes? In effect, the accuracy maximization problem is cast as a search task, which will efficiently find a local minimum of the loss function. By repeating the search hundreds of times and assembling the results, the local minima are likely to culminate in the global minimum, conducting a cross-validation on hold-out data guards against overfitting. There are significant similarities and differences across the two regimes. Similarly, each regime is modeled strongly in that a GBM has low error while explaining a high proportion of the variance. Each model uses different variables, however, and their relative importance shifts significantly from regime to regime. Population Density and State, which are fixed, increase dramatically in importance, replacing Non-Home Dwell Time and LEX-Out-State, which were dynamic during the prior lockdown regime. As shown in Table 5, the state of residence shifted from important in Lockdown Regime (relative importance = 0.349) to highly important in Reopen Regime (relative importance = 0.632). This emphasizes that states, geographically fixed themselves and with regard to neighboring states, were an essential pathway for infection. Geography matters much more than Climate Temperature or Political Color. That is, residents in a state that borders a state having a high case count will be more likely to be infected than residents of a state not bordering such a state. In the early stage of a pandemic, human activity can and does change substantially with different government policies. Even though the policies were not strictly enforced, they were strongly suggested and followed by many people. If a lockdown was issued by a particular state's government, people generally believed it was less safe to travel away from home, and, therefore, they exposed themselves to fewer people, thus reducing the rate of virus spread. If people are no longer under lockdown, they perceive that it is much safer to travel, even if it means encountering people who are infected. The LEX phone tracking data does confirm that lockdowns were effective. In the reopen regime, however, it is no longer government policy or movement that has a large effect. The impacts are in effect from the prior regime, but the State of residence and the Population Density become the most important and predictive, conditional on the prior regime. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \begin{tabular}{c} **Lockdown** \\ **Regime** \\ \end{tabular} & \begin{tabular}{c} **Reopen** \\ **Regime** \\ \end{tabular} & \begin{tabular}{c} **Percentage** \\ **Change** \\ \end{tabular} & **Average** \\ \hline \multirow{2}{*}{Variable} & \begin{tabular}{c} Variable \\ Importance \\ \end{tabular} & \begin{tabular}{c} Variable \\ Importance \\ \end{tabular} & \
\begin{tabular}{c} Variable \\ Importance \\ \end{tabular} &
\begin{tabular}{c} Variable \\ Importance \\ \end{tabular} \\ \hline Pop. Density (log) & 0.546 & 1.000 & 83\% & 0.773 \\ \hline LEX-Out-State & 0.801 & 0.415 & \(-\)48\% & 0.608 \\ \hline Non-Home Dwell Time (Log) & 1.000 & 0.121 & \(-\)88\% & 0.561 \\ \hline State & 0.349 & 0.632 & 81\% & 0.491 \\ \hline LEX-Total (In-State + Out-State) & 0.530 & 0.195 & \(-\)63\% & 0.363 \\ \hline Political Color & 0.212 & 0.269 & 27\% & 0.241 \\ \hline Day-of-Week & 0.292 & 0.054 & \(-\)82\% & 0.173 \\ \hline Climate Temperature & 0.152 & 0.178 & 17\% & 0.165 \\ \hline Health Rank & 0.178 & 0.134 & \(-\)25\% & 0.156 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Variable Importance Within and Across the Two Regimes for Gradient Boosted Machine. Governors varied greatly in their willingness to lockdown residents, schools, and non-essential businesses. Political Color is an important variable across both regimes, as is Health Rank. Both of these variables are amenable to long-term collective influence through changes in elected officials and healthcare systems.