Does climate help modeling COVID-19 risk and to what extent?

Fig, the intensity and polarity of SHAP values for the explanatory variables in separate hemi- sphere are also in line with those for the entire globe (Fig 7), although for some variables in the southern hemisphere polarity this similarity is not as explicit as for the northern hemisphere. For example, while UV still shows a negative association in both hemispheres, the distribution of SHAP score for the southern hemisphere is less marked than in the northern hemisphere. By contrast, rainfall displays a clear negative correlation in the southern hemisphere that is not clearly visible in the northern hemisphere. For completeness, we include the feature importance results for the Lasso, Elastic Net, and random forest models at a global scale (S5 Fig). All point to UV as one of the most important parameters. For Lasso and Elastic Net we report regression coefficients. For the random forest tree, we use the Gini importance score. Econometric analysis The econometric analysis was carried out using a panel data fixed-effects model. Confirmed daily cases of COVID-19 in log-scale were regressed against climate and air-quality factors, with reference to cross-sectional and time fixed effects. We could not add in the regression the moving averages of the dependent variable as we did for the machine learning analysis because this inclusion would violate the assumptions underlying the fixed effects estimator. If the inde- pendent variable is correlated with the error term in a regression model (endogeneity), then

the estimate of the regression coefficient would be inconsistent. Moreover, adding one or more autocorrelated terms to the regression would remove most of the model variance, mak- ing the effects of the other independent variables less significant (leading to smaller βn and larger standard errors). Note that the nominal magnitude of the regression coefficient of every single explanatory variable is likely to be biased due to the undetermined confounding effects. For this reason, we mainly focus our discussion of the results on the significance and polarity of the coefficients. Before proceeding with the econometric analysis, we test our data for stationarity, since non-stationary data may lead to spurious regression results thus falsely indicating the existence of a relationship between two variables [81]. For each time series variable considered in the econometric study, we run the Fisher-type unit-root test based on augmented Dickey-Fuller tests at 0 and 1 lag. Table 3 provides a summary of the results for the variables with moving averages at 7 days. We omit the test results for other window sizes for which we obtain the same outcome. The four tests all strongly reject the null hypothesis that all the panels contain unit roots for each variable under consideration and we can therefore proceed with the analysis. The statistical significance of the regression coefficients is computed by clustering the regression standard error at the country/admin level, to account for error correlation within

the geographical areas where our unit of observation was collected. For each location, we select days with a minimum of 10 confirmed COVID-19 cases, and we limit our analysis to the loca- tions with at least 90 data records (3 months’ worth of data), in line with the other analyses. The results are reported in Table 4 for all the T-day moving averages and time-variant regres- sors (see Methodology section). The regression model has a R2 value of 0.73 over 65,369 obser- vations, which shows that the independent and dependent variables are significantly correlated. UV radiation shows strong negative correlation with COVID-19 spread, while tem- perature has a positive association, in line with the statistical correlation and feature impor- tance analyses discussed in the previous two sections. Both results are statistically significant (P < 0.01). For other climatic factors, the econometric analysis is congruent with the feature importance analysis, but either the coefficients are not statistically significant, or the PLOS ONE Does climate help modeling COVID-19 risk and to what extent? PLOS ONE | https://doi.org/10.1371/journal.pone.0273078 September 7, 2022 17 / 27