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To ensure a correct model specification, we assessed the quadratic form of the linear predictor.

In the current model specification, we choose controls that are matched for cases in terms of biological, environmental, or demographical factors.

It has to be mentioned that to simplify model specification, we considered random effects capturing jointly the heterogeineity across studies and across virus strains in the same study.

To ensure a parsimonious model specification, we then removed each time-varying term to evaluate its contribution and kept in the model only those that improved predictive accuracy (using the 'base' set of covariates in the second-stage model).

To further make the point about the sensitivity of logistic regression to model specification, we simulated data from a logistic model where each of the 8 subgroups defined by X1, X2 and X3 has an arbitrary conditional probability.

To test for the sensitivity of the results to model specification, we also performed multivariate analysis using an arcsin transformation of the dependent variable, as per Speybroeck et al. [ 26].

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By examining different model specifications, we test alternative descriptions of the behavior of decision makers.

In addition, in some model specifications, we included a binary variable for if the respondent reports difficulty in accessing sports facilities [14].

After testing several model specifications, we ultimately choose the model with the highest predictive power adjusted for the number of explanatory variables (adjusted R2) and with the smallest root mean squared error (RMSE).

After estimating several model specifications, we produced the final specifications shown in Table  2.

For all model specifications, we compared the results from "naïve" estimates where the choice of health insurance use was assumed to be exogenous, to the results we obtained using models with instrumental variables.

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