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Other model specifications such as log transformation of the measures did not substantively change our findings.

Other model specifications such as time horizon and discount rate are encoded in variables.

31 In addition other model specifications such as the generalised MNL 43 and latent class model 44 45 specifications will be explored.

We will also explore the use of alternative model specifications such as panel latent class models and generalized multinomial logit models to estimate preferences for community engagement.

The results were generally insensitive to model specifications such as lag structure of O3 concentrations and degree of freedom for time trend.

In sensitivity analyses, we explored the association of long-term PM exposure and BP with different model specifications, such as including and excluding antihypertensive medication from the adjustment set.

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The purpose of fitting air pollution exposure in the logistic models is to prevent estimation of extreme values for the weights; all weighted models met the necessary condition for correct model specification such that the values for stabilized weights have a mean of one [ 47].

The key component, the differential equation system, is similar to other model specification languages such as NMTRAN (NONMEM), Monolix, or other systems.

28 As explained in the appendix, in order to verify if conditional models were removing the fixed effects of each panel, 26 we fit models with different specifications, such as unconditional negative binomial regression models and conditional Poisson regressions with robust standard errors.

Despite the fact that such model specifications would reduce the subjective character of our proposed model, they would probably impede the modeling of expected long-term trend changes in forecast years if past data do not already incorporate them.

Future analyses might reveal the pros and cons of such alternative model specifications.

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