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To obtain the asymptotic results for high SNR, we change some variables as, z 1 = γ th γ 1 ¯ and z 2 = γ th γ 2 ¯.

This kind of data limited our access to some variables, as is the case in terms of information related to previous induced abortion and late second trimester abortions.

Unlike the simultaneous, or structural equation, models, which treat some variables as endogenous and some as exogenous or predetermined (exogenous plus lagged endogenous), VAR models treat all variables as endogenous.

Unlike the standard 3SLS, the GMM estimator allows for heteroskedasticity in addition to cross-equation correlation where some variables (as merchant acceptance in our case) may appear both as exogenous and (lagged) endogenous variables in the different equations (Hansen 1982; Wooldridge 2002).

Because mixed-effects models treat some variables as fixed and some as random comparing the relative importance of variables from these two different classes can be difficult, as we explain below.

We compare a typical least squares mixed model ANOVA ("mixed model ANOVA") with a maximum likelihood mixed-effects model ("mixed-effects model") that treats some variables as fixed and some as random [7], [8] and a hierarchical or multilevel model ("multilevel model") that calculates variance components for all variables [9].

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Missing data are common in observational studies, and in the present study there were varying degrees of missing observations for some variables, some as high as 50%.

In this context, some of the former binary variables as well as monetary and capacity parameters need to be redefined.

Since some continuous variables such as costs, LOS, and number of days on ventilation did not follow a normal distribution, median and interquartile range (IQR) were reported for those variables as well.

There was also missing data for some variables (such as for injection drug use) as presented in Table  1.

Additionally, some variables such as crime rates merit further investigation as modifiers of heat and health associations in epidemiologic analyses.

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