In fact, we are not aware of any investigation of the recommended strength for IVs for nonlinear outcome models.
It may, for instance, be determined that the method works better for linear, rather than nonlinear, outcome models (such as either continuous outcomes, or probabilities of dichotomous outcomes rather than the outcome itself, despite the well-known shortcomings of such an outcome measure).
These can provide evidence of a nonlinear effect of the exposure on the outcome.
Serum Mg level was also treated as a continuous variable to model the nonlinear effect of serum Mg level on the outcome.
In the example of beauty, one needs to distinguish between inherently highly nonlinear responses of outcomes to differences in beauty and apparently nonlinear responses that arise because relative differences in looks matter more than absolute differences.
Figure 1 shows that nonlinear estimates of outcomes using Model 3 often have U-shaped relationships with paternal age, which may be statistically significant per Table 4 but not indicative of a clear negative relationship.
Most predictor variables were examined as continuous variables; a natural logarithm transformation was applied to those with skewed distributions and/or nonlinear associations with outcome.
GAMs are commonly used in air quality and air pollution/heat epidemiology studies where seasonal patterns in outcome variables (e.g., mortality) and nonlinear associations between health outcomes and, say, temperature, require additional modeling flexibility (Anderson and Bell 2009; Gasparrini and Armstrong 2011; Schwartz and Zanobetti 2000; Zhang and Batterman 2010).
Løken, Mogstad and Wiswall [29] find an increasing, concave relationship between household income and children's outcomes using nonlinear IV estimators.
Thus omitting parental education will induce a spurious nonlinear relationship between child outcomes and father's age, one that rises at first, reflecting greater educational attainment among parents aged 25 y compared with those aged 16 y, and then falls because parents aged 45 y have less education by simply having been born earlier.
