On Concurvity in nonlinear and nonparametric regression models

When data are affected by multicollinearity in the linear regression framework, then concurvity will be present in fitting a Generalized additive model (GAM). The term concurvity describes nonlinear dependencies among the predictor variables. As collinearity results in inflated variance of the estimated regression coefficients in the linear regression model, the result of the presence of concurvity leads to instability of the estimated coefficients in GAM. Even if the backfitting algorithm will always converge to a solution, in the case of concurvity the final solution of the backfitting procedure in fitting a GAM is influenced by the starting functions. While exact concurvity is highly unlikely, approximate concurvity, the analogue of multicollinearity, is of practical concern as it can lead to upwardly biased estimates of the parameters and to underestimation of their standard errors, increasing the risk of committing type I error. We compare the existing approaches to detect concurvity, pointing out their advantages and drawbacks, using several simulated and real data sets. As a result, a general criterion to detect concurvity in nonlinear and non parametric regression models will be provided to ensure the robustness of the parameters estimation.