When modeling dynamic processes for several inputs with freely existing data, such as data collected with normal process operations, the ability to accurately model the output response for a given input change is impeded when inputs are cross-correlated (i.e., pairwise) as this adversely affects accurate estimation of the causative effects of inputs on the response variable. The causative effects of the inputs can be evaluated functionally and analytically via the Jacobian matrix which is done in this work for NARMAX and Wiener structures that are linear and nonlinear in model parameters. This analysis shows that the Wiener structure with physically based nonlinear parametrization is superior. This conclusion is also supported in this work by a modeling study on a real distillation column consisting of eight test runs over a period of three years.