Estimating parameters of cognitive models is crucial to be able to accurately describe cognitive processing of individuals, under varying circumstances. To ensure that individual parameter estimates represent individual cognitive processes, it is important to consider model identification and specific influence. Model identification refers to whether a unique set of parameter estimates is associated with a particular pattern in the data; Specific influence means that certain experimental manipulations affect only specific cognitive processes, reflected in changes in only those parameters that represent those processes, and not others. These two general concepts also apply to cognitive models of more applied tasks and settings, such as driving. In the current work, we specifically test whether these two requirements hold in a commonly used cognitive model of visual control of steering behavior. For this model, we test the identifiability, and then estimate parameters of two experiments to understand how cognitive load and driving speed specifically influence parameter estimates of the model. The results indicate that the two-point visual control of steering model is identified, and that cognitive load and driving speed are related to different parameters.