Linear mixed effects models assume that a linear relationship exists between the predictors and the target variable. In many cases, this is a problematic assumption; whenever the target is expected to show any kind of saturation effect or have an exponential response with respect to any of the regressors, the linearity assumption needs to be removed.
In medicine and biology, this is usually the case, as dose response studies almost always exhibit a certain kind of saturation effect. The same happens for marketing studies, because spending increasing amounts of resources in order to drive sales up might be effective, but it won’t be effective if that spend is too large.
Fitting nonlinear mixed effects models is much harder than their linear counterpart. Here, we can’t rely on any matrix techniques and we need to attack the problem...
