Nonlinear Models and Regression

Since both the partial derivatives with respect to the model parameters are a function of either itself or the other parameter, the model is nonlinear in the parameters. Because Emax is dependent only on EC50, it is said to be conditionally linear on EC50. 

Do not worry about your difficulties in mathematics. I can assure you mine are still greater. 

A model is nonlinear if any of the partial derivatives with respect to any of the model parameters are dependent on any other model parameter or if any of the derivatives do not exist or are discontinuous. For example, the Emax pharmacodynamic model, 

However, for this model, the derivative is not continuous at x = xo and nonlinear least squares algorithms, ones that do not require derivatives, such as the Nelder Mead algorithm (which is discussed later in the chapter), are generally required to estimate the model parameters (Bartholomew, 2000). 

Models that are transformed in predictor variables to some inherently nonlinear function are not nonlinear. For example, the model 

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