Non linear model: A model which is non-linear in the parameters, for instance are

 

Some such type of models can be converted into the linear models by linearization (the second equation above, for instance, by taking logarithms throughout). Those which cannot are often referred to as the intrinsically non-linear, though these can often be approximated by the linear equations in some circumstances. Parameters in such type of models usually have to be estimated using an optimization procedure like the Newton-Raphson technique. In such models linear parameters are those for which second partial derivative of the model function with respect to parameter is zero (β1 and β3 in the first example given above); when this is not case (β2 and β4 in the ?rst example above) they are called as non-linear parameters.