Changes to the form of the model formula

In specifying a linear, or generalized linear model we could allow the regression parameters to be defined implicitly, and to be given names by transference from the column of the model matrix that they multiply.

In arbitrary nonlinear models no such simplicity applies and we have to specify the model as an ordinary expression that includes both determining variables and parameters together. For example to specify a model for a nonlinear regression such as above, we would use

y t1*x1/(x2 - t2)

where y is the response variable, x1 and x2 are determining variables and t1 and t2 are scalar parameters.

In such model formulæ all operators have their usual arithmetic expression meaning, and the useful facility of expanding factors and forming cross and nested structures is no longer available. All parameters must be explicitly defined in the formula, even if they come from a linear part of the model.