Use FO() in the model formula in rsm
to specify a first-order response surface (i.e., a linear function)
in its arguments. Use TWI() to generate two-way interactions, and PQ() to generate
pure quadratic terms (squares of the FO() terms). A call to
SO() creates all terms in FO(), TWI(), and PQ() (in that order) for those
variables. However, specifying SO() in a model formula in rsm will be replaced
by the explicit sum of model terms, so that the anova table shows separate sums of squares.
Other variables (such as blocks or factors) may be included in the model
but should never be included in the arguments to FO or SO.
PE is used for fitting pure-error models. It should not be used in
response-surface models. This function exists primarily for use
by loftest, but could be useful in other linear-model
contexts for fitting a model that interpolates the means at each distinct
combination of argument values.
The formula argument in TWI can simplify specifying models where only certain interactions are included. For example, TWI(formula = ~x1:(x2+x3)) is equivalent to TWI(x1,x2) + TWI(x1,x3). The formula is expanded using terms, and then only the second-order terms are retained. If this results in only one term, an error condition is raised. This is necessary to prevent rsm from getting confused in identifying second-order terms.