Formulas are expanded to accommodate special functions for continuous and mixture variables.
expand.formula(frml,varNames,const=TRUE,numerics=NULL)An expanded formula is returned.
A formula starting with ~ in the usual way.
A list of variable names to be used when a dot is used as shorthand for ``all variables.''
If FALSE, the constant will be suppressed.
A vector the same length as varNames, with TRUE for corresponding numeric variables. If missing, all variables will be assumed to be numeric.
Bob Wheeler bwheelerg@gmail.com
Please cite this program as follows:
Wheeler, R.E. (2004). expand.formula. AlgDesign. The R project for statistical computing https://www.r-project.org/
This function expands formulas to accommodate polynomial models for which R has minimal support. Assuming for illustration that there are three variables, A, B, and C, the following expressions may be used. In addition, a dot may be used to indicate that all variables in varNames are to be used.
All agruments to quad(), cubic(), and cubicS() must be numeric.
\(~.\) makes \(~ A + B + C\)
\(~.^p\) makes \(~ (A + B + C)^p\), where p is an integer
quad(A,B,C) makes \(~(A+B+C)^2+I(A^2)+I(B^2)+I(C^2)\)
cubic(A,B,C) makes \(~(A+B+C)^3+I(A^2)+I(B^2)+I(C^2)+I(A^3)+I(B^3)+I(C^3)\)
cubicS(A,B,C) makes \(~(A+B+C)^3+I(A*B*(A-B))+I(A*C*(A-C))+I(B*C*(B-C))\)
The cubicS() function produces a non-singular representation of a cubic model, when the
variables are mixture variables, that is when the rows of data sum to a constant
value, usually 1.0. Because of the mixture constraint, models containing mixture variables
should not have a constant term. The linear and quadratic models for mixture variables
A, B, and C are given by \(-1+(A+B+C)\) and \(-1+(A+B+C)^2\) respectively. See Gorman and Hinman [1962] for
details.
Gorman, J.W. and Hinman, J.E. (1962). Simplex lattice designs for multicomponent systems. Technometrics. 4-4. 463-487.