expand.formula {AlgDesign} | R Documentation |
Formulas are expanded to accommodate special functions for continuous and mixture variables.
expand.formula(frml,varNames,const=TRUE,numerics=NULL)
frml |
A formula starting with ~ in the usual way. |
varNames |
A list of variable names to be used when a dot is used as shorthand for “all variables.” |
const |
If FALSE, the constant will be suppressed. |
numerics |
A vector the same length as varNames, with TRUE for corresponding numeric variables. If missing, all variables will be assumed to be numeric. |
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.
An expanded formula is returned.
expand.formula() is called by model.matrix() through the method call model.matix.formula(), thus one may use the above special functions with model.matrix().
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/
Gorman, J.W. and Hinman, J.E. (1962). Simplex lattice designs for multicomponent systems. Technometrics. 4-4. 463-487.