expand.formula {AlgDesign} R Documentation

## Expanding a formula

### Description

Formulas are expanded to accommodate special functions for continuous and mixture variables.

### Usage

```expand.formula(frml,varNames,const=TRUE,numerics=NULL)
```

### Arguments

 `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.

### Details

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

• 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  for details.

### Value

An expanded formula is returned.

### Note

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().

### Author(s)

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/

### References

Gorman, J.W. and Hinman, J.E. (1962). Simplex lattice designs for multicomponent systems. Technometrics. 4-4. 463-487.

[Package AlgDesign version 1.2.0 Index]