R: Response-surface model components

FO {rsm} | R Documentation

## Response-surface model components

### Description

Use of one of these functions in a model is how you specify the portion of the model that is to be regarded as a response-surface component.

### Usage

    FO (...)
    TWI (..., formula)
    PQ (...)
    SO (...)
    PE (...)

### Arguments

`...` | The numerical predictors for the response surface, separated by commas.
`formula` | Alternative way to specify two-way interactions. Use `formula` or `...`, never both.

### Details

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.

### Value

The functions `FO`, `TWI`, `PQ`, and `SO` return a matrix whose columns are the required predictors.

`PE` returns a `factor` whose levels are all the distinct combinations of arguments provided to the function.

### Author(s)

Russell V. Lenth

### References

Lenth RV (2009) “Response-Surface Methods in R, Using rsm”, Journal of Statistical Software, 32(7), 1–17. http://www.jstatsoft.org/v32/i07/.

### See Also

`rsm`

### Examples

      ### See 'rsm' help for examples of FO, TWI, etc

      library(rsm)
      ### Test LOF for a regression model
      ChemReact.lm <- lm(Yield ~ Time*Temp, data = ChemReact1)
      PureError.lm <- update (ChemReact.lm, . ~ PE(Time,Temp))
      anova (ChemReact.lm, PureError.lm)

[Package rsm version 2.9 Index]