fdesigns (version 1.1)

P: Compute Profile Factor Polynomials

Description

A function to be used in the formula argument in pflm and pfglm. It computes polynomials of the basis functions of profile factors to be passed in functional models and find optimal designs.

Usage

P(x, deg)

Value

The function returns an attributes list. The list contains the polynomial coefficient matrix, the argument x, and the argument deg.

Arguments

x

A coefficient matrix from the basis expansion of a profile factor. The name passed needs to match the name of the profile factor in startd in pflm and pfglm.

deg

The degree of the polynomial effect for the profile factor.

Author

Damianos Michaelides <>, Antony Overstall, Dave Woods

Details

The function P is intented to be used in the formula argument in the function pflm and pfglm.

In the traditional linear models, polynomial effects of factors are handled using the function I. However, profile factors are expanded using basis functions and the coefficients are a matrix instead of a vector.

In other words, the function P is an extension to the function I, but for functional models with profile factors.

Examples

## Example 1:

d <- list(x1=matrix(runif(48), nrow=12))
within(d, example1 <- P(x = x1, deg = 2))

# \donttest{
## Example 2: Use the function in a formula
## This example involves finding a D-optimal design for a functional linear model of n=20 runs
## depending on two profile factors. In addition to the main effects, the model includes the
## interaction of the profile factors and the quadratic effect of the second profile factor. 
## The quadratic effect is identified in the formula argument using the \link[fdesigns]{P} function. 

example2 <- pflm(formula = ~ x1 + x2 + x1:x2 + P(x2, 2), nsd = 1, mc.cores = 1,
  npf = 2, tbounds = c(0, 1), nruns = 20, startd=NULL, dx = c(2, 2),
  knotsx = list(c(0.33, 0.66), c(0.25, 0.50, 0.75)), 
  pars = c("power", "power", "bspline", "bspline"), db = c(1, 1, 2, 2), 
  knotsb = list(c(), c(), c(0.25, 0.50, 0.75), c(0.25, 0.50, 0.75)), 
  criterion = "D", lambda = 1, tol = 0.0001, dlbound = -1, dubound = 1, 
  progress = FALSE)
# }