Package 'vdg' reference manual

Title:	Variance Dispersion Graphs and Fraction of Design Space Plots
Description:	Facilities for constructing variance dispersion graphs, fraction- of-design-space plots and similar graphics for exploring the properties of experimental designs. The design region is explored via random sampling, which allows for more flexibility than traditional variance dispersion graphs. A formula interface is leveraged to provide access to complex model formulae. Graphics can be constructed simultaneously for multiple experimental designs and/or multiple model formulae. Instead of using pointwise optimization to find the minimum and maximum scaled prediction variance curves, which can be inaccurate and time consuming, this package uses quantile regression as an alternative.
Authors:	Pieter Schoonees [aut, cre, cph], Niel le Roux [ctb]
Maintainer:	Pieter Schoonees <[email protected]>
License:	GPL (>= 2)
Version:	1.2.3
Built:	2024-10-25 05:03:05 UTC
Source:	https://github.com/cran/vdg

Variance Dispersion Graphs, Fraction-of-Design-Space Plots and Variants

Description

This package provides functionality for producing variance dispersion graphs (VDGs), fraction-of-design (FDS) plots and related graphics for assessing the prediction variance properties of experimental designs. Random sampling is used to assess the distribution of the prediction variance throughout the design region. Multiple design and/or model formulae can be assessed at the same time. Graphics are produced by the ggplot2 package.

Details

The workhorse function in the package is spv, which takes lists of experimental designs and / or model formulae and produces samples throughout the design region at which the prediction variance is evaluated. Depending on the type of input for the design and formula arguments, spv creates output objects of S3 classes spv, spvlist, spvforlist or spvlistforlist. The graphical output are obtained with the plot methods of these classes, and the which argument can be used to control the type of plots produced.

The design regions allowed for are typically spherical or cuboidal in nature, but the keepfun argument to spv can be used for rejection sampling. In this way nonstandard design regions can be allowed for. See also the type argument of spv. The output from the plot methods for objects created by spv are typically named lists of graphical objects created by ggplot2. These are best stored in an object and recreated by printing the required plot. Storing such graphical objects also enables post-hoc manipulation of the plots, such as changing the background colour by using ggplot2's theme function.

References

Pieter C. Schoonees, Niel J. le Roux, Roelof L.J. Coetzer (2016). Flexible Graphical Assessment of Experimental Designs in R: The vdg Package. Journal of Statistical Software, 74(3), 1-22. doi:10.18637/jss.v074.i03.

Design from the Vdgraph package

Description

This data frame is taken verbatim from the (now archived) Vdgraph package. See that package for the original reference.

Usage

D310
D310

Format

a data frame of 10 runs in three variables.

References

Lawson J, Vining G (2014). Vdgraph: Variance dispersion graphs and Fraction of design space plots for response surface designs. R package version 2.2-2, https://CRAN.R-project.org/package=Vdgraph.

Design from the Vdgraph package

Description

This data frame is taken verbatim from the (now archived) Vdgraph package. See that package for the original reference.

Usage

D416B
D416B

Format

a data frame of 16 runs in four variables.

References

Lawson J, Vining G (2014). Vdgraph: Variance dispersion graphs and Fraction of design space plots for response surface designs. R package version 2.2-2, https://CRAN.R-project.org/package=Vdgraph.

Design from the Vdgraph package

Description

This data frame is taken verbatim from the (now archived) Vdgraph package. See that package for the original reference.

Usage

D416C
D416C

Format

a data frame of 16 runs in four variables.

References

Lawson J, Vining G (2014). Vdgraph: Variance dispersion graphs and Fraction of design space plots for response surface designs. R package version 2.2-2, https://CRAN.R-project.org/package=Vdgraph.

Design from Goos & Jones

Description

This data frame contains the design of Table 5.4 in Goos & Jones (2011).

Usage

GJ54
GJ54

Format

a data frame of 15 runs in two variables: Time (seconds) and Temperature (Kelvin)

References

Goos, P., & Jones, B. (2011). Optimal design of experiments: a case study approach. John Wiley & Sons.

Latin Hypercube Sampling

Description

Different versions of latin hypercube sampling (LHS): ordinary LHS, midpoint LHS, symmetric LHS or randomized symmetric LHS. LHS is a method for constructing space-filling designs. They can be more efficient for hypercuboidal design regions than other sampling methods.

Usage

LHS(n, m = 3, lim = c(-1, 1))

MLHS(n, m = 3, lim = c(-1, 1))

SLHS(n, m = 3, lim = c(-1, 1))

RSLHS(n, m = 3, lim = c(-1, 1))
LHS(n, m = 3, lim = c(-1, 1))

MLHS(n, m = 3, lim = c(-1, 1))

SLHS(n, m = 3, lim = c(-1, 1))

RSLHS(n, m = 3, lim = c(-1, 1))

Arguments

`n`	number of design points to generate
`m`	number of design factors
`lim`	limits of the coordinates in all dimensions

Value

Matrix with samples as rows.

Author(s)

Pieter C. Schoonees

References

Examples


set.seed(1234)
pts <- seq(-1, 1, length = 11)

# Ordinary LHS
samp <- LHS(n = 10, m = 2)
plot(samp, main = "LHS")
abline(h = pts, v = pts, col = "lightgrey")

# Midpoint LHS
samp <- MLHS(n = 10, m = 2)
plot(samp, main = "MLHS")
abline(h = pts, v = pts, col = "lightgrey")

# Symmetric LHS
samp <- SLHS(n = 10, m = 2)
plot(samp, main = "SLHS")
abline(h = pts, v = pts, col = "lightgrey")

# Randomized Symmetric LHS
samp <- RSLHS(n = 10, m = 2)
plot(samp, main = "RSLHS")
abline(h = pts, v = pts, col = "lightgrey")
set.seed(1234)
pts <- seq(-1, 1, length = 11)

# Ordinary LHS
samp <- LHS(n = 10, m = 2)
plot(samp, main = "LHS")
abline(h = pts, v = pts, col = "lightgrey")

# Midpoint LHS
samp <- MLHS(n = 10, m = 2)
plot(samp, main = "MLHS")
abline(h = pts, v = pts, col = "lightgrey")

# Symmetric LHS
samp <- SLHS(n = 10, m = 2)
plot(samp, main = "SLHS")
abline(h = pts, v = pts, col = "lightgrey")

# Randomized Symmetric LHS
samp <- RSLHS(n = 10, m = 2)
plot(samp, main = "RSLHS")
abline(h = pts, v = pts, col = "lightgrey")

Compute Mean Spherical SPV

Description

Computes the matrix of spherical region moments for a given model formula and a vector of radii, and uses this to calculate the mean spherical SPV for each of the radii. The function expmat calculates the matrix containing the exponents of each model factor within each model term as columns. Only simple formulae are allowed for. Only products of terms should be included in calls to I. The power operator ^ should be used instead of sqrt. Models should contain only monomial terms.

Usage

meanspv(formula, radii, FtF.inv, n)

expmat(formula)
meanspv(formula, radii, FtF.inv, n)

expmat(formula)

Arguments

`formula`	model formula
`radii`	numeric vector or radii at which to calculate the matrix of spherical region moments
`FtF.inv`	inverse of F'F, where F is the design matrix
`n`	integer giving the number of design runs

Author(s)

Pieter C. Schoonees

References

Examples

f1 <- formula(~ x1*x2)
expmat(f1)
f2 <- update(f1, ~ . + I(x1^2) + I(x2^2))
expmat(f2)
f3 <- update(f2, ~ . + I(x2^0.4))
expmat(f3)
f4 <- update(f3, ~ . + I(x1^2):I(x2^2))
expmat(f4)
f5 <- update(f4, ~ . + I(x1^3*x2^0.5))
expmat(f5)
f1 <- formula(~ x1*x2)
expmat(f1)
f2 <- update(f1, ~ . + I(x1^2) + I(x2^2))
expmat(f2)
f3 <- update(f2, ~ . + I(x2^0.4))
expmat(f3)
f4 <- update(f3, ~ . + I(x1^2):I(x2^2))
expmat(f4)
f5 <- update(f4, ~ . + I(x1^3*x2^0.5))
expmat(f5)

Plot VDGs or FDS plots

Description

Produce Variance Dispersion Graphs and/or Fraction of Design Space plots for experimental designs. There are methods for the S3 classes spv, spvlist, spvforlist and spvlistforlist – see spv.

Usage

## S3 method for class 'spv'
plot(
  x,
  which = c("fds", "vdgsim", "vdgquantile", "vdgboth", "boxplots"),
  np = 50,
  alpha = 7/sqrt(length(x$spv)),
  points.colour = "#39BEB1",
  points.size = 2,
  tau = c(0.05, 0.95),
  radii = 21,
  hexbin = FALSE,
  bins = 80,
  df = 10,
  lines.size = 1,
  origin = rep(0, ncol(x$sample)),
  method,
  arrange = FALSE,
  ...
)

## S3 method for class 'spvforlist'
plot(
  x,
  which = c("fds", "vdgsim", "vdgquantile", "vdgboth", "boxplots"),
  np = 50,
  alpha = 7/sqrt(length(x[[1]]$spv)),
  points.colour = "#39BEB1",
  points.size = 2,
  tau = c(0.05, 0.95),
  radii = 21,
  hexbin = FALSE,
  bins = 80,
  df = 10,
  lines.size = 1,
  origin = rep(0, ncol(x[[1]]$sample)),
  method,
  arrange = FALSE,
  ...
)

## S3 method for class 'spvlist'
plot(
  x,
  which = c("fds", "vdgsim", "vdgquantile", "vdgboth", "boxplots"),
  np = 50,
  alpha = 7/sqrt(length(x[[1]]$spv)),
  points.colour = "#39BEB1",
  points.size = 2,
  tau = c(0.05, 0.95),
  radii = 21,
  hexbin = FALSE,
  bins = 80,
  VRFDS = FALSE,
  df = 10,
  lines.size = 1,
  origin = rep(0, ncol(x[[1]]$sample)),
  method,
  arrange = FALSE,
  ...
)

## S3 method for class 'spvlistforlist'
plot(
  x,
  which = c("fds", "vdgsim", "vdgquantile", "vdgboth", "boxplots"),
  np = 50,
  alpha = 7/sqrt(length(x[[1]][[1]]$spv)),
  points.colour = "#39BEB1",
  points.size = 2,
  tau = c(0.05, 0.95),
  radii = 21,
  hexbin = FALSE,
  bins = 80,
  df = 10,
  lines.size = 1,
  origin = rep(0, ncol(x[[1]][[1]]$sample)),
  method,
  arrange = FALSE,
  ...
)
## S3 method for class 'spv'
plot(
  x,
  which = c("fds", "vdgsim", "vdgquantile", "vdgboth", "boxplots"),
  np = 50,
  alpha = 7/sqrt(length(x$spv)),
  points.colour = "#39BEB1",
  points.size = 2,
  tau = c(0.05, 0.95),
  radii = 21,
  hexbin = FALSE,
  bins = 80,
  df = 10,
  lines.size = 1,
  origin = rep(0, ncol(x$sample)),
  method,
  arrange = FALSE,
  ...
)

## S3 method for class 'spvforlist'
plot(
  x,
  which = c("fds", "vdgsim", "vdgquantile", "vdgboth", "boxplots"),
  np = 50,
  alpha = 7/sqrt(length(x[[1]]$spv)),
  points.colour = "#39BEB1",
  points.size = 2,
  tau = c(0.05, 0.95),
  radii = 21,
  hexbin = FALSE,
  bins = 80,
  df = 10,
  lines.size = 1,
  origin = rep(0, ncol(x[[1]]$sample)),
  method,
  arrange = FALSE,
  ...
)

## S3 method for class 'spvlist'
plot(
  x,
  which = c("fds", "vdgsim", "vdgquantile", "vdgboth", "boxplots"),
  np = 50,
  alpha = 7/sqrt(length(x[[1]]$spv)),
  points.colour = "#39BEB1",
  points.size = 2,
  tau = c(0.05, 0.95),
  radii = 21,
  hexbin = FALSE,
  bins = 80,
  VRFDS = FALSE,
  df = 10,
  lines.size = 1,
  origin = rep(0, ncol(x[[1]]$sample)),
  method,
  arrange = FALSE,
  ...
)

## S3 method for class 'spvlistforlist'
plot(
  x,
  which = c("fds", "vdgsim", "vdgquantile", "vdgboth", "boxplots"),
  np = 50,
  alpha = 7/sqrt(length(x[[1]][[1]]$spv)),
  points.colour = "#39BEB1",
  points.size = 2,
  tau = c(0.05, 0.95),
  radii = 21,
  hexbin = FALSE,
  bins = 80,
  df = 10,
  lines.size = 1,
  origin = rep(0, ncol(x[[1]][[1]]$sample)),
  method,
  arrange = FALSE,
  ...
)

Arguments

`x`	an object of type `spv` for a single experimental design or an object of type `spvlist` for multiple designs.
`which`	either a numeric vector of integers or a character vector indicating which plots to produce. The possible plots are: `1` or `"fds"` A (variance ratio) FDS plot `2` or `"vdgsim"` A VDG with only the simulated prediction variance points plotted `3` or `"vdgquantile"` A VDG with only the quantile regression lines corresponding to `tau` shown `4` or `"vdgboth"` A combination of `2` and `3` `5` or `"boxplots"` Parallel boxplots of the prediction variance
`np`	scalar; the number of points to use for calculating the fraction of design space criterion.
`alpha`	the alpha transparency coefficient for the plots
`points.colour`	colour for points in scatterplot of SPV against the radius
`points.size`	size for points in scatterplot of SPV against the radius
`tau`	the tau parameter for `rq` (quantile regression)
`radii`	either a numeric vector containing the radii to use for calculating the mean spherical SPV over the spherical design space, or an integer (length one vector) giving the number of radii to use for calculationg the mean spherical SPV. If missing, the mean spherical SPV is not used.
`hexbin`	logical indicating whether hexagonal binning should be used to display density instead of colour transparency
`bins`	argument passed to `stat_binhex` to determine the number of hexagons used for binning.
`df`	degrees-of-freedom parameter passed to `bs`
`lines.size`	line size passed to `geom_line`
`origin`	numeric vector specifying the origin of the design space
`method`	optional; passed to `dist` to overwrite defaults of "Euclidean" for spherical regions or "supremum" for cubiodal regions
`arrange`	Logical indicating whether to return a single graphical object arranging the resulting plots in a single plot window via `grid.arrange`, or whether to return the list of graphical objects containing the plots.
`...`	additional arguments passed to `dist`
`VRFDS`	logical indicating whether to construct a variance ratio FDS plot or not (only for class `spvlist`). The first design is used as reference design in case of `VRFDS` is `TRUE`

Value

Returns a list of ggplot graphical objects (or grobs) with names corresponding to the character version of which. These plot objects can be manipulated by changing plot aesthetics and theme elements.

Author(s)

Pieter C. Schoonees

References

Examples


# Single design (class 'spv')
# Larger n should be used in actual cases
library(rsm)
bbd3 <- as.data.frame(bbd(3)[,3:5])
colnames(bbd3) <- paste0("x", 1:3)
quad.3f <- formula(~ x1*x2*x3 - x1:x2:x3 + I(x1^2) + I(x2^2) + I(x3^2))
set.seed(1234)
out <- spv(n = 1000, design = bbd3, type = "spherical", formula = quad.3f)
out
plot(out)

# List of designs (class 'spvlist')
## Not run: 
data(SCDH5); data(SCDDL5)
des.list <- list(SCDH5 = SCDH5, SCDDL5 = SCDDL5)
quad.5f <- formula(~ x1 + x2 + x3 + x4 + x5 + x1:x2 + x1:x3 + x1:x4 + x1:x5
                    + x2:x3 + x2:x4 + x2:x5 + x3:x4 + x3:x5 + x4:x5 
                   + I(x1^2) + I(x2^2) + I(x3^2) + I(x4^2) + I(x5^2))
out2 <- spv(n = 500, design = des.list, type = "spherical", formula = quad.5f)
out2
plot(out2)

## End(Not run)

# List of formulae (class 'spvforlist')
## Not run: 
fact3 <- expand.grid(x1 = c(-1,1), x2 = c(-1, 1), x3 = c(-1,1))
lin.3f <- formula(~ x1 + x2 + x3)
int.3f <- formula(~ (x1+x2+x3)^2)
set.seed(4312)
out3 <- spv(n = 500, design = fact3, type = "cuboidal", 
             formula = list(linear = lin.3f, interaction = int.3f))
out3
plot(out3)

## End(Not run)

# List of formulae and designs (class 'spvlistforlist')
## Not run: 
fact3.n <- rbind(fact3, 0, 0, 0)
set.seed(4312)
out4 <- spv(n = 200, design = list(factorial = fact3, factorial.with.cntr = fact3.n), 
             type = "cuboidal", formula = list(linear = lin.3f, interaction = int.3f))
out4
plot(out4)

## End(Not run)
# Single design (class 'spv')
# Larger n should be used in actual cases
library(rsm)
bbd3 <- as.data.frame(bbd(3)[,3:5])
colnames(bbd3) <- paste0("x", 1:3)
quad.3f <- formula(~ x1*x2*x3 - x1:x2:x3 + I(x1^2) + I(x2^2) + I(x3^2))
set.seed(1234)
out <- spv(n = 1000, design = bbd3, type = "spherical", formula = quad.3f)
out
plot(out)

# List of designs (class 'spvlist')
## Not run: 
data(SCDH5); data(SCDDL5)
des.list <- list(SCDH5 = SCDH5, SCDDL5 = SCDDL5)
quad.5f <- formula(~ x1 + x2 + x3 + x4 + x5 + x1:x2 + x1:x3 + x1:x4 + x1:x5
                    + x2:x3 + x2:x4 + x2:x5 + x3:x4 + x3:x5 + x4:x5 
                   + I(x1^2) + I(x2^2) + I(x3^2) + I(x4^2) + I(x5^2))
out2 <- spv(n = 500, design = des.list, type = "spherical", formula = quad.5f)
out2
plot(out2)

## End(Not run)

# List of formulae (class 'spvforlist')
## Not run: 
fact3 <- expand.grid(x1 = c(-1,1), x2 = c(-1, 1), x3 = c(-1,1))
lin.3f <- formula(~ x1 + x2 + x3)
int.3f <- formula(~ (x1+x2+x3)^2)
set.seed(4312)
out3 <- spv(n = 500, design = fact3, type = "cuboidal", 
             formula = list(linear = lin.3f, interaction = int.3f))
out3
plot(out3)

## End(Not run)

# List of formulae and designs (class 'spvlistforlist')
## Not run: 
fact3.n <- rbind(fact3, 0, 0, 0)
set.seed(4312)
out4 <- spv(n = 200, design = list(factorial = fact3, factorial.with.cntr = fact3.n), 
             type = "cuboidal", formula = list(linear = lin.3f, interaction = int.3f))
out4
plot(out4)

## End(Not run)

Print Method for S3 `spv` classes

Description

Simple print methods for S3 classes spv, spvlist, spvforlist and spvlistforlist. See plot.spv for examples.

Usage

## S3 method for class 'spv'
print(x, ...)

## S3 method for class 'spvforlist'
print(x, ...)

## S3 method for class 'spvlist'
print(x, ...)

## S3 method for class 'spvlistforlist'
print(x, ...)
## S3 method for class 'spv'
print(x, ...)

## S3 method for class 'spvforlist'
print(x, ...)

## S3 method for class 'spvlist'
print(x, ...)

## S3 method for class 'spvlistforlist'
print(x, ...)

Arguments

`x`	Object of class `spv` or `spvlist`
`...`	Unimplemented

Author(s)

Pieter C. Schoonees

References

Sampling for hyperspheres/hypercubes

Description

Sample uniformly in or on a hyperspheres or hypercubes.

Usage

runif_cube(n, m = 2, max.dist = 1, at = FALSE, nr.dist = 21)

runif_sphere(n, m = 2, max.radius = sqrt(m), at = FALSE, nr.rad = 21)
runif_cube(n, m = 2, max.dist = 1, at = FALSE, nr.dist = 21)

runif_sphere(n, m = 2, max.radius = sqrt(m), at = FALSE, nr.rad = 21)

Arguments

`n`	number of points to sample
`m`	number of design factors
`max.dist`	maximum distance from origin (L-infinity norm/supremum distance) for the hypercuboidal design region (enveloping hypercube)
`at`	logical indicating whether to sample on concentric hyperspheres/hypercubes or not. With this option `n` is distributed proportionally across radii / supremum distances so that the density of samples on each concentric hypercube / hypersphere are uniform across the different hyperspheres / hypercubes..
`nr.dist`	the number of concentric hypercubes to use in case at is `TRUE`
`max.radius`	maximum radius of the hyperspherical design region (enveloping hypersphere)
`nr.rad`	number of concentric hyperspheres to sample on in case of `at` being `TRUE`

Author(s)

Pieter C. Schoonees

References

Examples


set.seed(1234)
runif_sphere(n = 10)

set.seed(1234)
samp <- runif_sphere(n = 500, at = TRUE)
plot(samp, asp = 1)
set.seed(1234)
runif_sphere(n = 10)

set.seed(1234)
samp <- runif_sphere(n = 500, at = TRUE)
plot(samp, asp = 1)

Sampler Function

Description

This is a wrapper for the sampling funcions of the vdg package. It extracts design properties from the design passed to it to take appropriate samples.

Usage

sampler(
  n,
  design,
  type = c("spherical", "cuboidal", "lhs", "mlhs", "slhs", "rslhs", "custom"),
  at = FALSE,
  custom.fun = NULL,
  ...
)
sampler(
  n,
  design,
  type = c("spherical", "cuboidal", "lhs", "mlhs", "slhs", "rslhs", "custom"),
  at = FALSE,
  custom.fun = NULL,
  ...
)

Arguments

`n`	number of points to sample
`design`	design for which the sample is required (either a matrix or data frame)
`type`	type of design region/sampling method. One of "spherical", "cuboidal", "lhs", "mlhs", "slhs", "rslhs" or "custom". Option "custom" requires `custom.fun` to be non-`NULL`.
`at`	logical; should sampling be done on the surface of hyperspheres or hypercubes? Not used for LHS methods.
`custom.fun`	A custom sampling function, used in conjunction with `type = "custom"`. The first and second arguments must be the sample size and dimension respectively.
`...`	other arguments passed to the underlying sampling functions.

Value

Matrix with samples as rows, with S3 class smpl

Author(s)

Pieter C. Schoonees

References

Examples

## Default spherical design region
set.seed(1896)
samp1 <- sampler(n = 100, design = expand.grid(x = -1:1, y = -1:1))
plot(samp1)

## Supplying a custom sampling function based on lhs::improvedLHS()
library("lhs")
sfun <- function(n, k, dup = 1) 2 * improvedLHS(n, k, dup = dup) - 1
samp2 <- sampler(n = 100, design = expand.grid(x = -1:1, y = -1:1),
                 type = "custom", custom.fun = sfun)
plot(samp2)
## Default spherical design region
set.seed(1896)
samp1 <- sampler(n = 100, design = expand.grid(x = -1:1, y = -1:1))
plot(samp1)

## Supplying a custom sampling function based on lhs::improvedLHS()
library("lhs")
sfun <- function(n, k, dup = 1) 2 * improvedLHS(n, k, dup = dup) - 1
samp2 <- sampler(n = 100, design = expand.grid(x = -1:1, y = -1:1),
                 type = "custom", custom.fun = sfun)
plot(samp2)

Design from the Vdgraph package

Description

This data frame is taken verbatim from the (now archived) Vdgraph package. See that package for the original reference.

Usage

SCDDL5
SCDDL5

Format

a data frame of 23 runs in five variables.

References

Lawson J, Vining G (2014). Vdgraph: Variance dispersion graphs and Fraction of design space plots for response surface designs. R package version 2.2-2, https://CRAN.R-project.org/package=Vdgraph.

Design from the Vdgraph package

Description

This data frame is taken verbatim from the (now archived) Vdgraph package. See that package for the original reference.

Usage

SCDH5
SCDH5

Format

a data frame of 28 runs in four variables.

References

Lawson J, Vining G (2014). Vdgraph: Variance dispersion graphs and Fraction of design space plots for response surface designs. R package version 2.2-2, https://CRAN.R-project.org/package=Vdgraph.

Calculate the Scaled Prediction Variance (or SPV)

Description

Calculates the SPV for a sample of points in a design region of specified type. Sampling is done by calling sampler.

Usage

spv(
  n,
  design,
  type = "spherical",
  formula,
  at = FALSE,
  keepfun,
  sample,
  unscaled = FALSE,
  ...
)

## S3 method for class 'data.frame'
spv(
  n,
  design,
  type = c("spherical", "cuboidal", "lhs", "mlhs", "slhs", "rslhs", "custom"),
  formula,
  at = FALSE,
  keepfun,
  sample,
  unscaled = FALSE,
  ...
)

## S3 method for class 'list'
spv(
  n,
  design,
  type = c("spherical", "cuboidal", "lhs", "mlhs", "slhs", "rslhs", "custom"),
  formula,
  at = FALSE,
  keepfun,
  sample,
  unscaled = FALSE,
  ...
)

## S3 method for class 'matrix'
spv(
  n,
  design,
  type = c("spherical", "cuboidal", "lhs", "mlhs", "slhs", "rslhs", "custom"),
  formula,
  at = FALSE,
  keepfun,
  sample,
  unscaled = FALSE,
  ...
)
spv(
  n,
  design,
  type = "spherical",
  formula,
  at = FALSE,
  keepfun,
  sample,
  unscaled = FALSE,
  ...
)

## S3 method for class 'data.frame'
spv(
  n,
  design,
  type = c("spherical", "cuboidal", "lhs", "mlhs", "slhs", "rslhs", "custom"),
  formula,
  at = FALSE,
  keepfun,
  sample,
  unscaled = FALSE,
  ...
)

## S3 method for class 'list'
spv(
  n,
  design,
  type = c("spherical", "cuboidal", "lhs", "mlhs", "slhs", "rslhs", "custom"),
  formula,
  at = FALSE,
  keepfun,
  sample,
  unscaled = FALSE,
  ...
)

## S3 method for class 'matrix'
spv(
  n,
  design,
  type = c("spherical", "cuboidal", "lhs", "mlhs", "slhs", "rslhs", "custom"),
  formula,
  at = FALSE,
  keepfun,
  sample,
  unscaled = FALSE,
  ...
)

Arguments

`n`	number of samples to take
`design`	a design or list of designs. Each design must be either a matrix or a data.frame or coercible to a data.frame.
`type`	type of sampling passed to `sampler`
`formula`	either a single model formula of a list of formulae
`at`	only used when type is `'spherical'` or `'cuboidal'`
`keepfun`	optional; function operating on the columns of a matrix with the same number of columns as design which return a logical value for including a specific point in the sample or not. Useful for rejection sampling for nonstandard design regions.
`sample`	optional; if not missing it should contain a matrix or data.frame containing points sampled over the required design region. If it is not missing, no further sampling will be done: the SPV is simply evaluated at these points.
`unscaled`	logical indicating whether to use the unscaled prediction variance (UPV) instead of the scale prediction variance (SPV)
`...`	additional arguments passed to `sampler`. This enables the used of user-specified sampling functions via the `custom.fun` argument to `sampler`.

Value

Object of class 'spv', 'spvlist', 'spvforlist' or 'spvlistforlist', depending on whether single designs/formulas are passed or lists of these.

Author(s)

Pieter C. Schoonees

References

Examples


# Single design (class 'spv')
library(rsm)
bbd3 <- as.data.frame(bbd(3)[,3:5])
colnames(bbd3) <- paste0("x", 1:3)
quad.3f <- formula(~(x1 + x2 + x3)^2 - x1:x2:x3)
out <- spv(n = 1000, design = bbd3, type = "spherical", formula = quad.3f)
out
# Single design (class 'spv')
library(rsm)
bbd3 <- as.data.frame(bbd(3)[,3:5])
colnames(bbd3) <- paste0("x", 1:3)
quad.3f <- formula(~(x1 + x2 + x3)^2 - x1:x2:x3)
out <- spv(n = 1000, design = bbd3, type = "spherical", formula = quad.3f)
out

Standardize or Unstandarize the Column Range

Description

Simple functions for rescaling a data matrix to a coded design and back. stdrange converts the design in actual measurements into a coded design, while ustdrange reverses the process (if the correct arguments are given).

Usage

stdrange(x, mins = apply(x, 2, min), maxs = apply(x, 2, max))

ustdrange(x, mins, maxs)
stdrange(x, mins = apply(x, 2, min), maxs = apply(x, 2, max))

ustdrange(x, mins, maxs)

Arguments

`x`	matrix containing the design, or an object coercible to a matrix.
`mins`	vector of original values, one for each column, which should be recoded to the value -1; or which have alreadty been recoded to -1. This and the next argument are both recycled if not of the correct length.
`maxs`	vector of original values which should be recoded as 1, or which have already been recoded to 1.

Author(s)

Pieter C. Schoonees

Package 'vdg'

Help Index

Variance Dispersion Graphs, Fraction-of-Design-Space Plots and Variants

Description

Details

References

See Also

Design from the Vdgraph package

Description

Usage

Format

References

Design from the Vdgraph package

Description

Usage

Format

References

Design from the Vdgraph package

Description

Usage

Format

References

Design from Goos & Jones

Description

Usage

Format

References

Latin Hypercube Sampling

Description

Usage

Arguments

Value

Author(s)

References

Examples

Compute Mean Spherical SPV

Description

Usage

Arguments

Author(s)

References

Examples

Plot VDGs or FDS plots

Description

Usage

Arguments

Value

Author(s)

References

Examples

Print Method for S3 spv classes

Description

Usage

Arguments

Author(s)

References

Sampling for hyperspheres/hypercubes

Description

Usage

Arguments

Author(s)

References

Examples

Sampler Function

Description

Usage

Arguments

Value

Author(s)

References

See Also

Examples

Design from the Vdgraph package

Description

Usage

Format

References

Design from the Vdgraph package

Description

Usage

Print Method for S3 `spv` classes