LatticeDesign (version 4.0-1)

InterleavedMaximinDMixVars: Interleaved lattice-based maximin distance designs for mixed continuous, ordinal, and binary variables

Description

Generates an interleaved lattice-based maximin distance design for mixed continuous, ordinal, and binary variables.

Usage

InterleavedMaximinDMixVars(p,n,discrete_dims,ordinal_levels,weight=rep(1,p));
ILMmDMixVarsAlg6(p,n,discrete_dims,ordinal_levels,weight=rep(1,p));
ILMmDMixVarsAlg8(p,n,discrete_dims,ordinal_levels,weight=rep(1,p),N=1,ReturnAll=0);
ILMmDMixVarsAlg9(p,n,discrete_dims,ordinal_levels,weight=rep(1,p),pfrom=8);

Value

The value returned from the function is a list containing the following components:

Design

The generated design.

SeparationDistance

The separation distance of the generated design.

m

The actual number of points of the generated design.

DesignTransformed

The generated design that is transformed to the rectangular design space given the weights.

weight

The weight used in the distance measure, higher for more important variable.

s_vector

The numbers of distinct levels of the generated design.

L01

The base design.

Arguments

p

Number of dimensions, must be an integer greater than one.

n

Targeted number of points, must be an integer greater than one.

discrete_dims

Index of discrete variables in 1:p.

ordinal_levels

Allowable levels of ordinal variables by a matrix.

weight

Optional, the weights used in the distance measure, higher for more important variable.

N

Number of results saved.

ReturnAll

Whether or not outputing all designs with the highest separation distance, regardless of their sample size.

pfrom

Number of dimensions to supplement from.

Details

These functions generate an interleaved lattice-based maximin distance design for mixed continuous, ordinal, and binary variables in p dimensions and at most n points, following the algorithms provided in the paper "Maximin distance designs for mixed continuous, ordinal, and binary variables". Function InterleavedMaximinDMixVars uses the recommended algorithm provided in the paper. Functions ILMmDMixVarsAlg6, ILMmDMixVarsAlg8, and ILMmDMixVarsAlg9 use Algorithms 6, 8, and 9, respectively. For ILMmDMixVarsAlg6, p must be no greater than 5. For ILMmDMixVarsAlg8, p must be no greater than 8.

References

Lan, Hui and He, Xu (2025). "maximin distance designs for mixed continuous, ordinal, and binary variables", arXiv:2507.23405v1.

Examples

ordinal_levels_inpaper <- list(
  Q1 = c(0, 1),
  Q2 = c(0, 0.5, 1),
  Q3 = c(0, 0.1, 0.3, 0.6, 1),
  Q4 = c(0, 0.25, 0.5, 0.75, 1),
  Q5 = c(0, 0.2, 0.3, 0.5, 0.7, 1),
  Q6 = c(0, 0.2, 0.4, 0.6, 0.8, 1),
  Q7 = c(0, 0.1, 0.3, 0.5, 0.7, 0.9, 1),
  Q8 = c(0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1)
)

discrete_dims <- c(2,4)
ordinal_levels <- list(
  v1 = ordinal_levels_inpaper$Q6,
  v2 = ordinal_levels_inpaper$Q7
)
res <- InterleavedMaximinDMixVars(p=4,n=50,discrete_dims,ordinal_levels,weight=(3/4)^(0:3));
res$Design

discrete_dims <- c()
ordinal_levels <- c()
res <- InterleavedMaximinDMixVars(p=3,n=50,discrete_dims,ordinal_levels,weight=rep(1,3));
res$Design

discrete_dims <- c(1,2,3)
ordinal_levels <- list(
  v1 = ordinal_levels_inpaper$Q8,
  v2 = ordinal_levels_inpaper$Q3,
  v3 = ordinal_levels_inpaper$Q8
)
res <- ILMmDMixVarsAlg6(p=3,n=30,discrete_dims,ordinal_levels);
res$Design

discrete_dims <- c(3,4,5)
ordinal_levels <- list(
  v1 = ordinal_levels_inpaper$Q1,
  v2 = ordinal_levels_inpaper$Q5,
  v3 = ordinal_levels_inpaper$Q8
)
res <- ILMmDMixVarsAlg8(p=5,n=40,discrete_dims,ordinal_levels);
res$Design

discrete_dims <- c(4:10)
ordinal_levels <- list(
  v1 = ordinal_levels_inpaper$Q1,
  v2 = ordinal_levels_inpaper$Q1,
  v3 = ordinal_levels_inpaper$Q1,
  v4 = ordinal_levels_inpaper$Q2,
  v5 = ordinal_levels_inpaper$Q3,
  v6 = ordinal_levels_inpaper$Q4,
  v7 = ordinal_levels_inpaper$Q5
)
res <- ILMmDMixVarsAlg9(p=10,n=60,discrete_dims,ordinal_levels,pfrom=5);
res$Design