greedy_orthogonalization_curation2

This function takes a set of allocation vectors and pares them down one-by-one
by eliminating the vector that can result in the largest reduction in Avg[ |r_ij| ].
It is recommended to begin with a set of unmirrored vectors for speed. Then add the mirrors later
for whichever subset you wish.

Computes experimental designs for a
two-arm experiment with covariates via a number of methods:
(0) complete randomization and randomization with forced-balance,
(1) Greedily optimizing a
balance objective function via pairwise switching. This optimization
provides lower variance for the treatment effect estimator (and higher
power) while preserving a design that is close to complete randomization.
We return all iterations of the designs for use in a permutation test,
(2) The second is via numerical optimization
(via 'gurobi' which must be installed, see <https://www.gurobi.com/documentation/9.1/quickstart_windows/r_ins_the_r_package.html>)
a la Bertsimas and Kallus,
(3) rerandomization,
(4) Karp's method for one covariate,
(5) exhaustive enumeration to find the
optimal solution (only for small sample sizes),
(6) Binary pair matching using the 'nbpMatching' library,
(7) Binary pair matching plus design number (1) to further optimize balance,
(8) Binary pair matching plus design number (3) to further optimize balance,
(9) Hadamard designs,
(10) Simultaneous Multiple Kernels.
In (1-9) we allow for three objective functions:
Mahalanobis distance,
Sum of absolute differences standardized and
Kernel distances via the 'kernlab' library. This package is the result of a stream of research that can be found in
Krieger, A, Azriel, D and Kapelner, A "Nearly Random Designs with Greatly Improved Balance" (2016) <arXiv:1612.02315>,
Krieger, A, Azriel, D and Kapelner, A "Better Experimental Design by Hybridizing Binary Matching with Imbalance
Optimization" (2021) <arXiv:2012.03330>.

Adam Kapelner

GreedyExperimentalDesign

Greedy Experimental Design Construction

David Azriel

Abba Krieger

greedy_orthogonalization_curation2 function

<dl><dt>W</dt>
<dd>A matrix in $-1, 1^R x n$ which have R allocation vectors for an experiment of sample size n.</dd>
<dt>R0</dt>
<dd>The minimum number of vectors to consider in a design. The default is the true bottom, two.</dd>
<dt>verbose</dt>
<dd>Default is <code>FALSE</code> but if not, it will print out a message for each iteration.</dd></dl>

Arguments

Author

Curate More Orthogonal Vectors Greedily — greedy_orthogonalization_curation2

<dl>

<dt>W</dt>
<dd>A matrix in $-1, 1^R x n$ which have R allocation vectors for an experiment of sample size n.</dd>


<dt>R0</dt>
<dd>The minimum number of vectors to consider in a design. The default is the true bottom, two.</dd>


<dt>verbose</dt>
<dd>Default is <code>FALSE</code> but if not, it will print out a message for each iteration.</dd>

</dl>

greedy_orthogonalization_curation2: Curate More Orthogonal Vectors Greedily

Description

Usage

Value

Arguments

Author