initOptimalExperimentalDesignObject

This method creates an object of type optimal_experimental_design and will immediately initiate
a search through $1_T$ space. Since this search takes exponential time, for most machines, 
this method is futile beyond 28 samples. You've been warned! For debugging, you can use set 
<code>num_cores = 1</code> to be assured of deterministic output.

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

initOptimalExperimentalDesignObject function

<dl><dt>X</dt>
<dd>The design matrix with $n$ rows (one for each subject) and $p$ columns 
(one for each measurement on the subject). This is the design matrix you wish 
to search for a more optimal design.</dd>
<dt>objective</dt>
<dd>The objective function to use when searching design space. This is a string
with valid values "<code>mahal_dist</code>" (the default), "<code>abs_sum_diff</code>" or "<code>kernel</code>".</dd>
<dt>Kgram</dt>
<dd>If the <code>objective = kernel</code>, this argument is required to be an <code>n x n</code> matrix whose
entries are the evaluation of the kernel function between subject i and subject j. Default is <code>NULL</code>.</dd>
<dt>wait</dt>
<dd>Should the <code>R</code> terminal hang until all <code>max_designs</code> vectors are found? The 
deafult is <code>FALSE</code>.</dd>
<dt>start</dt>
<dd>Should we start searching immediately (default is <code>TRUE</code>).</dd>
<dt>num_cores</dt>
<dd>The number of CPU cores you wish to use during the search. The default is <code>1</code>.</dd></dl>

Arguments

Author

Begin a Search for the Optimal Solution — initOptimalExperimentalDesignObject

<dl>

<dt>X</dt>
<dd>The design matrix with $n$ rows (one for each subject) and $p$ columns 
(one for each measurement on the subject). This is the design matrix you wish 
to search for a more optimal design.</dd>


<dt>objective</dt>
<dd>The objective function to use when searching design space. This is a string
with valid values "<code>mahal_dist</code>" (the default), "<code>abs_sum_diff</code>" or "<code>kernel</code>".</dd>


<dt>Kgram</dt>
<dd>If the <code>objective = kernel</code>, this argument is required to be an <code>n x n</code> matrix whose
entries are the evaluation of the kernel function between subject i and subject j. Default is <code>NULL</code>.</dd>


<dt>wait</dt>
<dd>Should the <code>R</code> terminal hang until all <code>max_designs</code> vectors are found? The 
deafult is <code>FALSE</code>.</dd>


<dt>start</dt>
<dd>Should we start searching immediately (default is <code>TRUE</code>).</dd>


<dt>num_cores</dt>
<dd>The number of CPU cores you wish to use during the search. The default is <code>1</code>.</dd>

</dl>

initOptimalExperimentalDesignObject: Begin a Search for the Optimal Solution

Description

Usage

Value

Arguments

Author