compute_gram_matrix

Computes the Gram Matrix for a user-specified kernel using the library <code>kernlab</code>. Note that 
this function automatically standardizes the columns of the data entered.

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

compute_gram_matrix 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>kernel_type</dt>
<dd>One of the following: "vanilla", "rbf", "poly", "tanh", "bessel", "laplace", 
"anova" or "spline".</dd>
<dt>params</dt>
<dd>A vector of numeric parameters. Each <code>kernel_type</code> has different numbers of
parameters required. For more information see documentation for the <code>kernlab</code> library.</dd></dl>

Arguments

Author

Gram Matrix Computation — compute_gram_matrix

<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>kernel_type</dt>
<dd>One of the following: "vanilla", "rbf", "poly", "tanh", "bessel", "laplace", 
"anova" or "spline".</dd>


<dt>params</dt>
<dd>A vector of numeric parameters. Each <code>kernel_type</code> has different numbers of
parameters required. For more information see documentation for the <code>kernlab</code> library.</dd>

</dl>

compute_gram_matrix: Gram Matrix Computation

Description

Usage

Value

Arguments

Author