randomized_rounding

The linear programming solution of <code>balance_LP()</code> that is used
within <code>optimize_controls()</code> sometimes selects fractional units.
Here, we select any unit the linear programming solution chose with coefficient 1.
Then, we select the remaining required number of units from those that have
fractional solutions by sampling with probabilities equal to the linear
programming solution and fixed sample size. Used within <code>optimize_controls()</code>
if <code>correct_sizes = TRUE</code>.

internal

Natural strata can be used in observational studies to balance
the distributions of many covariates across any number of treatment
groups and any number of comparisons. These strata have proportional
amounts of units within each stratum across the treatments, allowing
for simple interpretation and aggregation across strata. Within each
stratum, the units are chosen using randomized rounding of a linear
program that balances many covariates. For more details, see Brumberg et al. (2022) <doi:10.1111/rssa.12848> and Brumberg et al.(2023) <doi:10.1093/jrsssc/qlad010>.
To solve the linear program, the 'Gurobi' commercial optimization software
is recommended, but not required. The 'gurobi' R package can be installed by following the instructions at <https://docs.gurobi.com/projects/optimizer/en/current/reference/r/setup.html> after claiming your free academic license at <https://www.gurobi.com/academia/academic-program-and-licenses/>.

Katherine Brumberg

natstrat

Obtain Unweighted Natural Strata that Balance Many Covariates

randomized_rounding function

<dl><dt>o</dt>
<dd>linear programming results, as found in the `o` element of the
returned list from <code>balance_LP()</code>.</dd>
<dt>N</dt>
<dd>the total number of available controls in the data.</dd>
<dt>st</dt>
<dd>a stratum vector with the <code>i</code>th entry equal to the
stratum of unit <code>i</code>. This should have the same order of units and length
as <code>z</code>.</dd>
<dt>st_vals</dt>
<dd>the unique stratum levels contained in <code>st</code>.</dd>
<dt>S</dt>
<dd>the number of unique stratum levels contained in <code>st</code>.</dd>
<dt>z</dt>
<dd>a factor with the <code>i</code>th entry equal to the treatment of unit <code>i</code>.</dd></dl>

Arguments

Sample integer solution from linear programming solution with correct sample sizes — randomized_rounding

<dl>

<dt>o</dt>
<dd>linear programming results, as found in the `o` element of the
returned list from <code>balance_LP()</code>.</dd>


<dt>N</dt>
<dd>the total number of available controls in the data.</dd>


<dt>st</dt>
<dd>a stratum vector with the <code>i</code>th entry equal to the
stratum of unit <code>i</code>. This should have the same order of units and length
as <code>z</code>.</dd>


<dt>st_vals</dt>
<dd>the unique stratum levels contained in <code>st</code>.</dd>


<dt>S</dt>
<dd>the number of unique stratum levels contained in <code>st</code>.</dd>


<dt>z</dt>
<dd>a factor with the <code>i</code>th entry equal to the treatment of unit <code>i</code>.</dd>

</dl>

randomized_rounding: Sample integer solution from linear programming solution with correct sample sizes

Description

Usage

Value

Arguments