qp_solver_nloptr

This function solves a quadratic programming problem using the Sequential Least Squares Programming (SLSQP) algorithm from the <code>nloptr</code> package.

Provides functions to calculate the minimum and maximum possible
values of Cronbach's alpha when item-level missing data are present.
Cronbach's alpha (Cronbach, 1951 <doi:10.1007/BF02310555>) is one of the most widely used
measures of internal consistency in the social, behavioral, and medical sciences
(Bland & Altman, 1997 <doi:10.1136/bmj.314.7080.572>; Tavakol & Dennick, 2011
<doi:10.5116/ijme.4dfb.8dfd>). However, conventional implementations assume
complete data, and listwise deletion is often applied when missingness occurs,
which can lead to biased or overly optimistic reliability estimates (Enders, 2003
<doi:10.1037/1082-989X.8.3.322>). This package implements computational strategies
including enumeration, Monte Carlo sampling, and optimization algorithms
(e.g., Genetic Algorithm, Differential Evolution, Sequential Least Squares
Programming) to obtain sharp lower and upper bounds of Cronbach's alpha under
arbitrary missing data patterns. The approach is motivated by Manski's partial
identification framework and pessimistic bounding ideas from optimization literature.

Biying Zhou

missalpha

Find Range of Cronbach Alpha with a Dataset Including Missing
Data

Feng Ji

qp_solver_nloptr function

<dl><dt>n</dt>
<dd>An integer representing the number of decision variables.</dd>
<dt>A</dt>
<dd>A matrix representing the quadratic coefficients.</dd>
<dt>b</dt>
<dd>A numeric vector representing the linear coefficients.</dd>
<dt>c</dt>
<dd>A numeric scalar representing the constant term in the objective function.</dd>
<dt>x_max</dt>
<dd>An integer representing the upper bound for the decision variables. Default is 1.</dd>
<dt>print_message</dt>
<dd>A logical value indicating whether to print optimization details. Default is FALSE.</dd>
<dt>xtol_rel</dt>
<dd>A numeric value specifying the relative tolerance for convergence. Default is <code>1e-8</code>.</dd>
<dt>maxeval</dt>
<dd>An integer specifying the maximum number of function evaluations. Default is 10000.</dd>
<dt>print_level</dt>
<dd>An integer controlling the verbosity of output. Default is 0.</dd>
<dt>...</dt>
<dd>Additional control parameters for <code>nloptr</code>.</dd></dl>

Arguments

Solve Quadratic Programming Problem using nloptr — qp_solver_nloptr

<dl>

<dt>n</dt>
<dd>An integer representing the number of decision variables.</dd>


<dt>A</dt>
<dd>A matrix representing the quadratic coefficients.</dd>


<dt>b</dt>
<dd>A numeric vector representing the linear coefficients.</dd>


<dt>c</dt>
<dd>A numeric scalar representing the constant term in the objective function.</dd>


<dt>x_max</dt>
<dd>An integer representing the upper bound for the decision variables. Default is 1.</dd>


<dt>print_message</dt>
<dd>A logical value indicating whether to print optimization details. Default is FALSE.</dd>


<dt>xtol_rel</dt>
<dd>A numeric value specifying the relative tolerance for convergence. Default is <code>1e-8</code>.</dd>


<dt>maxeval</dt>
<dd>An integer specifying the maximum number of function evaluations. Default is 10000.</dd>


<dt>print_level</dt>
<dd>An integer controlling the verbosity of output. Default is 0.</dd>


<dt>...</dt>
<dd>Additional control parameters for <code>nloptr</code>.</dd>

</dl>

qp_solver_nloptr: Solve Quadratic Programming Problem using nloptr

Description

Usage

Value

Arguments

See Also