Ab_drop_fixed

Often inequalities refer to all probability parameters of a multinomial distribution.
This function allows to transform the inequalities into the appropriate format
<code>A * x &lt;b</code> with respect to the free parameters only.

Implements Gibbs sampling and Bayes factors for multinomial models with
linear inequality constraints on the vector of probability parameters. As
special cases, the model class includes models that predict a linear order
of binomial probabilities (e.g., p[1] < p[2] < p[3] < .50) and mixture models
assuming that the parameter vector p must be inside the convex hull of a
finite number of predicted patterns (i.e., vertices). A formal definition of
inequality-constrained multinomial models and the implemented computational
methods is provided in: Heck, D.W., & Davis-Stober, C.P. (2019).
Multinomial models with linear inequality constraints: Overview and improvements
of computational methods for Bayesian inference. Journal of Mathematical
Psychology, 91, 70-87. <doi:10.1016/j.jmp.2019.03.004>.
Inequality-constrained multinomial models have applications in the area of
judgment and decision making to fit and test random utility models
(Regenwetter, M., Dana, J., & Davis-Stober, C.P. (2011). Transitivity of
preferences. Psychological Review, 118, 42–56, <doi:10.1037/a0021150>) or to
perform outcome-based strategy classification to select the decision strategy
that provides the best account for a vector of observed choice frequencies
(Heck, D.W., Hilbig, B.E., & Moshagen, M. (2017). From information
processing to decisions: Formalizing and comparing probabilistic choice models.
Cognitive Psychology, 96, 26–40. <doi:10.1016/j.cogpsych.2017.05.003>).

Daniel W. Heck

multinomineq

Bayesian Inference for Multinomial Models with Inequality
Constraints

Ab_drop_fixed function

<dl><dt>A</dt>
<dd>a matrix defining the convex polytope via <code>A*x &lt;= b</code>.
The columns of <code>A</code> do not include the last choice option per item type and
thus the number of columns must be equal to <code>sum(options-1)</code>
(e.g., the column order of <code>A</code> for <code>k = c(a1,a2,a2, b1,b2)</code>
is <code>c(a1,a2, b1)</code>).</dd>
<dt>b</dt>
<dd>a vector of the same length as the number of rows of <code>A</code>.</dd>
<dt>options</dt>
<dd>number of observable categories/probabilities for each item
type/multinomial distribution, e.g., <code>c(3,2)</code> for a ternary and binary item.</dd></dl>

Arguments

Drop fixed columns in the Ab-Representation — Ab_drop_fixed

<dl>

<dt>A</dt>
<dd>a matrix defining the convex polytope via <code>A*x &lt;= b</code>.
The columns of <code>A</code> do not include the last choice option per item type and
thus the number of columns must be equal to <code>sum(options-1)</code>
(e.g., the column order of <code>A</code> for <code>k = c(a1,a2,a2, b1,b2)</code>
is <code>c(a1,a2, b1)</code>).</dd>


<dt>b</dt>
<dd>a vector of the same length as the number of rows of <code>A</code>.</dd>


<dt>options</dt>
<dd>number of observable categories/probabilities for each item
type/multinomial distribution, e.g., <code>c(3,2)</code> for a ternary and binary item.</dd>

</dl>

Ab_drop_fixed: Drop fixed columns in the Ab-Representation

Description

Usage

Arguments

Examples