rpdirichlet

Random samples from the prior/posterior (i.e., product-Dirichlet) of the unconstrained
product-multinomial model (the encompassing model).

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

rpdirichlet function

<dl><dt>n</dt>
<dd>number of samples</dd>
<dt>alpha</dt>
<dd>Dirichlet parameters concatenated across independent conditions
(e.g., a1,a2, b1,b2,b3)</dd>
<dt>options</dt>
<dd>the number of choice options per item type, e.g., <code>c(2,3)</code>
for a binary and ternary condition.
The sum of <code>options</code> must be equal to the length of <code>alpha</code>.</dd>
<dt>drop_fixed</dt>
<dd>whether the output matrix includes the last probability for each category
(which is not a free parameter since probabilities must sum to one).</dd></dl>

Arguments

Random Samples from the Product-Dirichlet Distribution — rpdirichlet

<dl>

<dt>n</dt>
<dd>number of samples</dd>


<dt>alpha</dt>
<dd>Dirichlet parameters concatenated across independent conditions
(e.g., a1,a2, b1,b2,b3)</dd>


<dt>options</dt>
<dd>the number of choice options per item type, e.g., <code>c(2,3)</code>
for a binary and ternary condition.
The sum of <code>options</code> must be equal to the length of <code>alpha</code>.</dd>


<dt>drop_fixed</dt>
<dd>whether the output matrix includes the last probability for each category
(which is not a free parameter since probabilities must sum to one).</dd>

</dl>

rpdirichlet: Random Samples from the Product-Dirichlet Distribution

Description

Usage

Arguments

Examples