The R package `multinomineq`

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).

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) 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).

## Installation & Vignette

Instructions how to install the R package are available on Github: https://github.com/danheck/multinomineq/

The package vignette provides a short introduction of how to apply the main functions of `multinomineq`

:

```
vignette('multinomineq_intro')
```

The vignette is also available https://www.dwheck.de/vignettes/multinomineq_intro.html.

## References

A formal definition of inequality-constrained multinomial models and the implemented computational methods for Bayesian inference 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

[BibTeX] [Abstract] [Data and R Scripts] [GitHub] [arXiv]Many psychological theories can be operationalized as linear inequality constraints on the parameters of multinomial distributions (e.g., discrete choice analysis). These constraints can be described in two equivalent ways: Either as the solution set to a system of linear inequalities or as the convex hull of a set of extremal points (vertices). For both representations, we describe a general Gibbs sampler for drawing posterior samples in order to carry out Bayesian analyses. We also summarize alternative sampling methods for estimating Bayes factors for these model representations using the encompassing Bayes factor method. We introduce the R package multinomineq , which provides an easily-accessible interface to a computationally efficient implementation of these techniques.

`@article{heck2019multinomial, title = {Multinomial Models with Linear Inequality Constraints: {{Overview}} and Improvements of Computational Methods for {{Bayesian}} Inference}, shorttitle = {Multinomial Models with Linear Inequality Constraints}, author = {Heck, Daniel W and Davis-Stober, Clintin P}, date = {2019}, journaltitle = {Journal of Mathematical Psychology}, volume = {91}, pages = {70--87}, doi = {10.1016/j.jmp.2019.03.004}, abstract = {Many psychological theories can be operationalized as linear inequality constraints on the parameters of multinomial distributions (e.g., discrete choice analysis). These constraints can be described in two equivalent ways: Either as the solution set to a system of linear inequalities or as the convex hull of a set of extremal points (vertices). For both representations, we describe a general Gibbs sampler for drawing posterior samples in order to carry out Bayesian analyses. We also summarize alternative sampling methods for estimating Bayes factors for these model representations using the encompassing Bayes factor method. We introduce the R package multinomineq , which provides an easily-accessible interface to a computationally efficient implementation of these techniques.}, arxivnumber = {1808.07140}, github = {https://github.com/danheck/multinomineq}, osf = {https://osf.io/xv9u3} }`

Please cite this paper if you use `multinomineq`

in publications.