Bayesian Inference for Multinomial Models with Inequality Constraints
Unique Patterns/Item Types of Strategy Predictions
Transform Vertex/Inequality Representation of Polytope
Drop fixed columns in the Ab-Representation
Automatic Construction of Ab-Representation for Common Inequality Cons...
Get Constraints for Product-Multinomial Probabilities
Sort Inequalities by Acceptance Rate
Bayes Factor for Linear Inequality Constraints
Bayes Factor with Inequality and (Approximate) Equality Constraints
Bayes Factor for Nonlinear Inequality Constraints
Converts Binary to Multinomial Frequencies
Count How Many Samples Satisfy Linear Inequalities (Binomial)
Count How Many Samples Satisfy Linear Inequalities (Multinomial)
Compute Bayes Factor Using Prior/Posterior Counts
Drop or Add Fixed Dimensions for Multinomial Probabilities/Frequencies
Find a Point/Parameter Vector Within a Convex Polytope
Check Whether Points are Inside a Convex Polytope
Check Whether Choice Frequencies are in Polytope
Maximum-likelihood Estimate
Get Posterior/NML Model Weights
multinomineq: Bayesian Inference for Inequality-Constrained Multinomia...
Nonparametric Item Response Theory (NIRT)
Aggregation of Individual Bayes Factors
Transform Bayes Factors to Posterior Model Probabilities
Posterior Predictive p-Values
Random Generation for Independent Multinomial Distributions
Random Samples from the Product-Dirichlet Distribution
Posterior Sampling for Inequality-Constrained Multinomial Models
Posterior Sampling for Multinomial Models with Nonlinear Inequalities
Ab-Representation for Stochastic Dominance of Histogram Bins
Bayes Factor for Stochastic Dominance of Continuous Distributions
Log-Marginal Likelihood for Decision Strategy
Strategy Predictions for Multiattribute Decisions
Strategy Classification: Posterior Model Probabilities
Transform Pattern of Predictions to Polytope
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>).