Methods for model-based clustering of multinomial counts under the presence of covariates using mixtures of multinomial logit models, as implemented in Papastamoulis (2023) <DOI:10.1007/s11634-023-00547-5>. These models are estimated under  a frequentist as well as a Bayesian setup using the Expectation-Maximization algorithm and Markov chain Monte Carlo sampling (MCMC), respectively. The (unknown) number of clusters is selected according to the Integrated Completed Likelihood criterion (for the frequentist model), and estimating the number of non-empty components using overfitting mixture models after imposing suitable sparse prior assumptions on the mixing proportions (in the Bayesian case), see Rousseau and Mengersen (2011) <DOI:10.1111/j.1467-9868.2011.00781.x>. In the latter case, various MCMC chains run in parallel and are allowed to switch states. The final MCMC output is suitably post-processed in order to undo label switching using the Equivalence Classes Representatives (ECR) algorithm, as described in Papastamoulis (2016) <DOI:10.18637/jss.v069.c01>.

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>).