{
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  "Package": "multinomineq",
  "Type": "Package",
  "Title": "Bayesian Inference for Multinomial Models with Inequality\nConstraints",
  "Version": "0.2.6",
  "Date": "2024-02-19",
  "Authors@R": "person(\"Daniel W.\", \"Heck\", \nemail = \"daniel.heck@uni-marburg.de\",\nrole = c(\"aut\",\"cre\"),\ncomment = c(ORCID = \"0000-0002-6302-9252\"))",
  "Maintainer": "Daniel W. Heck <daniel.heck@uni-marburg.de>",
  "Description": "Implements Gibbs sampling and Bayes factors for\nmultinomial models with linear inequality constraints on the\nvector of probability parameters. As special cases, the model\nclass includes models that predict a linear order of binomial\nprobabilities (e.g., p[1] < p[2] < p[3] < .50) and mixture\nmodels assuming that the parameter vector p must be inside the\nconvex hull of a finite number of predicted patterns (i.e.,\nvertices). A formal definition of inequality-constrained\nmultinomial models and the implemented computational methods is\nprovided in: Heck, D.W., & Davis-Stober, C.P. (2019).\nMultinomial models with linear inequality constraints: Overview\nand improvements of computational methods for Bayesian\ninference. Journal of Mathematical Psychology, 91, 70-87.\n<doi:10.1016/j.jmp.2019.03.004>. Inequality-constrained\nmultinomial models have applications in the area of judgment\nand decision making to fit and test random utility models\n(Regenwetter, M., Dana, J., & Davis-Stober, C.P. (2011).\nTransitivity of preferences. Psychological Review, 118, 42–56,\n<doi:10.1037/a0021150>) or to perform outcome-based strategy\nclassification to select the decision strategy that provides\nthe best account for a vector of observed choice frequencies\n(Heck, D.W., Hilbig, B.E., & Moshagen, M. (2017). From\ninformation processing to decisions: Formalizing and comparing\nprobabilistic choice models. Cognitive Psychology, 96, 26–40.\n<doi:10.1016/j.cogpsych.2017.05.003>).",
  "License": "GPL-3",
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  "Repository": "https://danheck.r-universe.dev",
  "Date/Publication": "2025-07-22 16:02:58 UTC",
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  "NeedsCompilation": "yes",
  "Packaged": {
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    "User": "root"
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  "Author": "Daniel W. Heck [aut, cre] (ORCID:\n<https://orcid.org/0000-0002-6302-9252>)",
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  "_created": "2026-09-26T07:41:15.000Z",
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    "Ab_max",
    "Ab_multinom",
    "Ab_sort",
    "Ab_to_V",
    "add_fixed",
    "bf_binom",
    "bf_equality",
    "bf_multinom",
    "bf_nonlinear",
    "binom_to_multinom",
    "count_binom",
    "count_multinom",
    "count_nonlinear",
    "count_to_bf",
    "drop_fixed",
    "find_inside",
    "inside",
    "inside_binom",
    "inside_multinom",
    "ml_binom",
    "ml_multinom",
    "model_weights",
    "nirt_to_Ab",
    "population_bf",
    "postprob",
    "ppp_binom",
    "ppp_multinom",
    "rpbinom",
    "rpdirichlet",
    "rpmultinom",
    "sampling_binom",
    "sampling_multinom",
    "sampling_nonlinear",
    "stochdom_Ab",
    "stochdom_bf",
    "strategy_marginal",
    "strategy_multiattribute",
    "strategy_postprob",
    "strategy_to_Ab",
    "strategy_unique",
    "V_to_Ab"
  ],
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      "title": "Data: Multiattribute Decisions (Heck, Hilbig & Moshagen, 2017)",
      "object": "heck2017",
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      "title": "Data: Multiattribute Decisions (Heck, Hilbig & Moshagen, 2017)",
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        "wadd",
        "logoddsdiff",
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        "itemtype",
        "reversedorder",
        "choice",
        "rt",
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        "a1",
        "a2",
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        "b1",
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        "b4"
      ],
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    },
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      "title": "Data: Multiattribute Decisions (Hilbig & Moshagen, 2014)",
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      "class": [
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      "fields": [
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        "B2",
        "B3"
      ],
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      "table": true,
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    },
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      "name": "karabatsos2004",
      "title": "Data: Item Responses Theory (Karabatsos & Sheu, 2004)",
      "object": "karabatsos2004",
      "class": [
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      "fields": [],
      "table": false,
      "tojson": true
    },
    {
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      "title": "Data: Ternary Risky Choices (Regenwetter & Davis-Stober, 2012)",
      "object": "regenwetter2012",
      "class": [
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        "array"
      ],
      "fields": [
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        "gamble_set",
        "a>b",
        "b>a",
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        "a>c",
        "c>a",
        "a=c",
        "a>d",
        "d>a",
        "a=d",
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        "c>b",
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        "b>d",
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      "page": "multinomineq-package",
      "title": "multinomineq: Bayesian Inference for Inequality-Constrained Multinomial Models",
      "topics": [
        "multinomineq-package",
        "multinomineq"
      ]
    },
    {
      "page": "Ab_drop_fixed",
      "title": "Drop fixed columns in the Ab-Representation",
      "topics": [
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    },
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      "page": "Ab_max",
      "title": "Automatic Construction of Ab-Representation for Common Inequality Constraints",
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      "page": "Ab_multinom",
      "title": "Get Constraints for Product-Multinomial Probabilities",
      "topics": [
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      "topics": [
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      "page": "bf_binom",
      "title": "Bayes Factor for Linear Inequality Constraints",
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      "title": "Count How Many Samples Satisfy Linear Inequalities (Binomial)",
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      "title": "Count How Many Samples Satisfy Linear Inequalities (Multinomial)",
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      "title": "Compute Bayes Factor Using Prior/Posterior Counts",
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    {
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        "drop_fixed"
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    },
    {
      "page": "find_inside",
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      "page": "hilbig2014",
      "title": "Data: Multiattribute Decisions (Hilbig & Moshagen, 2014)",
      "topics": [
        "hilbig2014"
      ]
    },
    {
      "page": "inside",
      "title": "Check Whether Points are Inside a Convex Polytope",
      "topics": [
        "inside"
      ]
    },
    {
      "page": "inside_binom",
      "title": "Check Whether Choice Frequencies are in Polytope",
      "topics": [
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        "inside_multinom"
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      "page": "ml_binom",
      "title": "Maximum-likelihood Estimate",
      "topics": [
        "ml_binom",
        "ml_multinom"
      ]
    },
    {
      "page": "model_weights",
      "title": "Get Posterior/NML Model Weights",
      "topics": [
        "model_weights"
      ]
    },
    {
      "page": "nirt_to_Ab",
      "title": "Nonparametric Item Response Theory (NIRT)",
      "topics": [
        "nirt_to_Ab"
      ]
    },
    {
      "page": "population_bf",
      "title": "Aggregation of Individual Bayes Factors",
      "topics": [
        "population_bf"
      ]
    },
    {
      "page": "postprob",
      "title": "Transform Bayes Factors to Posterior Model Probabilities",
      "topics": [
        "postprob"
      ]
    },
    {
      "page": "ppp_binom",
      "title": "Posterior Predictive p-Values",
      "topics": [
        "ppp_binom",
        "ppp_multinom"
      ]
    },
    {
      "page": "regenwetter2012",
      "title": "Data: Ternary Risky Choices (Regenwetter & Davis-Stober, 2012)",
      "topics": [
        "regenwetter2012"
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    },
    {
      "page": "rpbinom",
      "title": "Random Generation for Independent Multinomial Distributions",
      "topics": [
        "rpbinom",
        "rpmultinom"
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    },
    {
      "page": "rpdirichlet",
      "title": "Random Samples from the Product-Dirichlet Distribution",
      "topics": [
        "rpdirichlet"
      ]
    },
    {
      "page": "sampling_multinom",
      "title": "Posterior Sampling for Inequality-Constrained Multinomial Models",
      "topics": [
        "sampling_binom",
        "sampling_multinom"
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    },
    {
      "page": "sampling_nonlinear",
      "title": "Posterior Sampling for Multinomial Models with Nonlinear Inequalities",
      "topics": [
        "sampling_nonlinear"
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    },
    {
      "page": "stochdom_Ab",
      "title": "Ab-Representation for Stochastic Dominance of Histogram Bins",
      "topics": [
        "stochdom_Ab"
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    },
    {
      "page": "stochdom_bf",
      "title": "Bayes Factor for Stochastic Dominance of Continuous Distributions",
      "topics": [
        "stochdom_bf"
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      "page": "strategy_marginal",
      "title": "Log-Marginal Likelihood for Decision Strategy",
      "topics": [
        "strategy_marginal"
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    {
      "page": "strategy_multiattribute",
      "title": "Strategy Predictions for Multiattribute Decisions",
      "topics": [
        "strategy_multiattribute"
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      "page": "strategy_postprob",
      "title": "Strategy Classification: Posterior Model Probabilities",
      "topics": [
        "strategy_postprob"
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      "title": "Transform Pattern of Predictions to Polytope",
      "topics": [
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    },
    {
      "page": "strategy_unique",
      "title": "Unique Patterns/Item Types of Strategy Predictions",
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        "strategy_unique"
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      "page": "swop5",
      "title": "Strict Weak Order Polytope for 5 Elements and Ternary Choices",
      "topics": [
        "swop5"
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    {
      "page": "V_to_Ab",
      "title": "Transform Vertex/Inequality Representation of Polytope",
      "topics": [
        "Ab_to_V",
        "V_to_Ab"
      ]
    }
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        "Formal definition of multinomial models with inequality constraints",
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