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  "Title": "Multinomial Logit Models for Categorical Responses and Discrete\nChoices",
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  "Description": "Provides estimators for multinomial logit models in their\nconditional logit (for discrete choices) and baseline logit\nvariants (for categorical responses), optionally with\noverdispersion or random effects. Random effects models are\nestimated using the PQL technique (based on a Laplace\napproximation) or the MQL technique (based on a Solomon-Cox\napproximation). Estimates should be treated with caution if the\ngroup sizes are small.",
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      "class": [
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      "class": [
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        "resp"
      ],
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      "table": true,
      "tojson": true
    }
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      "title": "Overdispersion in Multinomial Logit Models",
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    },
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    },
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      "title": "`getSummary` Methods",
      "topics": [
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        "getSummary.mclogit",
        "getSummary.mmblogit",
        "getSummary.mmclogit"
      ]
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      "page": "mblogit",
      "title": "Baseline-Category Logit Models for Categorical and Multinomial Responses",
      "topics": [
        "fitted.mblogit",
        "mblogit",
        "print.mblogit",
        "print.mmblogit",
        "print.summary.mblogit",
        "print.summary.mmblogit",
        "summary.mblogit",
        "summary.mmblogit",
        "weights.mblogit"
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    },
    {
      "page": "mclogit",
      "title": "Conditional Logit Models and Mixed Conditional Logit Models",
      "topics": [
        "AIC.mclogit",
        "anova.mclogit",
        "BIC.mclogit",
        "deviance.mclogit",
        "fitted.mclogit",
        "logLik.mclogit",
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        "mmclogit.control"
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        "The problem",
        "$$\\mathcal{L}_{\\text{cpl}}(\\boldsymbol{y},\\boldsymbol{b})",
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        "\\ell(\\boldsymbol{y}|\\boldsymbol{0};\\boldsymbol{\\alpha})",
        "\\frac12\\boldsymbol{g}_0'\\left(\\boldsymbol{H}_0+\\boldsymbol{\\Sigma}^{-1}\\right)^{-1}\\boldsymbol{g}_0",
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        "$$\\ln\\frac",
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        "Application of the technique to conditional and baseline logit models",
        "In case of the models supported by the mclogit package, the difference betweenFirth's PML technique and conventional ML estimation is that it solves for eachcoefficient $\\alpha_q$ the modified gradient equation$$0",
        "U^*(\\alpha_q)",
        "\\frac{\\partial\\ell}{\\partial\\alpha_q}+\\frac12\\mathrm{tr}\\left((\\boldsymbol{X}'\\boldsymbol{W}\\boldsymbol{X})^{-1}\\boldsymbol{X}'\\frac{\\partial\\boldsymbol{W}}{\\partial\\alpha_q}\\boldsymbol{X}\\right)$$instead of$$0",
        "U(\\alpha_q)",
        "Like the conventional MLE, the mclogit package uses an IWLS-algorithm,however, using a modified working response vector with elements$$y_{ij}^*",
        "\\boldsymbol{x}{ij}'\\boldsymbol{\\alpha} +\\frac{y{ij}-\\pi_{ij}}{\\pi_{ij}}+\\frac12\\sum_r\\sum_s\\zeta_{ij,rs}I^{(r,s)}$$where $I^{(r,s)}$ is the $r,s$ element of$(\\boldsymbol{X}'\\boldsymbol{W}\\boldsymbol{X})^{-1}$and$$\\begin{aligned}\\zeta_{ij,rs}&=(x_{ijr}-\\sum_kx_{ikr}\\pi_{ik})(x_{ijs}-\\sum_l\\pi_{il}x_{ils})",
        "A comparison of results obtained with other packages",
        "References"
      ],
      "created": "2026-01-04 23:47:29",
      "modified": "2026-01-05 13:47:08",
      "commits": 3
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      "headings": [
        "$$\\ln\\frac",
        "References"
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      "modified": "2026-01-05 13:47:33",
      "commits": 3
    },
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      "engine": "knitr::rmarkdown",
      "headings": [
        "References"
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      "modified": "2023-12-27 13:30:07",
      "commits": 2
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      "source": "fitting-mclogit.Rmd",
      "filename": "fitting-mclogit.html",
      "title": "The IWLS algorithm used to fit conditional logit models",
      "engine": "knitr::rmarkdown",
      "headings": [
        "$$\\frac",
        "\\sum_",
        "\\sum_{i,j}\\boldsymbol{x}{ij}(n{ij}-n_{i+}\\pi_{ij})",
        "\\sum_{i,j}\\boldsymbol{x}{ij}n{i+}(y_{ij}-\\pi_{ij})",
        "$$\\frac",
        "\\sum_",
        "\\sum_{i,j,k}\\boldsymbol{x}{ij}n{i+}(\\delta_{jk}-\\pi_{ij}\\pi_{ik})\\boldsymbol{x}_{ij}'",
        "$$\\boldsymbol",
        "\\boldsymbol",
        "\\left(\\frac",
        "$$\\boldsymbol",
        "\\boldsymbol{X}'\\boldsymbol{W}\\boldsymbol{X}\\boldsymbol{\\alpha}^{(s)}+\\boldsymbol{X}'\\boldsymbol{N}(\\boldsymbol{y}-\\boldsymbol{\\pi})",
        "\\boldsymbol{X}'\\boldsymbol{W}\\left(\\boldsymbol{X}\\boldsymbol{\\alpha}^{(s)}+\\boldsymbol{W}^-\\boldsymbol{N}(\\boldsymbol{y}-\\boldsymbol{\\pi})\\right)",
        "$$\\boldsymbol",
        "$$y_",
        "References"
      ],
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      "modified": "2025-12-27 21:42:45",
      "commits": 3
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      "engine": "knitr::rmarkdown",
      "headings": [],
      "created": "2023-12-27 11:00:29",
      "modified": "2023-12-27 11:00:29",
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