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  "Package": "ForLion",
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  "Title": "'ForLion' Algorithm to Find D-Optimal Designs for Experiments",
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  "Maintainer": "Siting Lin <slin95@uic.edu>",
  "Description": "Designing experimental plans that involve both discrete\nand continuous factors with general parametric statistical\nmodels using the 'ForLion' algorithm and 'EW ForLion'\nalgorithm. The algorithms searches for locally optimal designs\nand EW optimal designs under the D-criterion. See Huang, Y.,\nLi, K., Mandal, A., & Yang, J., (2024)\n<doi:10.1007/s11222-024-10465-x> and Lin, S., Huang, Y., &\nYang, J. (2025) <doi:10.48550/arXiv.2505.00629>.",
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    "design_initial_self",
    "discrete_rv_self",
    "dprime_func_self",
    "EW_design_initial_GLM",
    "EW_design_initial_MLM",
    "EW_dprime_func_self",
    "EW_Fi_MLM_func",
    "EW_ForLion_GLM_Optimal",
    "EW_ForLion_MLM_Optimal",
    "EW_liftoneDoptimal_GLM_func",
    "EW_liftoneDoptimal_log_GLM_func",
    "EW_liftoneDoptimal_MLM_func",
    "EW_Xw_maineffects_self",
    "Fi_MLM_func",
    "ForLion_GLM_Optimal",
    "ForLion_MLM_Optimal",
    "GLM_Exact_Design",
    "liftoneDoptimal_GLM_func",
    "liftoneDoptimal_log_GLM_func",
    "liftoneDoptimal_MLM_func",
    "MLM_Exact_Design",
    "nu_cauchit_self",
    "nu_identity_self",
    "nu_log_self",
    "nu_logit_self",
    "nu_loglog_self",
    "nu_probit_self",
    "nu1_cauchit_self",
    "nu1_identity_self",
    "nu1_log_self",
    "nu1_logit_self",
    "nu1_loglog_self",
    "nu1_probit_self",
    "nu2_cauchit_self",
    "nu2_identity_self",
    "nu2_log_self",
    "nu2_logit_self",
    "nu2_loglog_self",
    "nu2_probit_self",
    "polynomial_sol_J3",
    "polynomial_sol_J4",
    "polynomial_sol_J5",
    "svd_inverse",
    "xmat_discrete_self",
    "Xw_maineffects_self"
  ],
  "_help": [
    {
      "page": "design_initial_self",
      "title": "function to generate initial design with design points and the approximate allocation",
      "topics": [
        "design_initial_self"
      ]
    },
    {
      "page": "discrete_rv_self",
      "title": "function to generate discrete uniform random variables for initial random design points in ForLion",
      "topics": [
        "discrete_rv_self"
      ]
    },
    {
      "page": "dprime_func_self",
      "title": "function to calculate du/dx in the gradient of d(x, Xi), will be used in ForLion_MLM_func() function, details see Appendix C in Huang, Li, Mandal, Yang (2024)",
      "topics": [
        "dprime_func_self"
      ]
    },
    {
      "page": "EW_design_initial_GLM",
      "title": "function to generate a initial EW Design for generalized linear models",
      "topics": [
        "EW_design_initial_GLM"
      ]
    },
    {
      "page": "EW_design_initial_MLM",
      "title": "function to generate a initial EW Design for multinomial logistic models",
      "topics": [
        "EW_design_initial_MLM"
      ]
    },
    {
      "page": "EW_dprime_func_self",
      "title": "function to calculate dEu/dx in the gradient of d(x, Xi), will be used in EW_ForLion_MLM_func() function",
      "topics": [
        "EW_dprime_func_self"
      ]
    },
    {
      "page": "EW_Fi_MLM_func",
      "title": "function to generate the expected fisher information at one design point xi for multinomial logit models",
      "topics": [
        "EW_Fi_MLM_func"
      ]
    },
    {
      "page": "EW_ForLion_GLM_Optimal",
      "title": "EW ForLion for generalized linear models",
      "topics": [
        "EW_ForLion_GLM_Optimal"
      ]
    },
    {
      "page": "EW_ForLion_MLM_Optimal",
      "title": "EW ForLion function for multinomial logit models",
      "topics": [
        "EW_ForLion_MLM_Optimal"
      ]
    },
    {
      "page": "EW_liftoneDoptimal_GLM_func",
      "title": "EW Lift-one algorithm for D-optimal approximate design",
      "topics": [
        "EW_liftoneDoptimal_GLM_func"
      ]
    },
    {
      "page": "EW_liftoneDoptimal_log_GLM_func",
      "title": "EW Lift-one algorithm for D-optimal approximate design in log scale",
      "topics": [
        "EW_liftoneDoptimal_log_GLM_func"
      ]
    },
    {
      "page": "EW_liftoneDoptimal_MLM_func",
      "title": "function of EW liftone for multinomial logit model",
      "topics": [
        "EW_liftoneDoptimal_MLM_func"
      ]
    },
    {
      "page": "EW_Xw_maineffects_self",
      "title": "function for calculating X=h(x) and E_w=E(nu(beta^T h(x))) given a design point x=(1,x1,...,xd)^T",
      "topics": [
        "EW_Xw_maineffects_self"
      ]
    },
    {
      "page": "Fi_MLM_func",
      "title": "function to generate fisher information at one design point xi for multinomial logit models",
      "topics": [
        "Fi_MLM_func"
      ]
    },
    {
      "page": "ForLion_GLM_Optimal",
      "title": "ForLion for generalized linear models",
      "topics": [
        "ForLion_GLM_Optimal"
      ]
    },
    {
      "page": "ForLion_MLM_Optimal",
      "title": "ForLion function for multinomial logit models",
      "topics": [
        "ForLion_MLM_Optimal"
      ]
    },
    {
      "page": "GLM_Exact_Design",
      "title": "rounding algorithm for generalized linear models",
      "topics": [
        "GLM_Exact_Design"
      ]
    },
    {
      "page": "liftoneDoptimal_GLM_func",
      "title": "Lift-one algorithm for D-optimal approximate design",
      "topics": [
        "liftoneDoptimal_GLM_func"
      ]
    },
    {
      "page": "liftoneDoptimal_log_GLM_func",
      "title": "Lift-one algorithm for D-optimal approximate design in log scale",
      "topics": [
        "liftoneDoptimal_log_GLM_func"
      ]
    },
    {
      "page": "liftoneDoptimal_MLM_func",
      "title": "function of liftone for multinomial logit model",
      "topics": [
        "liftoneDoptimal_MLM_func"
      ]
    },
    {
      "page": "MLM_Exact_Design",
      "title": "rounding algorithm for multinomial logit models",
      "topics": [
        "MLM_Exact_Design"
      ]
    },
    {
      "page": "nu_cauchit_self",
      "title": "function to calculate w = nu(eta) given eta for cauchit link",
      "topics": [
        "nu_cauchit_self"
      ]
    },
    {
      "page": "nu_identity_self",
      "title": "function to calculate w = nu(eta) given eta for identity link",
      "topics": [
        "nu_identity_self"
      ]
    },
    {
      "page": "nu_log_self",
      "title": "function to calculate w = nu(eta) given eta for log link",
      "topics": [
        "nu_log_self"
      ]
    },
    {
      "page": "nu_logit_self",
      "title": "function to calculate w = nu(eta) given eta for logit link",
      "topics": [
        "nu_logit_self"
      ]
    },
    {
      "page": "nu_loglog_self",
      "title": "function to calculate w = nu(eta) given eta for loglog link",
      "topics": [
        "nu_loglog_self"
      ]
    },
    {
      "page": "nu_probit_self",
      "title": "function to calculate w = nu(eta) given eta for probit link",
      "topics": [
        "nu_probit_self"
      ]
    },
    {
      "page": "nu1_cauchit_self",
      "title": "function to calculate first derivative of nu function given eta for cauchit link",
      "topics": [
        "nu1_cauchit_self"
      ]
    },
    {
      "page": "nu1_identity_self",
      "title": "function to calculate first derivative of nu function given eta for identity link",
      "topics": [
        "nu1_identity_self"
      ]
    },
    {
      "page": "nu1_log_self",
      "title": "function to calculate first derivative of nu function given eta for log link",
      "topics": [
        "nu1_log_self"
      ]
    },
    {
      "page": "nu1_logit_self",
      "title": "function to calculate the first derivative of nu function given eta for logit link",
      "topics": [
        "nu1_logit_self"
      ]
    },
    {
      "page": "nu1_loglog_self",
      "title": "function to calculate the first derivative of nu function given eta for log-log link",
      "topics": [
        "nu1_loglog_self"
      ]
    },
    {
      "page": "nu1_probit_self",
      "title": "function to calculate the first derivative of nu function given eta for probit link",
      "topics": [
        "nu1_probit_self"
      ]
    },
    {
      "page": "nu2_cauchit_self",
      "title": "function to calculate the second derivative of nu function given eta for cauchit link",
      "topics": [
        "nu2_cauchit_self"
      ]
    },
    {
      "page": "nu2_identity_self",
      "title": "function to calculate the second derivative of nu function given eta for identity link",
      "topics": [
        "nu2_identity_self"
      ]
    },
    {
      "page": "nu2_log_self",
      "title": "function to calculate the second derivative of nu function given eta for log link",
      "topics": [
        "nu2_log_self"
      ]
    },
    {
      "page": "nu2_logit_self",
      "title": "function to calculate the second derivative of nu function given eta for logit link",
      "topics": [
        "nu2_logit_self"
      ]
    },
    {
      "page": "nu2_loglog_self",
      "title": "function to calculate the second derivative of nu function given eta for loglog link",
      "topics": [
        "nu2_loglog_self"
      ]
    },
    {
      "page": "nu2_probit_self",
      "title": "function to calculate the second derivative of nu function given eta for probit link",
      "topics": [
        "nu2_probit_self"
      ]
    },
    {
      "page": "polynomial_sol_J3",
      "title": "functions to solve 2th order polynomial function given coefficients",
      "topics": [
        "polynomial_sol_J3"
      ]
    },
    {
      "page": "polynomial_sol_J4",
      "title": "functions to solve 3th order polynomial function given coefficients",
      "topics": [
        "polynomial_sol_J4"
      ]
    },
    {
      "page": "polynomial_sol_J5",
      "title": "functions to solve 4th order polynomial function given coefficients",
      "topics": [
        "polynomial_sol_J5"
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    },
    {
      "page": "print.design_output",
      "title": "Print Method for Design Output from ForLion Algorithms",
      "topics": [
        "print.design_output"
      ]
    },
    {
      "page": "print.list_output",
      "title": "Print Method for list_output Objects",
      "topics": [
        "print.list_output"
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      "page": "svd_inverse",
      "title": "SVD Inverse Of A Square Matrix",
      "topics": [
        "svd_inverse"
      ]
    },
    {
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      "title": "Generate initial designs within ForLion algorithms",
      "topics": [
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      "page": "Xw_maineffects_self",
      "title": "function for calculating X=h(x) and w=nu(beta^T h(x)) given a design point x = (x1,...,xd)^T",
      "topics": [
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      ]
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      "title": "Introduction to ForLion package",
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      "headings": [
        "Table of Contents",
        "Introduction",
        "Locally D-optimality and ForLion algorithm",
        "EW D-optimality and EW ForLion algorithm",
        "Applications in mixed factor experiments",
        "GLM Example",
        "Locally D-optimal approximate design",
        "Locally D-optimal exact design",
        "EW D-optimal approximate design",
        "MLM Example",
        "EW D-optimal exact design",
        "References:"
      ],
      "created": "2025-02-11 09:10:02",
      "modified": "2026-02-15 17:40:03",
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