'ForLion' Algorithm to Find D-Optimal Designs for Experiments

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Documentation for package ‘ForLion’ version 0.1.0

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design_initial_self function to generate random initial design with design points and the approximate allocation
discrete_rv_self function to generate discrete uniform random variables for initial random design points in ForLion
dprime_func_self 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)
EW_design_initial_self function to generate random initial design with design points and the approximate allocation (For EW)
EW_dprime_func_self Function to calculate dEu/dx in the gradient of d(x, Xi), will be used in EW_ForLion_MLM_func() function
EW_Fi_MLM_func Function to generate the Expectation of fisher information at one design point xi for multinomial logit models
EW_ForLion_GLM_Optimal EW ForLion for generalized linear models
EW_ForLion_MLM_Optimal EW ForLion function for multinomial logit models
EW_liftoneDoptimal_GLM_func EW Lift-one algorithm for D-optimal approximate design
EW_liftoneDoptimal_log_GLM_func EW Lift-one algorithm for D-optimal approximate design in log scale
EW_liftoneDoptimal_MLM_func function of EW liftone for multinomial logit model
EW_Xw_maineffects_self function for calculating X=h(x) and E_w=E(nu(beta^T h(x))) give a design point x=(1,x1,...,xd)^T
Fi_MLM_func Function to generate fisher information at one design point xi for multinomial logit models
ForLion_GLM_Optimal ForLion for generalized linear models
ForLion_MLM_Optimal ForLion function for multinomial logit models
GLM_Exact_Design Approximation to exact design algorithm for generalized linear model
liftoneDoptimal_GLM_func Lift-one algorithm for D-optimal approximate design
liftoneDoptimal_log_GLM_func Lift-one algorithm for D-optimal approximate design in log scale
liftoneDoptimal_MLM_func function of liftone for multinomial logit model
MLM_Exact_Design Approximation to exact design algorithm for multinomial logit model
nu1_cauchit_self Function to calculate first derivative of nu function given eta for cauchit link
nu1_identity_self function to calculate first derivative of nu function given eta for identity link
nu1_logit_self function to calculate the first derivative of nu function given eta for logit link
nu1_loglog_self function to calculate the first derivative of nu function given eta for log-log link
nu1_log_self function to calculate first derivative of nu function given eta for log link
nu1_probit_self function to calculate the first derivative of nu function given eta for probit link
nu2_cauchit_self function to calculate the second derivative of nu function given eta for cauchit link
nu2_identity_self function to calculate the second derivative of nu function given eta for identity link
nu2_logit_self function to calculate the second derivative of nu function given eta for logit link
nu2_loglog_self function to calculate the second derivative of nu function given eta for loglog link
nu2_log_self function to calculate the second derivative of nu function given eta for log link
nu2_probit_self function to calculate the second derivative of nu function given eta for probit link
nu_cauchit_self function to calculate w = nu(eta) given eta for cauchit link
nu_identity_self Function to calculate w = nu(eta) given eta for identity link
nu_logit_self function to calculate w = nu(eta) given eta for logit link
nu_loglog_self function to calculate w = nu(eta) given eta for loglog link
nu_log_self Function to calculate w = nu(eta) given eta for log link
nu_probit_self function to calculate w = nu(eta) given eta for probit link
print.design_output Print Method for Design Output from ForLion Algorithm
print.list_output Print Method for list_output Objects
svd_inverse SVD Inverse Of A Square Matrix This function returns the inverse of a matrix using singular value decomposition. If the matrix is a square matrix, this should be equivalent to using the solve function. If the matrix is not a square matrix, then the result is the Moore-Penrose pseudo inverse.
xmat_discrete_self Generate GLM random initial designs within ForLion algorithm
Xw_maineffects_self function for calculating X=h(x) and w=nu(beta^T h(x)) given a design point x = (x1,...,xd)^T