Optimization under null or alternative for multinomial model via Fisher scoring.

Usage

multinom_fisher_scoring(
  beta,
  X,
  Y,
  null = TRUE,
  strong = FALSE,
  null_j = NULL,
  j_ind = NULL,
  k_ind = NULL,
  tol = 1e-05,
  stepSize = 0.5,
  arm_c = 0.5,
  maxit = 250,
  pseudo_inv = FALSE
)

Arguments

beta: The initial values provided for the \(\beta\) parameters.
X: The \(n x p\) design matrix of covariates.
Y: The \(n x J\) data matrix of outcomes.
null: If TRUE, optimizes under the null, if FALSE, optimizes under the alternative. Defaults to TRUE.
strong: If FALSE, this function will compute the robust score statistic to test the weak null that for one specific \(j\), \(\beta_j = 0\) for the length \(p\) vector \(\beta_j\). If TRUE, this function instead computes the robust score statistic to test the strong null that \(\beta_1 = \beta_2 = \dots = \beta_{J-1} = 0\) for all length \(p\) vectors \(\beta_j\), \(j\in\{1,\ldots,J-1\}\). Default is FALSE.
null_j: If strong is FALSE, this argument must be supplied. This gives the category \(j\) in the weak null hypothesis that \(\beta_j = 0\). Default is NULL.
j_ind: If strong is FALSE and null_j is NULL, this argument must be supplied. This gives the category index of the individual covariate that is tested in the weak null hypothesis that \(\beta_{kj} = 0\).
k_ind: If strong is FALSE and null_j is NULL, this argument must be supplied. This gives the covariate index of the individual covariate that is tested in the weak null hypothesis that \(\beta_{kj} = 0\).
tol: The tolerance used to determine how much better update function value must be prior to stopping algorithm.
stepSize: The size of the step to take during the parameter update step.
arm_c: Control parameter for checking Armijo condition.
maxit: Maximum number of iterations for Fisher scoring. Defaults to 250.
pseudo_inv: Use the pseudo-inverse of the Fisher information matrix for the update (in case the inverse in computationally singular)

Value

The optimal beta values under the null or alternative model.

Author

Shirley Mathur