fits model with B_kj constrained to equal g(B_k) for constraint fn g

Usage

fit_null(
  B,
  Y,
  X,
  X_cup = NULL,
  k_constr,
  j_constr,
  j_ref,
  constraint_fn,
  constraint_grad_fn,
  rho_init = 1,
  tau = 1.2,
  kappa = 0.8,
  B_tol = 0.01,
  inner_tol = 0.01,
  constraint_tol = 1e-04,
  max_step = 5,
  c1 = 1e-04,
  maxit = 1000,
  inner_maxit = 25,
  verbose = FALSE,
  trackB = FALSE
)

Arguments

B: description
Y: Y (with augmentations)
X: design matrix
X_cup: design matrix for Y in long format. Defaults to NULL, in which case matrix is computed from X.
k_constr: row index of B to constrain
j_constr: col index of B to constrain
j_ref: column index of convenience constraint
constraint_fn: constraint function
constraint_grad_fn: gradient of constraint fn
rho_init: where to start quadratic penalty parameter
tau: how much to increment rho by each iteration
kappa: cutoff above which to increment rho. If distance to feasibility doesn't shrink by at least this factor in an iteration, increment rho by tau.
B_tol: tolerance for convergence in $max_k,j |B^t_kj - B^(t - 1)_kj|$
inner_tol: tolerance for inner loop
constraint_tol: tolerance for $|B_kj - g(B_k)|$
max_step: maximum step size
c1: constant for armijo rule
maxit: maximum iterations
inner_maxit: max iterations per inner loop
verbose: shout at you?
trackB: track value of beta across iterations and return?

Value

A list containing elements B, k_constr, j_constr, niter gap, u, rho, and Bs. B is a matrix containing parameter estimates under the null (obtained by maximum likelihood on augmented observations Y), k_constr, and j_constr give row and column indexes of the parameter fixed to be equal to the constraint function $g()$ under the null. niter is a scalar giving total number of outer iterations used to fit the null model, gap gives the final value of $g(B_k constr) - B_k constr, j constr$, u and rho are final values of augmented Lagrangian parameters, and Bs is a data frame containing values of B by iteration if trackB was set equal to TRUE (otherwise it contains a NULL value).