pl_theta: Profile likelihood for theta, the analysis model parameters

In sarahlotspeich/logreg2ph_R_only: Implements Sieve Maximum Likelihood Estimation (SMLE) Approach for Two-Phase Logistic Regression

Profile likelihood for theta, the analysis model parameters

Description

This function returns the value of the profile log-likelihood for parameters theta of the analysis model P(Y|X,C) after perturbing element k of theta by some small amount h_N.

Usage

pl_theta(
  k,
  theta,
  h_N,
  n,
  N,
  Y_unval,
  Y_val,
  X_unval,
  X_val,
  C,
  Bspline,
  comp_dat_all,
  theta_pred,
  gamma_pred,
  gamma0 = NULL,
  p0 = NULL,
  p_val_num = NULL,
  TOL,
  MAX_ITER
)

Arguments

k	A numeric index between 1 and the dimension of theta for the element of theta to be perturbed
theta	Parameters for the analysis model (a column vector) at convergence, resulting from the EM algorithm
h_N	Size of the small perturbation in theta[k], by default chosen to be h_N = N ^ ( - 1 / 2)
n	Phase II sample size
N	Phase I sample size
Y_unval	Column names with the unvalidated outcome. If Y_unval is null, the outcome is assumed to be error-free.
Y_val	Column names with the validated outcome.
X_unval	Column name(s) with the unvalidated predictors. If X_unval and X_val are null, all precictors are assumed to be error-free.
X_val	Column name(s) with the validated predictors. If X_unval and X_val are null, all precictors are assumed to be error-free.
C	(Optional) Column name(s) with additional error-free covariates.
Bspline	Vector of column names containing the B-spline basis functions.
comp_dat_all	Augmented dataset containing rows for each combination of unvalidated subjects' data with values from Phase II (a matrix)
theta_pred	Vector of columns in comp_dat_all that pertain to the predictors in the analysis model.
gamma_pred	Vector of columns in comp_dat_all that pertain to the predictors in the outcome error model.
gamma0	Starting values for gamma, the parameters for the outcome error model (a column vector)
p0	Starting values for p, the B-spline coefficients for the approximated covariate error model (a matrix)
p_val_num	Contributions of validated subjects to the numerator for p, which are fixed (a matrix)
TOL	Tolerance between iterations in the EM algorithm used to define convergence.
MAX_ITER	Maximum number of iterations allowed in the EM algorithm.
Validated	Column name with the validation indicator. The validation indicator can be defined as Validated = 1 or TRUE if the subject was validated and Validated = 0 or FALSE otherwise.

Value

Profile likelihood for theta after perturbing element k by h_N.

sarahlotspeich/logreg2ph_R_only documentation built on Jan. 20, 2025, 6:20 p.m.