params_se: Standard Error of the Parameters

In TimeDepFrail: Time Dependent Shared Frailty Cox Model

Standard Error of the Parameters

Description

Function for computing the standard error of each optimal parameter, estimated through the constraint multi-dimensional optimization. The procedure for the computation is based on the numerical approximation of the second derivative of the log-likelihood function, by the 'centered finite difference scheme' with an accuracy of the second order.

Usage

params_se(
  optimal_params,
  params_range_min,
  params_range_max,
  dataset,
  centre,
  time_axis,
  dropout_matrix,
  e_matrix,
  h_dd
)

Arguments

optimal_params	Numerical vector of optimal parameters. Its length (i.e. number of parameters) is equal to n_p.
params_range_min	Numerical vector of length equal to n_p, containing the minimum range of each parameter.
params_range_max	Numerical vector of length equal to n_p, containing the maximum range of each parameter.
dataset	Dataset containing the value of the regressors for all individuals in the study.
centre	vector containing the group membership of each individual and that induces the clustering subdivision.
time_axis	Temporal domain. Its number of intervals corresponds to the length of the time-domain minus 1
dropout_matrix	Binary matrix of dimension (n_individuals, n_intervals). The sum of the elements of each row must be (1), if the associated individual failed in a precise interval, and (0) if the individual did not fail in the @time-axis. Therefore, if an individual failed in the time-domain, the interval in which he failed will have value (1) and the others (0).
e_matrix	Matrix of dimension (n_individuals, n_intervals) where each element contains the resolution of the temporal integral for that individual in that interval, thorugh the 'e_time_fun' function.
h_dd	Discretization step for the numerical approximation of the second derivative fo the loglikelihood function.

Details

The standrd error of each parameter is computed as the inverse of the square root of the 'Information matrix', that in turn is computed as the opposite of the 'Hessian matrix'. Only its diagonal is built and its elements are separatey evaluated through a numerical approximation of the second derivative of the log-likelihood function.

The function requires the optimal parameter vector and other parameters-related variables, to check:

• the right numerosity of the parameter vector

• the correct range existence of each parameter (i.e. each parameter lies in its range).

Value

Vector of parameter standard error, of length equal to the number of model parameters.

TimeDepFrail documentation built on April 11, 2025, 5:41 p.m.