ll_AdPaik_1D: One-Dimensional Log-Likelihood Function to be Optimized
In TimeDepFrail: Time Dependent Shared Frailty Cox Model

ll_AdPaik_1D

R Documentation

One-Dimensional Log-Likelihood Function to be Optimized

Description

Model log-likelihood function to be optimized only with respect to a parameter. To correctly identify this parameter inside the model and inside the vector of all parameter, it is necessary to provide also the position (index) of this parameter in the vector.

This function is internally used by the main function @AdPaikModel to perform, as said, the one-dimensional optimization through 'optimize'. It cannot be used to evaluate the log-likelihood function at a vector of parameter and at the provided data. For this purpose, we have to use another implemented function, called @ll_AdPaik_eval.

Usage

ll_AdPaik_1D(
  x,
  index,
  params,
  dataset,
  centre,
  time_axis,
  dropout_matrix,
  e_matrix
)

Arguments

`x`	Value of the parameter, with respect to which the log-likelihood function has to be optimized.
`index`	Index of the parameter inside the parameter vector. For instance, if we need to optimize the log-likelihood function with respect to the first regressor, then @x will be generic but @index will be equal to (n_intervals + 1) because in the parameter vector the first regressor appears after the baseline log-hazard group (n_intervals elements).
`params`	Parameter vector.
`dataset`	Matrix containing only the formula regressors, that is the regressors appearing in the formula object provided by the user and eventually modified if they are categorical (nd therefore transformed into dummy variables).
`centre`	Individual membership to the clusters.
`time_axis`	Temporal domain.
`dropout_matrix`	Binary matrix indicating in which interval of the time domain an individual failed. For an individual, the sum of the row elements must be equal to 1 (if he/she failed) or 0 (if he/she does not failed). It has dimension equal to (n_individuals, n_intervals).
`e_matrix`	Matrix of dimension (n_individual, n_intervals), where each element contains the evaluation of the temporal integral, performed through the function @param time_int_eval.

Details

This function firstly divides the individuals according to their group/cluster membership, extracting group customized dataset and other variables, and then compute the group log-likelihood function through the function @ll_AdPaik_centre_1D. The produced group log-likelihood value is summed together the other values into a unique result, that corresponds to the overall (and final) log-likelihood value.