R: Core likelihood calculation function for the direct approach

ML2directInf {missreg}

R Documentation

Core likelihood calculation function for the direct approach

Description

A sub-function called by MLdirectInf to provide the value, score vector and information matrix at theta for the so-called profile loglikelihood l_P(theta) of the form l(theta, delta) within each s-stratum with stratified two-phase sampled data. It reduces to an unstratified approach when nstrata=1.

Usage

ML2directInf(theta, nderivs = 2, modelfn, hmodelfn, x, y, Aposn, 
             Acounts, Bposn, Bcounts, hvalue, Cmult, delta, 
             off.set = matrix(0, dim(x)[1], dim(x)[3]), inxStrat, 
             control.inner = mlefn.control.inner(...), ...)

Arguments

`theta`	Starting values for parameters `theta` in the regression model.
`nderivs`	Number of derivatives to be calculated. Either 0 (loglikelihood value only), 1 (also return score vector), or 2 (also return information matrix).
`modelfn`	A class of sub-functions called by `ML2directInf` to supply values and their derivatives with respect to the `eta's` (M linear predictors with respect to `theta`) for the model of interest `f(Y\|X;theta)`.
`hmodelfn`	A class of sub-functions called by `ML2directInf` to supply values and their derivatives with respect to the `eta's` for `pr(h_k\|x_j;theta)` under the same class of models.
`x`	A 3-dimensional array (RCM) specifying the covariates values, with R the number of observations, C the length of `theta` and M the number of linear predictors used.
`y`	The response of interest, can be eitehr a vector or matrix.
`Aposn`	A vector specifying the positions of those observations with the set of complete (x, y)-values from s-stratum.
`Acounts`	A vector specifying the frequency of each observation (`n_i`) with the set of complete (x,y)-values from s-stratum.
`Bposn`	A vector specifying the positions of those observations with the x-values observed in s-stratum; `NULL` in prospective sampling.
`Bcounts`	A vector specifying the frequency of each observation (`m_j`) with the x-values observed in s-stratum; `NULL` in prospective sampling.
`hvalue`	The `h_k^(s)` in the loglikelihood.
`Cmult`	The `r_k^(s)` in the loglikelihood.
`delta`	The `delta_j^(s)` in the loglikelihood.
`off.set`	The offset provided in a matrix form (R*M) with R the number of observations and M the number of linear predictors used.
`inxStrat`	See `ML2Inf`.
`control.inner`	Specify control parameters for inner iterations nested within the `mlefn` function call. See `mlefn` for details.
`...`	Further arguments passed to or from related functions.

Details

This is the core function in the direct approach to calculate the value, score vector and observed information matrix at theta for the profile loglikelihood l_P(theta) of the form
l^(s)(theta,delta^(s)) within each s-stratum.

It is an inner function called by MLdirectInf.

Value

A list with the following components.

`loglk`	Log-likelihood value obtained from the current `theta` values.
`score`	Score vector obtained from the current `theta` values when `nderivs>=1`; `NULL` otherwise.
`inf`	Observed information matrix obtained from the current `theta` values when `nderivs=2`; `NULL` otherwise.
`delta`	A vector of length J providing values for `delta_j^(s)` either as its entry values or updated from the inner iterative process when `Bposn` is not `NULL`.

Author(s)

Chris Wild, Yannan Jiang

References

Description of the missreg Library, Wild and Jiang, 2007.