R: Core likelihood calculation function for the discrete partition version

ML2Inf {missreg}

R Documentation

Core likelihood calculation function for the discrete partition version

Description

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

Usage

ML2Inf(theta, nderivs = 2, ProspModInf, StratModInf, x, y, Aposn, 
       Acounts, Bposn, Bcounts, rvec, Qs, usage = "thetaonly", 
       thetaparts = 0, paruse = "auto", inxStrat, 
       off.set = matrix(0, dim(x)[1], dim(x)[3]), 
       control.inner = mlefn.control.inner(...), ...)

Arguments

`theta`	Starting values for parameters `theta` in the regression model unless `usage` below is `"combined"`, in which case `theta` should contain starting values for the `theta` parameters followed by starting values fo the `rho` or `xi` parameters (which will be stripped off on entry to the function).
`nderivs`	Number of derivatives to be calculated. Either 0 (loglikelihood value only), 1 (also return score vector), or 2 (also return information matrix).
`ProspModInf`	A class of sub-functions called by `ML2Inf` to supply values and their derivatives for the first (A) part of the loglikelihood regarding to the model of interest.
`StratModInf`	A class of sub-functions called by `ML2Inf` to supply values and their derivatives for the third (B) part of the loglikelihood regarding to the `h`-distribution at the first phase.
`x`	See `MEtaProspModInf`.
`y`	See `MEtaProspModInf`.
`Aposn`	A vector specifying the positions of those observations contributed to the A part of the loglikelihood in the data matrix.
`Acounts`	A vector specifying the frequency of each observation (`n_i`) contributed to the A part of the loglikelihood.
`Bposn`	A vector specifying the positions of those observations contributed to the B part of the loglikelihood in the data matrix.
`Bcounts`	A vector specifying the frequency of each observation (`m_j`) contributed to the B part of the loglikelihood.
`rvec`	The `r_k^(s)` in the loglikelihood.
`Qs`	The `Q_k^(s)` in the loglikelihood.
`usage`	Work with and report results for the following three conditions: (1) `"thetaonly"` (profile other parameters); (2) `"combined"` (fit both `theta` and `rho/xi` simultaneously); and (3) `"Qfixed"` (fix other parameters).
`thetaparts`	A vector of length 2 specifying the number of `theta` and `rho/xi` parameters as appropriate; Used only if `usage="combined"`.
`paruse`	The choice of using either `rho` or `xi` parameters as follows: (1) `"rhos"`; (2) `"xis"`; or (3) `"auto"` (function to choose the `rho's` if no more than one `r_k^(s)=0` and the `xi's` otherwise). Any other string is treated as the last option.
`inxStrat`	Optional to enable printing a diagnostic when `ML2Inf` fails and has been called from `MLInf`.
`off.set`	See `MEtaProspModInf`.
`control.inner`	Specify control parameters for inner iterations nested within the `mlefn` function call.
`...`	Further arguments passed to or from related functions.

Details

This is the core function at the distrete partition version to calculate the value, score vector and observed information matrix at theta for the so-called profile loglikelihood l*^(s)(theta,Q^(s)). It is an inner function called by MLInf to supply values of l* and its derivatives within each s-stratum.

See "Description of the missreg Library" for more details.

Value

A list with the following components.

`loglk`	Log-likelihood obtained from the current `theta` values.
`score`	Score vector obtained from the current `theta` values when `nderivs>=1`; `NULL` otherwise.
`inf`	Observed information matrix obainted from the current `theta` values when `nderivs=2`; `NULL` otherwise.
`Qs`	A vector of length K providing values for `Q_k^(s)` either as its entry values or updated from the inner iterative process when `r_k^(s)` is not equal to 0 and `usage="thetaonly"`.

Author(s)

Chris Wild, Yannan Jiang

References

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