R: Strata Model Information function for models with M linear predictors.

MEtaStratModInf {missreg}

R Documentation

Strata Model Information function for models with M linear predictors.

Description

A sub-function called by ML2Inf to supply values and its derivatives for the third part of the profile loglikelihood regarding to the h-distribution at the first phase using the discrete partition version.

Usage

MEtaStratModInf(theta, nderivs=2, x, Bcounts, ptildes, stratfn, 
                off.set=0, ...)

Arguments

`theta`	Vector of the parameter values.
`nderivs`	Number of derivatives to be calculated; see `MEtaProspModInf`.
`x`	See `MEtaProspModInf`.
`Bcounts`	An optional vector of weights (`m_j`) to be used in the fitting process.
`ptildes`	A vector of length K (total number of distinct `h`-values observed) providing values for `p_k` within each `s`-stratum.
`stratfn`	A class of sub-functions called by `MEtaStratModInf` to calcualte the values and their derivatives with respect to the linear predictor (`eta's`) of X for `pr(h_k\|x_j;theta)` and `sum_k{p_k*pr(h_k\|x_j;theta)}` within each s-stratum.
`off.set`	See `MEtaProspModInf`.
`...`	Further arguments passed to or from related functions.

Details

This sub-function is used jointly with MEtaProspModInf for regression models with a fixed number of M linear predictors. It calculates the values and their derivatives for the third part of the profile loglikelihood in the form of l*(theta,Q) within each s-stratum

sum_j{m_j^(s)*log{sum_k{p_k^(s)*pr(h_k^(s)|x_j^(s);theta)}}}

with respect to theta through the M linear predictors (m=1,...,M),

eta_{jm}=o_{jm}+x_{j(m)}^T*theta

See "Description of the missreg Library" for all 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 obtained from the current `theta` values when `nderivs=2`; `NULL` otherwise.
`Qstar`	A matrix (J*K) providing values for `pr(h_k\|x_j;theta)` within each s-stratum.
`dQstar`	A 3-dimensional array (JKC) providing the first derivative of `pr(h_k\|x_j;theta)` w.r.t. `theta_c` (c=1,...,C).
`SptQstar`	A vector of length J providing values for `sum_k{p_k*pr(h_k\|x_j;theta)}`.
`dSptQstar`	A matrix (JC) providing the first derivative of `sum_k{p_kpr(h_k\|x_j;theta)}` w.r.t. `theta_c` (c=1,...,C).

Author(s)

Chris Wild, Yannan Jiang

References

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