lapadj {bqtl}

Approximate marginal posterior for chosen model

Description

lapadj provides the Laplace approximation to the marginal posterior (over coefficients and dispersion parameter) for a given genetical model for a quantitative trait. A by-product is the parameter value corresponding to the maximum posterior or likelihood.

Usage

 lapadj(reg.formula, ana.obj,  
         rparm = NULL,  tol = 1e-10,
	return.hess = FALSE, mode.names = NULL, mode.mat = NULL,
          maxit = 100, nem = 1,setup.only=FALSE,subset=NULL,casewt=NULL,
         start.parm=NULL, ...)

Arguments

reg.formula

A formula, like y~add.X.3+dom.X.3+add.x.45*add.x.72

ana.obj

Seemake.analysis.obj, which returns objects like this

rparm

One of the following:

A scalar that will be used as the ridge parameter for all design terms except for the intercept ridge parameter which is set to zero

A vector who named elements can be matched by the design term names returned in $reg.vec. If no term named "intercept" is provided,

rparm["intercept"] will be set to zero.

A vector with (q-1)*k elements (this works when there are no interactions specified). If names are provided, these will be used for matching.

Positive entries are 'ridge' parameters or variance ratios in a Bayesian prior for the regression coefficients. Larger values imply more shrinkage or a more concentrated prior for the regresion coefficients.

tol

Iteration control parameter

return.hess

Logical, include the Hessian in the output?

mode.names

names to use as dimnames(mode.mat)[[2]]

mode.mat

Not usually set by the user. A matrix which indicates the values of regressor variables corresponding to the allele states. If mode.mat is not given by the user, ana.obj$mode.mat is used.

maxit

Maximum Number of iterations to perform

nem

Number of EM iterations to use in reinitializing the pseudo-Hessian

setup.only

If TRUE, do not run. Return an object that can be use for a direct call to .C

subset

expression to evaluate using ana.obj$data as the environment

casewt

a vector of non-negative weights

start.parm

Vector of starting values for the maximization

...

other objects needed in fitting

Details

The core of this function is a quasi-Newton optimizer due to Minami (1993) that has a computational burden that is only a bit more than the EM algorithm, but features fast convergence. This is used to find the mode of the posterior. Once this is in hand, one can find the Laplace approximation to the marginal likelihood. In addition, some useful quantities are provided that help in estimating the marginal posterior over groups of models.

Value

A list with components to be used in constructing approximations to the marginal posterior or a list that can be used to call the underlying C code directly. In the former case, these are:

adj

The ratio of the laplace approximation to the posterior for the correct likelihood to the laplace approximation to the posterior for the linearized likelihood

logpost

The logarithm of the posterior or likelihood at the mode

parm

the location of the mode

posterior

The laplace approximation of the marginal posterior for the exact likelihood

hk.approx

Laplace approximation to the linearized likelihood

hk.exact

Exact marginal posterior for the linearized likelihood

reg.vec

A vector of the variables used

rparm

Values of ridge parameters used in this problem.

Author(s)

Charles C. Berry [e-mail]

References

Berry C.C.(1998) Computationally Efficient Bayesian QTL Mapping in Experimental Crosses. ASA Proceedings of the Biometrics Section. 164–169.

Minami M. (1993) Variance estimation for simultaneous response growth curve models. Thesis (Ph. D.)–University of California, San Diego, Department of Mathematics.