bqtl (version 1.0-7)

lapadj: 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, loc.right, marker.distances, state.matrix,
marker.names=dimnames(state.matrix)[[2]], rparm=NULL, casewt=NULL,
tol=9.9e-09, return.hess=F, mode.names=NULL, mode.mat=NULL,
nc = 1), method="BC1", maxit=100, nem=1, start.parm=NULL, ...)

Arguments

reg.formula

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

loc.right

Seemake.analysis.obj, which returns objects like this. It is a matrix of pointers to the next marker with a known state on the current chromosome (if any).

marker.distances

Distances between the markers in the 'lambda' metric. -log(lambda)/2 is the Haldane map distance. Linkage groups are separated by values of 0.0.

state.matrix

Seemake.analysis.obj, which returns objects like this. An n by k by q array. q is 2 for method="BC1" and 3 for method="F2". Each element encodes the probability of the allele state con

marker.names

The names by which the markers are known.

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

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.

method

Currently, "BC1", "F2", "RI.self" and "RI.sib" are recognized.

maxit

Maximum Number of iterations to perform

nem

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

start.parm

Vector of starting values for the maximization

...

other objects needed in fitting

Value

• A list with components to be used in constructing approximations to the marginal posterior. 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.

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.

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.