estimateMVbeta: Zero mean multivariate t-dist. with covariate dependent...

Description Usage Arguments Details Value Author(s) References See Also

View source: R/PLWandLMW.R

Description

Estimate the parameters m and v of the multivariate t-distribution with zero expectation, where v is modeled as smooth function of a covariate. The covariance matrix Sigma is assumed to be known.

Usage

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estimateMVbeta(y, x, Sigma, maxIter = 200, epsilon = 1e-06,
    verbose = FALSE, nknots = 10, nOut = 2000, nIn = 4000,
    iterInit = 3, br = NULL)

Arguments

y

Data matrix

x

Covariate vector

Sigma

Covariance matrix

maxIter

Maximum number of iterations

epsilon

Convergence criterion

verbose

Print computation info or not

nknots

Number of knots of spline for v

nOut

Parameter for calculating knots, see getKnots

nIn

Parameter for calculating knots, see getKnots

iterInit

Number of iteration in when initiating Sigma

br

Knots, overrides nknots, n.out and n.in

Details

The multivariate t-distribution is parametrized as:

y|c ~ N(mu,c*Sigma)

c ~ InvGamma(m/2,m*v/2)

where v is function of the covariate x: v(x) and N denotes a multivariate normal distribution, Sigma is a covariance matrix and InvGamma(a,b) is the inverse-gamma distribution with density function

f(x)=b^a exp{-b/x} x^{-a-1} /Gamma(a)

A cubic spline is used to parameterize the smooth function v(x)

v(x)=exp{H(x)^T beta}

where H:R->R^(2p-1) is a set B-spline basis functions for a given set of p interior spline-knots, see chapter 5 of Hastie (2001). In this application mu equals zero, and m is the degrees of freedom.

Value

Sigma

The input covariance matrix for y

m

Estimated shape parameter for inverse-gamma prior for gene variances

v

Estimated scale parameter curve for inverse-gamma prior for gene variances

converged

TRUE if the EM algorithms converged

iter

Number of iterations

modS2

Moderated estimator of gene-specific variances

histLogS2

Histogram of log(s2) where s2 is the ordinary variance estimator

fittedDensityLogS2

The fitted density for log(s2)

logs2

Variance estimators, logged with base 2.

beta

Estimated parameter vector beta of spline for v(x)

knots

The knots used in spline for v(x)

x

The input vector covariate vector x

Author(s)

Magnus Astrand

References

Hastie, T., Tibshirani, R., and Friedman, J. (2001). The Elements of Statistical Learning, volume 1. Springer, first edition.

Kristiansson, E., Sjogren, A., Rudemo, M., Nerman, O. (2005). Weighted Analysis of Paired Microarray Experiments. Statistical Applications in Genetics and Molecular Biology 4(1)

Astrand, M. et al. (2007a). Improved covariance matrix estimators for weighted analysis of microarray data. Journal of Computational Biology, Accepted.

Astrand, M. et al. (2007b). Empirical Bayes models for multiple-probe type arrays at the probe level. Bioinformatics, Submitted 1 October 2007.

See Also

plw, lmw, estimateSigmaMVbeta


plw documentation built on April 28, 2020, 6:38 p.m.