LMN-package: Inference for Linear Models with Nuisance Parameters.

In mlysy/LMN: Inference for Linear Models with Nuisance Parameters

Inference for Linear Models with Nuisance Parameters.

Description

Efficient profile likelihood and marginal posteriors when nuisance parameters are those of linear regression models.

Details

Consider a model p(Y | B, Σ, θ) of the form

Y ~ Matrix-Normal(X(θ) B, V(θ), Σ),

where Y_(n x q) is the response matrix, X(θ)_(n x p) is a covariate matrix which depends on θ, B_(p x q) is the coefficient matrix, V(θ)_(n x n) and Σ_(q x q) are the between-row and between-column variance matrices, and (suppressing the dependence on θ) the Matrix-Normal distribution is defined by the multivariate normal distribution vec(Y) ~ N( vec(X B), Σ %x% V ), where vec(Y) is a vector of length nq stacking the columns of of Y, and Σ %x% V is the Kronecker product.

The model above is referred to as a Linear Model with Nuisance parameters (LMN) (B,Σ), with parameters of interest θ. That is, the LMN package provides tools to efficiently conduct inference on θ first, and subsequently on (B,Σ), by Frequentist profile likelihood or Bayesian marginal inference with a Matrix-Normal Inverse-Wishart (MNIW) conjugate prior on (B,Σ).

Author(s)

Maintainer: Martin Lysy [e-mail]

Authors:

• Bryan Yates

See Also

Useful links:

• https://github.com/mlysy/LMN/

• Report bugs at https://github.com/mlysy/LMN/issues

mlysy/LMN documentation built on March 25, 2022, 11:12 a.m.