SolveHMME: Solve Henderson's Mixed Model Equation.
In HMMEsolver: A Fast Solver for Henderson Mixed Model Equation via Row Operations

Description Usage Arguments Value References Examples

Consider a linear mixed model with normal random effects,

Y_{ij} = X_{ij}^Tβ + v_i + ε_{ij}

where i=1,…,n,\quad j=1,…,m, or it can be equivalently expressed using matrix notation,

Y = Xβ + Zv + ε

where Y\in \mathrm{R}^{nm} is a known vector of observations, X \in \mathrm{R}^{nm\times p} and Z \in \mathrm{R}^{nm\times n} design matrices for β and v respectively, β \in \mathrm{R}^p and v\in \mathrm{R}^n unknown vectors of fixed effects and random effects where v_i \sim N(0,λ_i), and ε \in \mathrm{R}^{nm} an unknown vector random errors independent of random effects. Note that Z does not need to be provided by a user since it is automatically created accordingly to the problem specification.

1	SolveHMME(X, Y, Mu, Lambda)

`X`	an (nm\times p) design matrix for β.
`Y`	a length-nm vector of observations.
`Mu`	a length-nm vector of initial values for μ_i = E(Y_i).
`Lambda`	a length-n vector of initial values for λ, variance of v_i \sim N(0,λ_i)

a named list containing

beta: a length-p vector of BLUE \hat{beta}.
v: a length-n vector of BLUP \hat{v}.
leverage: a length-(mn+n) vector of leverages.

\insertRef

henderson_estimation_1959HMMEsolver

\insertRef

robinson_that_1991HMMEsolver

\insertRef

mclean_unified_1991HMMEsolver

\insertRef

kim_fast_2017HMMEsolver

## small setting for data generation
n = 100; m = 2; p = 2
nm = n*m;   nmp = n*m*p

## generate artifical data
X = matrix(rnorm(nmp, 2,1), nm,p) # design matrix
Y = rnorm(nm, 2,1)                # observation

Mu = rep(1, times=nm)
Lambda = rep(1, times=n)

## solve
ans = SolveHMME(X, Y, Mu, Lambda)