tlnise {tlnise}R Documentation

TLNise

Description

Two level Normal independent sampling estimation

Usage

tlnise(Y, V, w = NA, V0 = NA, prior = NA, N = 1000, seed = 10,
       Tol = 1e-06, maxiter = 1000, intercept = TRUE, labelY = NA,
       labelYj = NA, labelw = NA, digits = 4, brief = 1, prnt = TRUE)

initTLNise()

Arguments

Y Jxp (or pxJ) matrix of p-dimensional Normal outcomes
V pxpxJ array of pxp Level-1 covariances (assumed known)
w Jxq (or qxJ) covariate matrix (adds column of 1's if not included and intercept = TRUE)
V0 "typical" Vj (default is average of Vj's)
prior prior parameter (see Details)
N number of Constrained Wishart draws for inference
seed seed for random number generator
Tol tolerance for determining modal convergence
maxiter maximum number of EM iterations for finding mode
intercept if TRUE, an intercept term is included in the regression
labelY optional names vector for the J observations
labelYj optional names vector for the p elements of Yj
labelw optional names vector for covariates
digits number of significant digits for reporting results
brief level of output, from 0 (minimum) to 2 (maximum)
prnt controls printing during execution

Details

The prior is p(B_0) = |B_0|^{(prior - p - 1)/2}.

Note that for the prior distribution, prior = -(p+1) corresponds to a uniform on level-2 covariance matrix A (default), prior = 0 is the Jeffreys' prior, and prior = (p+1) is the uniform prior on shrinkage matrix B0.

Value

tlnise returns a list, the precise contents of which depends on the value of the brief argument. Setting brief = 2 returns the maximum amount of information. Setting brief = 1 or brief = 0 returns a subset of that information.
If brief = 2, the a list with the following components is returned:

gamma matrix of posterior mean and SD estimates of Gamma, and thei ratios
theta pxJ matrix of posterior mean estimates for thetaj's
SDtheta pxJ matrix of posterior SD estimates for thetaj's
A pxp estimated posterior mean of variance matrix A
rtA p-vector of between group SD estimates
Dgamma rxr estimated posterior covariance matrix for Gamma
Vtheta pxpxJ array of estimated covariances for thetaj's
B0 pxpxN array of simulated B0 values
lr N-vector of log density ratios for each B0 value
lf N-vector of log f(B0|Y) evaluated at each B0
lf0 N-vector of log f0(B0|Y) evaluated at each B0 (f0 is the CWish envelope density for f)
df degrees of freedom for f0
Sigma scale matrix for f0
nvec number of matrices begun, diagonal and off-diagonal elements simulated to get N CWish matrices
nrej number of rejections that occurred at each step 1,..,p

Note

initTLNise needs to be called to initialize the random number generator used by tlnise. Once initTLNise is called, the seed argument to tlnise to be used (for reproducibility of results).

Author(s)

S-PLUS original by Philip Everson; R port by Roger D. Peng

References

Everson PJ, Morris CN (2000). “Inference for Multivariate Normal Hierarchical Models,” Journal of the Royal Statistical Society, Series B, 62 (6) 399–412.

Examples

x <- rnorm(10)  ## Second level
y <- rnorm(10, x)  ## First level means

initTLNise()
out <- tlnise(Y = y, V = rep(1, 10), w = rep(1, 10), seed = 1234)

[Package tlnise version 1.0 Index]