tlnise: TLNise
In tlnise: Two-Level Normal Independent Sampling Estimation

Description Usage Arguments Details Value Author(s) References Examples

Two level Normal independent sampling estimation

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

`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 the 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

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.

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

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

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

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

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

Two-level normal independent sampling estimation (version 1.1)
[1] ******** Prior Parameter = -2

[1] ******** Locating Posterior Mode ************ 

[1] Converged in 26 EM iterations.
[1] Posterior mode of B0:

       [,1]
[1,] 0.2368

[1] lf(modeB0) = -7.253 ; lf0(modeB0) = -6.101 ; adj = 1.151

[1] ******** Drawing Constrained Wisharts ******** 


[1] CWish acceptance rate = 1000 / 1000 = 1

[1] ******** Processing Draws ************** 

[1] Average scaled importance weight = 1

[1] Posterior mean estimate of A:
     [,1]
[1,]  3.3

[1] Between-group SD estimate:
      [,1]
[1,] 1.817