Description Usage Arguments Details Value Author(s) References Examples
Two level Normal independent sampling estimation
1 2 3 |
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 |
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 |
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.
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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
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