procotWeW {lazy.procrustes} R Documentation

## Weighted Expanded Orthogonal Procrustes Rotation The Ultimate Model

### Description

Weighted Expanded Orthogonal Procrustes Rotation
The Ultimate Model

### Usage

```procotWeW(A, C, V, estm = 0, estT = 1, estW = 0, estW2 = 0, W = NULL,
T = NULL, m = NULL, W2 = NULL, maxiter = 200, eps = 1e-06,
maxiter2 = 20, eps2 = 1e-06, print = 2)
```

### Arguments

 `A` The input matrix to be rotated `C` The target matrix `V` The weight matrix (known) `estm` = 1 to estimate m `estT` = 0 to avoid estimation of T `estW` = 1 to estimate scalar W = 2 to estimate diagonal W matrix `estW2` = 1 to estimate diagonal W2 matrix `W` Initial value of W or NULL `T` Initial value of T or NULL `m` Initial value of m or NULL `W2` Initial value of W2 or NULL `maxiter` max # of iterations `eps` convergence criterion for rmse `maxiter2` max # of iterations for procotWKS `eps2` convergence criterion for procotWKS `print` = 1 to print result

### Details

This program finds those A, m, W, W2 and orthonormal T which minimize
RSS = tr( ( C - Chat ) V ( C - Chat )' )
where Chat = A %*% W %*% T %*% W2 + matrix(1,nv) %*% t(m), W and W2 are diagonal matrices, T is an orthonormal rotation matrix,
m is the column mean vector.

Note that when estW=0, estW2=0 and estm=0, and the target matrix does not have missing elements,
this is equivalent to the usual orthogonal Procrustes rotation.

### Value

A list of:
B=A %*% W %*% T + matrix(1,nv,1)%*%t(m), T, m, W, W2 , Cm the updated target matrix, rmse=sqrt(RSS)

### Examples

``` seed <- 1701; n <- 20; nr <- 2; pmiss <- 0; errstd <- 0.05
set.seed(seed)
resg <- gendataWmm( 1, n, nr, genm=1, genW=2, genW2=1, genV=1
, pmiss=pmiss, errstd=errstd )
A <- resg\$A; V <- resg\$V
C <- resg\$C; Tg <- resg\$T; mg <- resg\$m; Wg <- resg\$W; W2g <- resg\$W2
res <- procotWeW( A, C, V, estm=1, estW=2, estW2=1, print=1 )
T <- res\$T; m <- res\$m; W <- res\$W; W2 <- res\$W2
Print( Tg-T, mg-m, fmt="7.3" )
Print( Wg-W, W2g-W2, fmt="7.3" )

```

[Package lazy.procrustes version 0.1.3 Index]