Keywords - Function groups - @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Library: stats
See also: draftman factor FluryStepUp pca CPCprop CPC CPCFGalg Jacobirot

Quantlet: CPCp
Description: CPCp computes the common eigenmatrix, eigenvalues, corresponding standard errors, and estimated population covariance matrices from sample covariances of k groups assuming q common eigenvectors in B; CPCp uses maximum likelihood

Reference(s):

Usage: {Bplus, lambdaplus, lambdaerror, psi}=CPCp(A,N,q,{Binitial})
Input:
A p x p x k array of k covariances
N k x 1 vector of weights, usually number of observations in group k
q scalar, determining the number of common components in B
Binitial p x p matrix, optional inital approximation to B, usually obtained from the CPC model (default). This parameter is useful when estimating iteratively several CPCp models from the same data.
Output:
Bplus p x p x k array of orthogonal transformation matrix with q common and p-q specific components
lambdaplus p x k matrix of p eigenvalues of each group k
lambdaerror p x k matrix of p standard errors of eigenvalues of each group k
psi p x p x k array of k estimated population covariance matrices

Note:

Example:
library("stats")
covar1=#(112.01, 106.64, 52.97)~#(106.64,108.13,54.75)~#(52.97,54.75,33.86)
covar2=#(86.08,81.66,40.24)~#(81.66,85.54,42.08)~#(40.24,42.08,26.66)
covar3=#(65.4,60.23,24.69)~#(60.23,62.27,23.47)~#(24.69,23.47,16.33)
covar4=#(88.66,79.11,41.32)~#(79.11,80.57,38.81)~#(41.32,38.81,23.97)
covar=reshape(covar1~covar2~covar3~covar4,#(3,3,4))
;Sample size
n=#(173,141,88,76)
q=1
ZZ=CPCp(covar,n,q)
ZZ

Result:
Contents of ZZ.Bplus

[,,1,1,1,1,1,1]
[1,]  0.67356  0.51816  0.52709
[2,]  0.66073 -0.10248  -0.7436
[3,]  0.33129 -0.84912  0.41139
[,,2,1,1,1,1,1]
[1,]  0.67356    0.552  0.49154
[2,]  0.66073  -0.1516 -0.73516
[3,]  0.33129 -0.81995  0.46683
[,,3,1,1,1,1,1]
[1,]  0.67356  0.15736  0.72218
[2,]  0.66073  0.30975 -0.68374
[3,]  0.33129 -0.93771 -0.10467
[,,4,1,1,1,1,1]
[1,]  0.67356 -0.36931 -0.64025
[2,]  0.66073 -0.087404  0.74552
[3,]  0.33129  0.92519 -0.18514

Contents of ZZ.lambdaplus

[1,]   244.27   188.39   133.55   183.87
[2,]    7.214   6.4869   6.9039   3.8194
[3,]   2.5201   3.4056   3.5447   5.5068

Contents of ZZ.lambdaerror

[1,]    26.34   22.517   20.249   30.026
[2,]   0.7779  0.77533   1.0468  0.62371
[3,]  0.27175  0.40705  0.53745  0.89925

Contents of ZZ.psi

[,,1,1,1,1,1,1]
[1,]   113.46   107.34   51.879
[2,]   107.34   108.11   53.324
[3,]   51.879   53.324   32.436
[,,2,1,1,1,1,1]
[1,]   88.269   82.067   39.883
[2,]   82.067   84.232   40.874
[3,]   39.883   40.874   25.779
[,,3,1,1,1,1,1]
[1,]   62.611   58.022   28.514
[2,]   58.022   60.623   27.481
[3,]   28.514   27.481   20.767
[,,4,1,1,1,1,1]
[1,]     86.2   79.326   40.378
[2,]   79.326   83.362   39.179
[3,]   40.378   39.179   23.638



Author: M. R. Fengler, W. Haerdle, 20010721 license MD*Tech
(C) MD*TECH Method and Data Technologies, 05.02.2006