rcormat: Randomly Generate Low-Rank Correlation Matrix

In cds: Constrained Dual Scaling for Detecting Response Styles

Description

Generate a correlation matrix as R = LL' where the rows of L are of length 1, L is of rank r and the matrix L is sparse (depending on sparse.prop. The loadings in L are sampled from a standard normal distribution, after which sparse.prop is used to set a randomly chosen number of loadings in each row equal to zero. To ensure that a correlation matrix results, the rows are normalized.

Usage

rcormat(m, r = 3L, sparse.prop = 0.5)

Arguments

m	integer; the number of variables.
r	integer; the required rank.
sparse.prop	the proportion of zeros in the rows of the matrix.

Value

A list with the following components:

R	The sampled correlation matrix
L	The loading matrix

Examples

R <- rcormat(m = 10)$R
eigen(R)

Example output

Loading required package: parallel
eigen() decomposition
$values
 [1]  4.910931e+00  3.620887e+00  1.468182e+00  1.988983e-16  1.569538e-16
 [6]  5.550830e-17  1.420566e-17  9.510624e-18 -6.189947e-16 -8.237576e-16

$vectors
             [,1]        [,2]        [,3]        [,4]         [,5]        [,6]
 [1,]  0.43315820 -0.14363209 -0.05142073  0.00000000  0.000000000  0.00000000
 [2,] -0.43266519  0.14676419  0.04276383  0.08538672  0.006620512 -0.11536890
 [3,] -0.38465009 -0.27441051 -0.02249575  0.29783823  0.366400655 -0.03835341
 [4,] -0.08174528  0.44739117 -0.40635371 -0.37681123  0.448485410  0.47167230
 [5,] -0.01531906  0.05638251 -0.82005437  0.45414466 -0.226616375 -0.21240230
 [6,]  0.35661127 -0.31957733 -0.06213944  0.16391617  0.722740298 -0.17093473
 [7,] -0.43315820  0.14363209  0.05142073  0.09812825  0.254692307 -0.10066344
 [8,] -0.35189784 -0.32558531  0.07397429 -0.14422450 -0.007553939 -0.15780107
 [9,] -0.12611803 -0.44503842 -0.37343003 -0.67832344 -0.068164542 -0.23459528
[10,] -0.12556544 -0.50236071 -0.07733698  0.19582228 -0.145902049  0.77352544
             [,7]        [,8]        [,9]       [,10]
 [1,]  0.68803580  0.00000000  0.00000000 -0.56187761
 [2,] -0.34659700 -0.01221666 -0.09734081 -0.79939583
 [3,]  0.20268600  0.25176015  0.66841195  0.02386959
 [4,]  0.08530931  0.22886940 -0.03871909 -0.03573288
 [5,]  0.01074149  0.04235402 -0.12501793  0.06197864
 [6,] -0.32216135 -0.08409800 -0.27658529 -0.03220031
 [7,]  0.42723308 -0.65537308 -0.26566776  0.14781040
 [8,]  0.23944616  0.57485377 -0.56697433  0.09838580
 [9,] -0.08589619 -0.28178778  0.19243608 -0.05446893
[10,] -0.08351003 -0.18932764 -0.14509053 -0.06356499

cds documentation built on May 2, 2019, 5:54 a.m.