expects as its input a matrix of correlations or covariances. It is included here to allow comparison with the dimensions identified by non-metric MDS procedures for the same data. An error is reported if the input matrix does not consist of correlations or covariances, i.e the product of one or more pairs of symmetric off-diagonal terms is greater than the product of the corresponding diagonal terms.
DATA:
2-way, 1-mode scalar products
TRANSFORM:
Linear
MODEL:
SCALAR PRODUCTS
Principal
components is a mathematical technique, with no underlying statistical model,
which is frequently used to identify a limited number of linear combinations of
the original variables that can be used to summarise the data, losing as little
information as possible. Technically, it simply produces an orthogonal rotation
of the input matrix to its principal axes, or eigenvectors. By default,
PRINCOMP will list all n eigenvalues (latent roots) and principal
components (eigenvectors) of a matrix of n variables.
In many
sets of multivariate data the variables will be measured in different units and
are standardised before analysis. This is equivalent to extracting the principal
components as eigenvectors of the matrix of correlations, rather than of the
covariance matrix. The eigenvalues and principal components of these matrices
are not generally the same, and choosing to analyse correlations is equivalent
to deciding to consider the variables to be equally important.
PRINCOMP automatically
lists all principal components of the input matrix. The size of the matrix is
given by N OF STIMULI and the matrix is read by the READ MATRIX
command. The format of the input matrix is given by the parameter DATA
TYPE in the PARAMETERS command.
PARAMETER
Keyword Default Description
INPUT
COMMANDS
Keyword
Function
N OF
STIMULI [number]
Number of stimuli in the analysis
LABELS [followed
by a series Optionally identify the
stimuli,
of
labels (<= 65 chars) followed by the subjects, as
each
on a separate required. Labels
should identify
line] all
variables, without omission.
DATA TYPE
1 1: Lower triangular matrix without
diagonal
2:
Lower triangular matrix with
diagonal
3:
Upper triangular matrix without
diagonal
4:
Upper triangular matrix with
diagonal
5:
Full symmetric matrix.
READ MATRIX
Start reading data for run
PLOT options (to
main output
file)
Option Description
COMPONENTS Plots
the principal
components.
If
a parameter is added, this specifies the
number
of
normalized principal components to be
plotted.
(Plotting
all components is liable to generate
a
rather
large output
file.)
ROOTS Produces
a 'scree plot' of the latent
roots
against
the principal components.
NOTES
1. The
READ MATRIX command is obligatory in PRINCOMP.
2. There are no
PRINT options as such in PRINCOMP.
By
default, the eigenvalues (or latent roots) of the input matrix
are
listed in descending order, together with the
corresponding
eigenvectors or principal components,
and the proportions of the
total variance accounted
for by each.
3. LABELS Allows you to add optional labels (following
the command
and then on successive lines) to identify
variables.
PROGRAM
LIMITS See also
Maximum no.
of stimuli = 300
Maximum no. of
dimensions = 8