Principal Component Analysis
 As
with Factor Analysis, Principal Component Analysis is a technique that attempts
to reduce complex data sets consisting of many different variables to a smaller
set of new variables that still manage to describe much of the variation in the
original data. These new variables, called Principal Components, are chosen to
be independent (i.e. the new variables are not correlated whereas the original,
untransformed variables may have been correlated) and to maximise the variance
found in the original data set. The more significant PCAs are selected based on
their eigenvalues, and hopefully far fewer PCA variables (e.g. one or two) are
required than there were original variables. These fewer Principal Components
can then be further analysed by Regression Analysis or ANOVA/MANOVA. Thus, the
role of Principal Component Analysis has been to reduce a large number of
variables into fewer, simpler ones. Principal Component Analysis is an
alternative to Factor Analysis (both seek to find a simpler structure for a set
of variables) but Principal Components are linear combinations of variables
whereas variables are linear combinations of Factors.
statistiXL provides a number of options for Principal Component Analysis. Either
the correlation or covariance matrix between variables can be selected as the
basis for analysis. All Principal Components can be extracted or a subset of
these based on limits such as the number to extract, the percent of variance to
explain or the value of an eigenvalue. Screeplots can be produced to help in
the visual determination of the appropriate number of Principal Components to
extract.
  Results
are presented in tabular and graphical form. Descriptive statistics and the
correlation or covariance matrix are displayed, if these options were selected.
The eigenvalues are then tabulated along with the percent of variance and
cumulative percent of total variance evident in the original dataset that each
of the extracted Principal Components explains. The Component Loadings are then
listed followed by the Principal Component score coefficients (eigenvectors).
The case-wise PCA scores for each extracted component are listed, if this
option was selected. Optional graphical output includes a Scree Plot and
Bivariate Scatterplots of the various pair-wise combinations of extracted
Principal Components.
The help file of statistiXL provides an introduction to Principal Component
Analysis, and gives an example of Principal Component Analysis.
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