I used to use SAS software, But recently I got acquainted with Statgraph 18 software. I think that's better. Especially in terms of drawing diagrams. What's your preference?
I routinely use Minitab 18 statistical package for PCA. It is convenient, powerful, makes all graphs, and based on Graphical User Interface dialog box- no any coding is needed.
Principal Components Analysis is accessed using
Stat > Multivariate > Principal Components. Use principal component analysis to help in understanding the underlying data structure and/or form a smaller number of uncorrelated variables (for example, to avoid multicollinearity in regression). An overview of principal component analysis can be found in most books on multivariate analysis.
Dialog box items are the following:
Variables: Choose the columns containing the variables to be included in the analysis. Number of components to compute: Enter the number of principal components to be extracted. If you do not specify the number of components and there are p variables selected, then p principal components will be extracted. If p is large, you may want just the first few. Type of Matrix Correlation: Choose to calculate the principal components using the correlation matrix. Use the correlation matrix if it makes sense to standardize variables (the usual choice when variables are measured by different scales). Covariance: Choose to calculate the principal components using the covariance matrix. Use the covariance matrix if you do not wish to standardize variables.
This is an example with original 32 data variables described in detail in section 5.1 of the book-see attached.
In this example only 9 principal components (9 linear combinations of the original 32 variables) are required to account for all original variables. Only 5 principal components are enough to approximate 94% of the original data. This indicates that a lot of variables in the original data matrix are highly correlated and contain no new information; most of them form a so-called information noise that hampers extracting meaningful information for contributing factors.
The plots generated in Minitab are attached: (i) Eigenvalue vs. component number and (ii) loading plot for PC1 vs PC2 for 32 variables (age groups, income groups, occupation groups, etc)