Principal Components Analysis

Using Principal Component Analysis in XLMiner™:

In XLMiner™, select Data Reduction and Exploration--> Principal Components ..., and specify the desired worksheet or data range to be processed. Move the variables to be used in the analysis from the Variables box to the Selected variables box, using the transfer (>) button.

Click Next, and the following dialog box comes up.

There are two options for specifying the number of principal components:

Fixed #components: You can specify a fixed number here.

Smallest #components explaining : This option lets you specify a percentage, and XLMiner™ will calculate the minimum number of principal components required to account for that percentage of variance.

Method : To compute Principal Components the data is matrix multiplied by a transformation matrix. This option lets you specify the choice of calculating this transformation matrix.

Use Covariance matrix : The covariance matrix is a square, symmetric matrix of size (number of variables by number of variables). The diagonal elements are variances and the off-diagonals are covariances. The eigenvalues and eigenvectors of the covariance matrix are computed and the transformation matrix is defined as the transpose of this eigenvector matrix.
Use Correlation matrix : An alternative method is to derive the transformation matrix on the eigenvectors of the correlation matrix instead of the covariance matrix. The correlation matrix is equivalent to a covariance matrix for the data where each variable has been standardized to zero mean and unit variance. This method tends to equalize the influence of each variable, inflating the influence of variables with relatively small variance and reducing the influence of variables with high variance.

Click Next, and the following dialog box comes up, where you specify the output to be shown:

Show standardized principal components: This option causes each principal component to be divided by the square root of its variance.

Show principal components score: This option results in the display of a matrix in which the columns are the principal components, the rows are the individual data records, and the value in each cell is the calculated score for that record on the relevant principal component.