Principal Components Analysis with SPSS. Karl L. Wuensch Dept of Psychology East Carolina University. When to Use PCA. You have a set of p continuous variables. You want to repackage their variance into m components. You will usually want m to be < p , but not always.
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
Karl L. Wuensch
Dept of Psychology
East Carolina University
Discriminant function analysis.
Problem with multicollinearity.
Used PCA to extract eight orthogonal components.
Predicted recommended verdict from these 8 components.
Transformed results back to the original scales.
Analyze, Data Reduction, Factor.
Scoot beer variables into box.
Click OK, and SPSS completes the Principal Components Analysis.
cost size alcohol reputat color aroma taste
cost 1.00 .832 .767 -.406 .018 -.046 -.064
size .832 1.00 .904 -.392 .179 .098 .026
alcohol .767 .904 1.00 -.463 .072 .044 .012
reputat -.406 -.392 -.463 1.00 -.372 -.443 -.443
color .018 .179 .072 -.372 1.00 .909 .903
aroma -.046 .098 .044 -.443 .909 1.00 .870
taste -.064 .026 .012 -.443 .903 .870 1.00
a. Measures of Sampling Adequacy (MSA) on main diagonal. Off diagonal are partial correlations x -1.
Scree is rubble at base of cliff.
For our beer data,
Big drop in eigenvalue between component 2 and component 3.
Components 3-7 are scree.
Try a 2 component solution.
Should also look at solution with one fewer and with one more component.
For the eigenvalues from the random sets, find the 95th percentile for each component.
Velicer's Average Squared Correlations
The smallest average squared correlation is
The number of components is 2
Second component is more interesting, economy versus quality.
The number of degrees by which I rotate the axes is the angle PSI. For these data, rotating the axes -40.63 degrees has the desired effect.
Component 2 = Economy (or cheap drunk) versus reputation.
But rotation splits the factor, producing an imaginary second factor and corrupting the first.
Can avoid this problem by including a garbage variable that will be removed prior to the final solution.
If SSL = 1, the component has extracted one variable’s worth of variance.
If only one variable loads well on a component, the component is not well defined.
If only two load well, it may be reliable, if the two variables are highly correlated with one another but not with other variables.