19-07-2012, 03:01 PM
Principal Component Analysis: Additional Topics
PrincipalComponentAnalysis_Outliers_Validation_Reliability.ppt (Size: 1.15 MB / Downloads: 239)
Split Sample Validation
To test the generalizability of findings from a principal component analysis, we could conduct a second research study to see if our findings are verified.
A less costly alternative is to split the sample randomly into two halves, do the principal component analysis on each half and compare the results.
If the communalities and the factor loadings are the same on the analysis on each half and the full data set, we have evidence that the findings are generalizable and valid because, in effect, the two analyses represent a study and a replication.
Misleading Results to Watch Out For
When we examine the communalities and factor loadings, we are matching up overall patterns, not exact results: the communalities should all be greater than 0.50 and the pattern of the factor loadings should be the same.
Sometimes the variables will switch their components (variables loading on the first component now load on the second and vice versa), but this does not invalidate our findings.
Sometimes, all of the signs of the factor loadings will reverse themselves (the plus's become minus's and the minus's become plus's), but this does not invalidate our findings because we interpret the size, not the sign of the loadings.
Reliability of Summated Scales
One of the common uses of factor analysis is the formation of summated scales, where we add the scores on all the variables loading on a component to create the score for the component.
To verify that the variables for a component are measuring similar entities that are legitimate to add together, we compute Chronbach's alpha.
If Chronbach's alpha is 0.70 or greater (0.60 or greater for exploratory research), we have support on the interval consistency of the items justifying their use in a summated scale.
Level of measurement requirement
Highest academic degree" [degree], "father's highest academic degree" [padeg], "mother's highest academic degree" [madeg], "spouse's highest academic degree" [spdeg], "general happiness" [happy], "happiness of marriage" [hapmar], "condition of health" [health], and "attitude toward life" [life] are ordinal level variables. If we follow the convention of treating ordinal level variables as metric variables, the level of measurement requirement for principal component analysis is satisfied. Since some data analysts do not agree with this convention, a note of caution should be included in our interpretation.