On the Fallibility of Principal Components in Research

Tenko Raykov*, George A. Marcoulides, Tenglong Li

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


The measurement error in principal components extracted from a set of fallible measures is discussed and evaluated. It is shown that as long as one or more measures in a given set of observed variables contains error of measurement, so also does any principal component obtained from the set. The error variance in any principal component is shown to be (a) bounded from below by the smallest error variance in a variable from the analyzed set and (b) bounded from above by the largest error variance in a variable from that set. In the case of a unidimensional set of analyzed measures, it is pointed out that the reliability and criterion validity of any principal component are bounded from above by these respective coefficients of the optimal linear combination with maximal reliability and criterion validity (for a criterion unrelated to the error terms in the individual measures). The discussed psychometric features of principal components are illustrated on a numerical data set.

Original languageEnglish
Pages (from-to)165-178
Number of pages14
JournalEducational and Psychological Measurement
Issue number1
Publication statusPublished - 1 Jan 2017
Externally publishedYes


  • criterion validity
  • error variance
  • measurement error
  • principal component
  • principal component analysis
  • reliability
  • validity

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