On the Unlikely Case of an Error-Free Principal Component From a Set of Fallible Measures

Tenko Raykov*, George A. Marcoulides, Tenglong Li

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


This note extends the results in the 2016 article by Raykov, Marcoulides, and Li to the case of correlated errors in a set of observed measures subjected to principal component analysis. It is shown that when at least two measures are fallible, the probability is zero for any principal component—and in particular for the first principal component—to be error-free. In conjunction with the findings in Raykov et al., it is concluded that in practice no principal component can be perfectly reliable for a set of observed variables that are not all free of measurement error, whether or not their error terms correlate, and hence no principal component can practically be error-free.

Original languageEnglish
Pages (from-to)708-712
Number of pages5
JournalEducational and Psychological Measurement
Issue number4
Publication statusPublished - 1 Aug 2018
Externally publishedYes


  • error variance
  • measurement error
  • observed variable
  • principal component
  • principal component analysis
  • reliability
  • variance

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