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ERIC Number: EJ1125342
Record Type: Journal
Publication Date: 2017-Jan
Pages: 14
Abstractor: As Provided
ISSN: ISSN-0013-1644
On the Fallibility of Principal Components in Research
Raykov, Tenko; Marcoulides, George A.; Li, Tenglong
Educational and Psychological Measurement, v77 n1 p165-178 Jan 2017
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.
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Publication Type: Journal Articles; Reports - Evaluative
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A