Parallel analysis, also known as Horn's parallel analysis, is a statistical method used to determine the number of components to keep in a principal component analysis or factors to keep in an

exploratory factor analysis In multivariate statistics, exploratory factor analysis (EFA) is a statistical method used to uncover the underlying structure of a relatively large set of variables. EFA is a technique within factor analysis whose overarching goal is to identify ...

. It is named after psychologist

John L. Horn John Leonard Horn (September 7, 1928 – August 18, 2006) was a scholar, cognitive psychologist and a pioneer in developing theories of multiple intelligence. The structure of mental abilities For his PhD research at the University of Illinois, ...

, who created the method, publishing it in the journal ''

Psychometrika ''Psychometrika'' is the official journal of the Psychometric Society, a professional body devoted to psychometrics and quantitative psychology. The journal covers quantitative methods for measurement and evaluation of human behavior, including ...

'' in 1965. The method compares the eigenvalues generated from the data matrix to the eigenvalues generated from a Monte-Carlo simulated matrix created from random data of the same size.

Evaluation and comparison with alternatives

Parallel analysis is regarded as one of the more accurate methods for determining the number of factors or components to retain. Since its original publication, multiple variations of parallel analysis have been proposed. Other methods of determining the number of factors or components to retain in an analysis include the scree plot, Kaiser rule, or Velicer's MAP test.

Anton Formann Anton K. Formann (August 27, 1949, Vienna, Austria – July 12, 2010, Vienna) was an Austrian research psychologist, statistician, and psychometrician. He is renowned for his contributions to item response theory (Rasch models), latent class a ...

provided both theoretical and empirical evidence that parallel analysis's application might not be appropriate in many cases since its performance is influenced by

sample size Sample size determination is the act of choosing the number of observations or replicates to include in a statistical sample. The sample size is an important feature of any empirical study in which the goal is to make inferences about a populatio ...

, item discrimination, and type of

correlation coefficient A correlation coefficient is a numerical measure of some type of correlation, meaning a statistical relationship between two variables. The variables may be two columns of a given data set of observations, often called a sample, or two components ...

Implementation

Parallel analysis has been implemented in

JASP JASP (Jeffreys’s Amazing Statistics Program) is a free and open-source program for statistical analysis supported by the University of Amsterdam. It is designed to be easy to use, and familiar to users of SPSS. It offers standard analysis pro ...

SPSS SPSS Statistics is a statistical software suite developed by IBM for data management, advanced analytics, multivariate analysis, business intelligence, and criminal investigation. Long produced by SPSS Inc., it was acquired by IBM in 2009. C ...

, SAS, STATA, and

MATLAB MATLAB (an abbreviation of "MATrix LABoratory") is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementa ...

and in multiple packages for the

R programming language R is a programming language for statistical computing and graphics supported by the R Core Team and the R Foundation for Statistical Computing. Created by statisticians Ross Ihaka and Robert Gentleman, R is used among data miners, bioinforma ...

, including the ''psych'' ''multicon'', ''hornpa'', and ''paran'' packages.

References

Multivariate statistics Factor analysis {{statistics-stub

Evaluation and comparison with alternatives

Implementation

See also

References