Varimax rotation
Encyclopedia
In statistics
, a varimax rotation is a change of coordinates used in principal component analysis and factor analysis
that maximizes the sum of the variance
s of the squared loadings. That is, it seeks a basis that most economically represents each individual—so that each individual can be well described by a linear combination
of only a few basis functions:
where γ = 1 for VARIMAX.
Suggested by Henry Felix Kaiser in 1958,
it is a popular scheme for orthogonal rotation which cleans up the factors as follows: "for each factor, high loadings (correlations) will result for a few variables; the rest will be near zero."
Varimax rotation is often used in surveys to see how groupings of questions (items) measure the same concept.
The advantages and disadvantages of the technique are discussed at the website of Columbia University
.
.
programming language the varimax method is implemented in the GPArotation library by Coen Bernaards and Robert Jennrich.
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
, a varimax rotation is a change of coordinates used in principal component analysis and factor analysis
Factor analysis
Factor analysis is a statistical method used to describe variability among observed, correlated variables in terms of a potentially lower number of unobserved, uncorrelated variables called factors. In other words, it is possible, for example, that variations in three or four observed variables...
that maximizes the sum of the variance
Variance
In probability theory and statistics, the variance is a measure of how far a set of numbers is spread out. It is one of several descriptors of a probability distribution, describing how far the numbers lie from the mean . In particular, the variance is one of the moments of a distribution...
s of the squared loadings. That is, it seeks a basis that most economically represents each individual—so that each individual can be well described by a linear combination
Linear combination
In mathematics, a linear combination is an expression constructed from a set of terms by multiplying each term by a constant and adding the results...
of only a few basis functions:
where γ = 1 for VARIMAX.
Suggested by Henry Felix Kaiser in 1958,
it is a popular scheme for orthogonal rotation which cleans up the factors as follows: "for each factor, high loadings (correlations) will result for a few variables; the rest will be near zero."
Varimax rotation is often used in surveys to see how groupings of questions (items) measure the same concept.
The advantages and disadvantages of the technique are discussed at the website of Columbia University
Columbia University
Columbia University in the City of New York is a private, Ivy League university in Manhattan, New York City. Columbia is the oldest institution of higher learning in the state of New York, the fifth oldest in the United States, and one of the country's nine Colonial Colleges founded before the...
.
Rotation in factor analysis
A summary of the use of varimax rotation and of other types of factor rotation is presented in this article on factor analysisFactor analysis
Factor analysis is a statistical method used to describe variability among observed, correlated variables in terms of a potentially lower number of unobserved, uncorrelated variables called factors. In other words, it is possible, for example, that variations in three or four observed variables...
.
Implementations
In the RR (programming language)
R is a programming language and software environment for statistical computing and graphics. The R language is widely used among statisticians for developing statistical software, and R is widely used for statistical software development and data analysis....
programming language the varimax method is implemented in the GPArotation library by Coen Bernaards and Robert Jennrich.
See also
- Factor analysisFactor analysisFactor analysis is a statistical method used to describe variability among observed, correlated variables in terms of a potentially lower number of unobserved, uncorrelated variables called factors. In other words, it is possible, for example, that variations in three or four observed variables...
- Empirical orthogonal functionsEmpirical orthogonal functionsIn statistics and signal processing, the method of empirical orthogonal function analysis is a decomposition of a signal or data set in terms of orthogonal basis functions which are determined from the data. It is the same as performing a principal components analysis on the data, except that the...
- Q methodologyQ methodologyQ Methodology is a research method used in psychology and other social sciences to study people's "subjectivity" -- that is, their viewpoint. Q was developed by psychologist William Stephenson...
- Rotation matrix
External links
- Factor rotations in Factor Analyses by Herve Abdi
- About Varimax
- Properties of Principal Components
- http://www2.imm.dtu.dk/pubdb/views/edoc_download.php/4041/pdf/imm4041.pdf