Editing Factor analysis (section)

==In psychometrics==
===History===
[[Charles Spearman]] was the first psychologist to discuss common factor analysis<ref name=":0">{{Cite book|last=Mulaik|first=Stanley A|title=Foundations of Factor Analysis. Second Edition|publisher=CRC Press|year=2010|isbn=978-1-4200-9961-4|location=Boca Raton, Florida|pages=6}}</ref> and did so in his 1904 paper.<ref>{{Cite journal|last=Spearman|first=Charles|date=1904|title=General intelligence objectively determined and measured|journal=American Journal of Psychology|volume=15|issue=2|pages=201–293|doi=10.2307/1412107|jstor=1412107}}</ref> It provided few details about his methods and was concerned with single-factor models.<ref>{{Cite journal|last=Bartholomew|first=D. J.|date=1995|title=Spearman and the origin and development of factor analysis|journal=British Journal of Mathematical and Statistical Psychology|volume=48|issue=2|pages=211–220|doi=10.1111/j.2044-8317.1995.tb01060.x}}</ref> He discovered that school children's scores on a wide variety of seemingly unrelated subjects were positively correlated, which led him to postulate that a single general mental ability, or ''[[G factor (psychometrics)|g]]'', underlies and shapes human cognitive performance.

The initial development of common factor analysis with multiple factors was given by [[Louis Leon Thurstone|Louis Thurstone]] in two papers in the early 1930s,<ref>{{Cite journal|last=Thurstone|first=Louis|date=1931|title=Multiple factor analysis|journal=Psychological Review|volume=38|issue=5|pages=406–427|doi=10.1037/h0069792}}</ref><ref>{{Cite journal|last=Thurstone|first=Louis|date=1934|title=The Vectors of Mind|journal=The Psychological Review|volume=41|pages=1–32|doi=10.1037/h0075959}}</ref> summarized in his 1935 book, ''[[The Vectors of Mind|The Vector of Mind]].''<ref>{{Cite book|last=Thurstone|first=L. L.|title=The Vectors of Mind. Multiple-Factor Analysis for the Isolation of Primary Traits.|publisher=University of Chicago Press|year=1935|location=Chicago, Illinois}}</ref> Thurstone introduced several important factor analysis concepts, including communality, uniqueness, and rotation.<ref>{{Cite book|last=Bock|first=Robert|title=Factor Analysis at 100|publisher=Lawrence Erlbaum Associates|year=2007|isbn=978-0-8058-6212-6 |editor=Cudeck, Robert |editor2=MacCallum, Robert C.|location=Mahwah, New Jersey|pages=37|chapter=Rethinking Thurstone}}</ref> He advocated for "simple structure", and developed methods of rotation that could be used as a way to achieve such structure.<ref name=":0" />

In [[Q methodology]], [[William Stephenson (psychologist)|William Stephenson]], a student of Spearman, distinguish between ''R'' factor analysis, oriented toward the study of inter-individual differences, and ''Q'' factor analysis oriented toward subjective intra-individual differences.<ref>{{cite book | author= Mckeown, Bruce | title= Q Methodology | isbn= 9781452242194 | oclc= 841672556| date= 2013-06-21 | publisher= SAGE Publications }}</ref><ref>{{cite journal |title=Technique of Factor Analysis |journal=Nature |last=Stephenson |first=W. |volume=136 |issue=3434 |page=297 |date=August 1935 |issn=0028-0836 |doi=10.1038/136297b0|bibcode=1935Natur.136..297S |s2cid=26952603 |doi-access=free }}</ref>

[[Raymond Cattell]] was a strong advocate of factor analysis and [[psychometrics]] and used Thurstone's multi-factor theory to explain intelligence. Cattell also developed the [[Scree plot|scree test]] and similarity coefficients.

===Applications in psychology===
Factor analysis is used to identify "factors" that explain a variety of results on different tests. For example, intelligence research found that people who get a high score on a test of verbal ability are also good on other tests that require verbal abilities. Researchers explained this by using factor analysis to isolate one factor, often called verbal intelligence, which represents the degree to which someone is able to solve problems involving verbal skills.{{Citation needed|reason="which researchers? What examples?"|date=July 2021}}

Factor analysis in psychology is most often associated with intelligence research. However, it also has been used to find factors in a broad range of domains such as personality, attitudes, beliefs, etc. It is linked to [[psychometrics]], as it can assess the validity of an instrument by finding if the instrument indeed measures the postulated factors.{{Citation needed|reason="Are there any studies which show any of the above claims?"|date=July 2021}}

===Advantages===
* Reduction of number of variables, by combining two or more variables into a single factor. For example, performance at running, ball throwing, batting, jumping and weight lifting could be combined into a single factor such as general athletic ability. Usually, in an item by people matrix, factors are selected by grouping related items. In the Q factor analysis technique, the matrix is transposed and factors are created by grouping related people. For example, liberals, libertarians, conservatives, and socialists might form into separate groups.
* Identification of groups of inter-related variables, to see how they are related to each other. For example, Carroll used factor analysis to build his [[Three Stratum Theory]]. He found that a factor called "broad visual perception" relates to how good an individual is at visual tasks. He also found a "broad auditory perception" factor, relating to auditory task capability. Furthermore, he found a global factor, called "g" or general intelligence, that relates to both "broad visual perception" and "broad auditory perception". This means someone with a high "g" is likely to have both a high "visual perception" capability and a high "auditory perception" capability, and that "g" therefore explains a good part of why someone is good or bad in both of those domains.

===Disadvantages===
* "...each orientation is equally acceptable mathematically. But different factorial theories proved to differ as much in terms of the orientations of factorial axes for a given solution as in terms of anything else, so that model fitting did not prove to be useful in distinguishing among theories." (Sternberg, 1977<ref name=Sternberg>{{cite book |last=Sternberg |first=R. J. |title=Metaphors of Mind: Conceptions of the Nature of Intelligence |year=1977 |location=New York |publisher=Cambridge University Press |pages=85–111 }}{{Verify source|date=November 2013}}</ref>). This means all rotations represent different underlying processes, but all rotations are equally valid outcomes of standard factor analysis optimization. Therefore, it is impossible to pick the proper rotation using factor analysis alone.
* Factor analysis can be only as good as the data allows. In psychology, where researchers often have to rely on less valid and reliable measures such as self-reports, this can be problematic.
* Interpreting factor analysis is based on using a "heuristic", which is a solution that is "convenient even if not absolutely true".<ref>{{cite web|title=Factor Analysis |access-date=July 22, 2004 |url=http://comp9.psych.cornell.edu/Darlington/factor.htm |url-status=dead |archive-url=https://web.archive.org/web/20040818062948/http://comp9.psych.cornell.edu/Darlington/factor.htm |archive-date=August 18, 2004 }}
</ref> More than one interpretation can be made of the same data factored the same way, and factor analysis cannot identify causality.