The varimax criterion for analytic rotation in factor analysis View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

1958-09

AUTHORS

Henry F. Kaiser

ABSTRACT

An analytic criterion for rotation is defined. The scientific advantage of analytic criteria over subjective (graphical) rotational procedures is discussed. Carroll's criterion and the quartimax criterion are briefly reviewed; the varimax criterion is outlined in detail and contrasted both logically and numerically with the quartimax criterion. It is shown that thenormal varimax solution probably coincides closely to the application of the principle of simple structure. However, it is proposed that the ultimate criterion of a rotational procedure is factorial invariance, not simple structure—although the two notions appear to be highly related. The normal varimax criterion is shown to be a two-dimensional generalization of the classic Spearman case, i.e., it shows perfect factorial invariance for two pure clusters. An example is given of the invariance of a normal varimax solution for more than two factors. The oblique normal varimax criterion is stated. A computational outline for the orthogonal normal varimax is appended. More... »

PAGES

187-200

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/bf02289233

DOI

http://dx.doi.org/10.1007/bf02289233

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1018991466


Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

JSON-LD is the canonical representation for SciGraph data.

TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

[
  {
    "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
    "about": [
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0103", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Numerical and Computational Mathematics", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Mathematical Sciences", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "name": [
            "University of Illinois, USA"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Kaiser", 
        "givenName": "Henry F.", 
        "id": "sg:person.010367773757.37", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010367773757.37"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "sg:pub.10.1007/bf02289228", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1004258279", 
          "https://doi.org/10.1007/bf02289228"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf02289228", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1004258279", 
          "https://doi.org/10.1007/bf02289228"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf02289025", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1016155263", 
          "https://doi.org/10.1007/bf02289025"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf02289025", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1016155263", 
          "https://doi.org/10.1007/bf02289025"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf02289089", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1019700882", 
          "https://doi.org/10.1007/bf02289089"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf02289089", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1019700882", 
          "https://doi.org/10.1007/bf02289089"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1111/j.2044-8317.1954.tb00147.x", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1034386198"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "1958-09", 
    "datePublishedReg": "1958-09-01", 
    "description": "An analytic criterion for rotation is defined. The scientific advantage of analytic criteria over subjective (graphical) rotational procedures is discussed. Carroll's criterion and the quartimax criterion are briefly reviewed; the varimax criterion is outlined in detail and contrasted both logically and numerically with the quartimax criterion. It is shown that thenormal varimax solution probably coincides closely to the application of the principle of simple structure. However, it is proposed that the ultimate criterion of a rotational procedure is factorial invariance, not simple structure\u2014although the two notions appear to be highly related. The normal varimax criterion is shown to be a two-dimensional generalization of the classic Spearman case, i.e., it shows perfect factorial invariance for two pure clusters. An example is given of the invariance of a normal varimax solution for more than two factors. The oblique normal varimax criterion is stated. A computational outline for the orthogonal normal varimax is appended.", 
    "genre": "research_article", 
    "id": "sg:pub.10.1007/bf02289233", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": false, 
    "isPartOf": [
      {
        "id": "sg:journal.1017907", 
        "issn": [
          "0033-3123", 
          "1860-0980"
        ], 
        "name": "Psychometrika", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "3", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "23"
      }
    ], 
    "name": "The varimax criterion for analytic rotation in factor analysis", 
    "pagination": "187-200", 
    "productId": [
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "5a7ce1ba96ddfac03392ed597ad822470062bb44fb8d3b14876c769b81422ef6"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/bf02289233"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1018991466"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/bf02289233", 
      "https://app.dimensions.ai/details/publication/pub.1018991466"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2019-04-11T12:42", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000363_0000000363/records_70061_00000000.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "http://link.springer.com/10.1007%2FBF02289233"
  }
]
 

Download the RDF metadata as:  json-ld nt turtle xml License info

HOW TO GET THIS DATA PROGRAMMATICALLY:

JSON-LD is a popular format for linked data which is fully compatible with JSON.

curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/bf02289233'

N-Triples is a line-based linked data format ideal for batch operations.

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/bf02289233'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/bf02289233'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/bf02289233'


 

This table displays all metadata directly associated to this object as RDF triples.

75 TRIPLES      21 PREDICATES      31 URIs      19 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/bf02289233 schema:about anzsrc-for:01
2 anzsrc-for:0103
3 schema:author Nf50a5e059d9f44c8a789dededbf44004
4 schema:citation sg:pub.10.1007/bf02289025
5 sg:pub.10.1007/bf02289089
6 sg:pub.10.1007/bf02289228
7 https://doi.org/10.1111/j.2044-8317.1954.tb00147.x
8 schema:datePublished 1958-09
9 schema:datePublishedReg 1958-09-01
10 schema:description An analytic criterion for rotation is defined. The scientific advantage of analytic criteria over subjective (graphical) rotational procedures is discussed. Carroll's criterion and the quartimax criterion are briefly reviewed; the varimax criterion is outlined in detail and contrasted both logically and numerically with the quartimax criterion. It is shown that thenormal varimax solution probably coincides closely to the application of the principle of simple structure. However, it is proposed that the ultimate criterion of a rotational procedure is factorial invariance, not simple structure—although the two notions appear to be highly related. The normal varimax criterion is shown to be a two-dimensional generalization of the classic Spearman case, i.e., it shows perfect factorial invariance for two pure clusters. An example is given of the invariance of a normal varimax solution for more than two factors. The oblique normal varimax criterion is stated. A computational outline for the orthogonal normal varimax is appended.
11 schema:genre research_article
12 schema:inLanguage en
13 schema:isAccessibleForFree false
14 schema:isPartOf N81abb4075d744444ad3e4be8f18ed4ae
15 Nbdc45b2012114a98a0cca54c4ea2c94b
16 sg:journal.1017907
17 schema:name The varimax criterion for analytic rotation in factor analysis
18 schema:pagination 187-200
19 schema:productId N1f1ab34474954a0c895d43e6aa84abed
20 N82a3fa12f9574357ae115b4973bc60ac
21 Naed9cc34d2f54278ba253e8494fecbbd
22 schema:sameAs https://app.dimensions.ai/details/publication/pub.1018991466
23 https://doi.org/10.1007/bf02289233
24 schema:sdDatePublished 2019-04-11T12:42
25 schema:sdLicense https://scigraph.springernature.com/explorer/license/
26 schema:sdPublisher N79433754d62244fb9a1f5b885f7eb20e
27 schema:url http://link.springer.com/10.1007%2FBF02289233
28 sgo:license sg:explorer/license/
29 sgo:sdDataset articles
30 rdf:type schema:ScholarlyArticle
31 N1db8e45a7b9e48fc9373fed311e00333 schema:name University of Illinois, USA
32 rdf:type schema:Organization
33 N1f1ab34474954a0c895d43e6aa84abed schema:name readcube_id
34 schema:value 5a7ce1ba96ddfac03392ed597ad822470062bb44fb8d3b14876c769b81422ef6
35 rdf:type schema:PropertyValue
36 N79433754d62244fb9a1f5b885f7eb20e schema:name Springer Nature - SN SciGraph project
37 rdf:type schema:Organization
38 N81abb4075d744444ad3e4be8f18ed4ae schema:volumeNumber 23
39 rdf:type schema:PublicationVolume
40 N82a3fa12f9574357ae115b4973bc60ac schema:name doi
41 schema:value 10.1007/bf02289233
42 rdf:type schema:PropertyValue
43 Naed9cc34d2f54278ba253e8494fecbbd schema:name dimensions_id
44 schema:value pub.1018991466
45 rdf:type schema:PropertyValue
46 Nbdc45b2012114a98a0cca54c4ea2c94b schema:issueNumber 3
47 rdf:type schema:PublicationIssue
48 Nf50a5e059d9f44c8a789dededbf44004 rdf:first sg:person.010367773757.37
49 rdf:rest rdf:nil
50 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
51 schema:name Mathematical Sciences
52 rdf:type schema:DefinedTerm
53 anzsrc-for:0103 schema:inDefinedTermSet anzsrc-for:
54 schema:name Numerical and Computational Mathematics
55 rdf:type schema:DefinedTerm
56 sg:journal.1017907 schema:issn 0033-3123
57 1860-0980
58 schema:name Psychometrika
59 rdf:type schema:Periodical
60 sg:person.010367773757.37 schema:affiliation N1db8e45a7b9e48fc9373fed311e00333
61 schema:familyName Kaiser
62 schema:givenName Henry F.
63 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010367773757.37
64 rdf:type schema:Person
65 sg:pub.10.1007/bf02289025 schema:sameAs https://app.dimensions.ai/details/publication/pub.1016155263
66 https://doi.org/10.1007/bf02289025
67 rdf:type schema:CreativeWork
68 sg:pub.10.1007/bf02289089 schema:sameAs https://app.dimensions.ai/details/publication/pub.1019700882
69 https://doi.org/10.1007/bf02289089
70 rdf:type schema:CreativeWork
71 sg:pub.10.1007/bf02289228 schema:sameAs https://app.dimensions.ai/details/publication/pub.1004258279
72 https://doi.org/10.1007/bf02289228
73 rdf:type schema:CreativeWork
74 https://doi.org/10.1111/j.2044-8317.1954.tb00147.x schema:sameAs https://app.dimensions.ai/details/publication/pub.1034386198
75 rdf:type schema:CreativeWork
 




Preview window. Press ESC to close (or click here)


...