Analysing multitrait–multimethod data with structural equation models for ordinal variables applying the WLSMV estimator: What sample size is needed for valid results?
Identifieur interne : 001B85 ( Istex/Corpus ); précédent : 001B84; suivant : 001B86Analysing multitrait–multimethod data with structural equation models for ordinal variables applying the WLSMV estimator: What sample size is needed for valid results?
Auteurs : Fridtjof W. Nussbeck ; Michael. Eid ; Tanja. LischetzkeSource :
- British Journal of Mathematical and Statistical Psychology [ 0007-1102 ] ; 2006-05.
Abstract
Convergent and discriminant validity of psychological constructs can best be examined in the framework of multitrait–multimethod (MTMM) analysis. To gain information at the level of single items, MTMM models for categorical variables have to be applied. The CTC(M−1) model is presented as an example of an MTMM model for ordinal variables. Based on an empirical application of the CTC(M−1) model, a complex simulation study was conducted to examine the sample size requirements of the robust weighted least squares mean‐ and variance‐adjusted χ2 test of model fit (WLSMV estimator) implemented in Mplus. In particular, the simulation study analysed the χ2 approximation, the parameter estimation bias, the standard error bias, and the reliability of the WLSMV estimator depending on the varying number of items per trait–method unit (ranging from 2 to 8) and varying sample sizes (250, 500, 750, and 1000 observations). The results showed that the WLSMV estimator provided a good – albeit slightly liberal – χ2 approximation and stable and reliable parameter estimates for models of reasonable complexity (2–4 items) and small sample sizes (at least 250 observations). When more complex models with 5 or more items were analysed, larger sample sizes of at least 500 observations were needed. The most complex model with 9 trait–method units and 8 items (72 observed variables) requires sample sizes of at least 1000 observations.
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DOI: 10.1348/000711005X67490
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Nussbeck</name><affiliation><mods:affiliation>University of Geneva, Switzerland</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: fridtjof.nussbeck@pse.unige.ch</mods:affiliation></affiliation></author><author><name sortKey="Eid, Michael" sort="Eid, Michael" uniqKey="Eid M" first="Michael." last="Eid">Michael. Eid</name><affiliation><mods:affiliation>University of Geneva, Switzerland</mods:affiliation></affiliation></author><author><name sortKey="Lischetzke, Tanja" sort="Lischetzke, Tanja" uniqKey="Lischetzke T" first="Tanja." last="Lischetzke">Tanja. Lischetzke</name><affiliation><mods:affiliation>University of Geneva, Switzerland</mods:affiliation></affiliation></author></analytic><monogr></monogr><series><title level="j">British Journal of Mathematical and Statistical Psychology</title><idno type="ISSN">0007-1102</idno><idno type="eISSN">2044-8317</idno><imprint><publisher>Blackwell Publishing Ltd</publisher><pubPlace>Oxford, UK</pubPlace><date type="published" when="2006-05">2006-05</date><biblScope unit="volume">59</biblScope><biblScope unit="issue">1</biblScope><biblScope unit="page" from="195">195</biblScope><biblScope unit="page" to="213">213</biblScope></imprint><idno type="ISSN">0007-1102</idno></series><idno type="istex">58486F3DD5F805F9F368E8D7D2B36C0BD14408A7</idno><idno type="DOI">10.1348/000711005X67490</idno><idno type="ArticleID">BMSP171</idno></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0007-1102</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Convergent and discriminant validity of psychological constructs can best be examined in the framework of multitrait–multimethod (MTMM) analysis. To gain information at the level of single items, MTMM models for categorical variables have to be applied. The CTC(M−1) model is presented as an example of an MTMM model for ordinal variables. Based on an empirical application of the CTC(M−1) model, a complex simulation study was conducted to examine the sample size requirements of the robust weighted least squares mean‐ and variance‐adjusted χ2 test of model fit (WLSMV estimator) implemented in Mplus. In particular, the simulation study analysed the χ2 approximation, the parameter estimation bias, the standard error bias, and the reliability of the WLSMV estimator depending on the varying number of items per trait–method unit (ranging from 2 to 8) and varying sample sizes (250, 500, 750, and 1000 observations). The results showed that the WLSMV estimator provided a good – albeit slightly liberal – χ2 approximation and stable and reliable parameter estimates for models of reasonable complexity (2–4 items) and small sample sizes (at least 250 observations). When more complex models with 5 or more items were analysed, larger sample sizes of at least 500 observations were needed. The most complex model with 9 trait–method units and 8 items (72 observed variables) requires sample sizes of at least 1000 observations.</div></front></TEI><istex><corpusName>wiley</corpusName><author><json:item><name>Fridtjof W. Nussbeck</name><affiliations><json:string>University of Geneva, Switzerland</json:string><json:string>E-mail: fridtjof.nussbeck@pse.unige.ch</json:string></affiliations></json:item><json:item><name>Michael. Eid</name><affiliations><json:string>University of Geneva, Switzerland</json:string></affiliations></json:item><json:item><name>Tanja. Lischetzke</name><affiliations><json:string>University of Geneva, Switzerland</json:string></affiliations></json:item></author><articleId><json:string>BMSP171</json:string></articleId><language><json:string>eng</json:string></language><originalGenre><json:string>article</json:string></originalGenre><abstract>Convergent and discriminant validity of psychological constructs can best be examined in the framework of multitrait–multimethod (MTMM) analysis. To gain information at the level of single items, MTMM models for categorical variables have to be applied. The CTC(M−1) model is presented as an example of an MTMM model for ordinal variables. Based on an empirical application of the CTC(M−1) model, a complex simulation study was conducted to examine the sample size requirements of the robust weighted least squares mean‐ and variance‐adjusted χ2 test of model fit (WLSMV estimator) implemented in Mplus. In particular, the simulation study analysed the χ2 approximation, the parameter estimation bias, the standard error bias, and the reliability of the WLSMV estimator depending on the varying number of items per trait–method unit (ranging from 2 to 8) and varying sample sizes (250, 500, 750, and 1000 observations). The results showed that the WLSMV estimator provided a good – albeit slightly liberal – χ2 approximation and stable and reliable parameter estimates for models of reasonable complexity (2–4 items) and small sample sizes (at least 250 observations). When more complex models with 5 or more items were analysed, larger sample sizes of at least 500 observations were needed. The most complex model with 9 trait–method units and 8 items (72 observed variables) requires sample sizes of at least 1000 observations.</abstract><qualityIndicators><score>9.152</score><pdfVersion>1.6</pdfVersion><pdfPageSize>612 x 850 pts</pdfPageSize><refBibsNative>true</refBibsNative><abstractCharCount>1429</abstractCharCount><pdfWordCount>7572</pdfWordCount><pdfCharCount>48046</pdfCharCount><pdfPageCount>19</pdfPageCount><abstractWordCount>221</abstractWordCount></qualityIndicators><title>Analysing multitrait–multimethod data with structural equation models for ordinal variables applying the WLSMV estimator: What sample size is needed for valid results?</title><refBibs><json:item><host><author></author><title>Bollen, K. A. Structural equations with latent variables New York: Wiley 1989.</title></host></json:item><json:item><author><json:item><name>M.‐W Browne</name></json:item></author><host><volume>37</volume><pages><last>83</last><first>62</first></pages><author></author><title>British Journal of Mathematical and Statistical Psychology</title></host><title>Asymptotically distribution‐free methods for the analysis of covariance structures</title></json:item><json:item><author><json:item><name>D. T. Campbell</name></json:item><json:item><name>D. W. Fiske</name></json:item></author><host><volume>56</volume><pages><last>105</last><first>81</first></pages><author></author><title>Psychological Bulletin</title></host><title>Convergent and discriminant validation by the multitrait‐multimethod matrix</title></json:item><json:item><author><json:item><name>C. P. Chou</name></json:item><json:item><name>P. M. Bentler</name></json:item></author><host><pages><last>55</last><first>37</first></pages><author></author><title>Structural equation modeling: Concepts, issues, and applications</title></host><title>Estimates and tests in structural equation modeling</title></json:item><json:item><author><json:item><name>L. Dumenci</name></json:item></author><host><pages><last>611</last><first>583</first></pages><author></author><title>Handbook of applied multivariate statistics and mathematical modeling</title></host><title>Multitrait‐multimethod analysis</title></json:item><json:item><author><json:item><name>B. Efron</name></json:item></author><host><volume>7</volume><pages><last>26</last><first>1</first></pages><author></author><title>Annals of Statistics</title></host><title>Bootstrap methods: Another look at the jackknife</title></json:item><json:item><host><author></author><title>Efron, B. The jackknife, the bootstrap and other resampling plans Philadelphia, PA: SIAM 1982.</title></host></json:item><json:item><host><author></author><title>Eid, M. Modelle der Messung von Personen in Situationen [Models for measuring persons in situations] Weinheim: Psychologie Verlags Union 1995.</title></host></json:item><json:item><author><json:item><name>M. Eid</name></json:item></author><host><volume>65</volume><pages><last>261</last><first>241</first></pages><author></author><title>Psychometrika</title></host><title>A multitrait‐multimethod model with minimal assumptions</title></json:item><json:item><author><json:item><name>M. Eid</name></json:item><json:item><name>T. Lischetzke</name></json:item><json:item><name>F. W. Nussbeck</name></json:item></author><host><author></author><title>Handbook of multimethod measurement in psychology</title></host><title>Structural equation models for multitrait‐multimethod data</title></json:item><json:item><author><json:item><name>M. Eid</name></json:item><json:item><name>T. Lischetzke</name></json:item><json:item><name>F. W. Nussbeck</name></json:item><json:item><name>L. I. Trierweiler</name></json:item></author><host><volume>8</volume><pages><last>60</last><first>38</first></pages><author></author><title>Psychological Methods</title></host><title>Separating trait effects from trait‐specific method effects in multitrait‐multimethod models: A multiple‐indicator CT‐C(M‐1) model</title></json:item><json:item><author><json:item><name>D. B. Flora</name></json:item><json:item><name>P. J. Curran</name></json:item></author><host><volume>9</volume><pages><last>491</last><first>466</first></pages><author></author><title>Psychological Methods</title></host><title>An empirical evaluation of alternative models of estimation for confirmatory factor analysis with ordinal data</title></json:item><json:item><author><json:item><name>D. A. Grayson</name></json:item><json:item><name>H. W. Marsh</name></json:item></author><host><volume>59</volume><pages><last>134</last><first>121</first></pages><author></author><title>Psychometrika</title></host><title>Identification with deficient rank loading matrices in confirmatory factor analysis: Multitrait‐multimethod models</title></json:item><json:item><author><json:item><name>H. W. Marsh</name></json:item></author><host><volume>13</volume><pages><last>361</last><first>335</first></pages><author></author><title>Applied Psychological Measurement</title></host><title>Confirmatory factor analyses of multitrait‐multimethod data: Many problems and a few solutions</title></json:item><json:item><author><json:item><name>H. W. Marsh</name></json:item></author><host><volume>6</volume><pages><last>81</last><first>49</first></pages><author></author><title>Applied Measurement in Education</title></host><title>Multitrait‐multimethod analyses: Inferring each trait–method combination with multiple indicators</title></json:item><json:item><author><json:item><name>H. W. Marsh</name></json:item><json:item><name>B. M. Byrne</name></json:item></author><host><volume>28</volume><pages><last>349</last><first>313</first></pages><author></author><title>Multivariate Behavioral Research</title></host><title>Confirmatory factor analysis of multitrait‐multimethod self‐concept data: Between‐group and within‐group invariance constraints</title></json:item><json:item><author><json:item><name>H. W. Marsh</name></json:item><json:item><name>D. Grayson</name></json:item></author><host><pages><last>198</last><first>177</first></pages><author></author><title>Structural equation modeling: Concepts, issues, and applications</title></host><title>Latent variable models of multitrait‐multimethod data</title></json:item><json:item><author><json:item><name>H. W. Marsh</name></json:item><json:item><name>D. Hocevar</name></json:item></author><host><volume>73</volume><pages><last>117</last><first>107</first></pages><author></author><title>Journal of Applied Psychology</title></host><title>A new, more powerful approach to multitrait‐multimethod analyses: Application of second‐order confirmatory factor analysis</title></json:item><json:item><author><json:item><name>R. R. McCrae</name></json:item></author><host><volume>43</volume><pages><last>303</last><first>293</first></pages><author></author><title>Journal of Personality and Social Psychology</title></host><title>Consensual validation of personality traits: Evidence from self‐reports and ratings</title></json:item><json:item><author><json:item><name>B. O. Muthén</name></json:item></author><host><volume>49</volume><pages><last>45</last><first>22</first></pages><author></author><title>Journal of Econometrics</title></host><title>Latent variable structural equation modeling with categorical variables</title></json:item><json:item><host><author></author><title>Robust inference using weighted least squares and quadratic estimating equations in latent variable modeling with categorical and continuous outcomesPsychometrika</title></host></json:item><json:item><author><json:item><name>L. K. Muthén</name></json:item><json:item><name>B. O. Muthén</name></json:item></author><host><volume>9</volume><pages><last>620</last><first>599</first></pages><author></author><title>Structural Equation Modeling</title></host><title>How to use a Monte Carlo study to decide on sample size and determine power</title></json:item><json:item><host><author></author><title>Muthén, L. K. Muthén, B. O. Mplus user's guide Los Angeles: Author 2004.</title></host></json:item><json:item><author><json:item><name>A. Satorra</name></json:item></author><host><volume>54</volume><pages><last>151</last><first>131</first></pages><author></author><title>Psychometrika</title></host><title>Alternative test criteria in covariance structure analysis: A unified approach</title></json:item><json:item><author><json:item><name>A. Satorra</name></json:item></author><host><pages><last>278</last><first>249</first></pages><author></author><title>Sociological methodology 1992</title></host><title>Asymptotoic robust inferences in the analysis of mean and covariance structures</title></json:item><json:item><author><json:item><name>K. Schermelleh‐Engel</name></json:item><json:item><name>H. Moosbrugger</name></json:item><json:item><name>H. Müller</name></json:item></author><host><volume>8</volume><pages><last>74</last><first>23</first></pages><author></author><title>Methods of Psychological Research</title></host><title>Evaluating the fit of structural equation models: Tests of significance and descriptive goodness‐of‐fit measures</title></json:item><json:item><author><json:item><name>A. L. Stanton</name></json:item><json:item><name>S. B. Kirk</name></json:item><json:item><name>C. L. Cameron</name></json:item><json:item><name>S. Danoff‐Burg</name></json:item></author><host><volume>78</volume><pages><last>1169</last><first>1150</first></pages><author></author><title>Journal of Personality and Social Psychology</title></host><title>Coping through emotional approach: Scale construction and validation</title></json:item><json:item><author><json:item><name>R. Steyer</name></json:item><json:item><name>P. Schwenkmezger</name></json:item><json:item><name>P. Notz</name></json:item><json:item><name>M. Eid</name></json:item></author><host><volume>40</volume><pages><last>328</last><first>320</first></pages><author></author><title>Diagnostica</title></host><title>Testtheoretische Analysen des Mehrdimensionalen Befindlichkeitsfragebogen (MDBF) [Theoretical analysis of the Multidimensional Mood Questionnaire (MMQ)]</title></json:item><json:item><author><json:item><name>Y. Takane</name></json:item><json:item><name>J. De Leeuw</name></json:item></author><host><volume>52</volume><pages><last>408</last><first>393</first></pages><author></author><title>Psychometrika</title></host><title>On the relationship between item response theory and factor analysis of discretized variables</title></json:item><json:item><author><json:item><name>L. I. Trierweiler</name></json:item><json:item><name>M. Eid</name></json:item><json:item><name>T. Lischetzke</name></json:item></author><host><volume>82</volume><pages><last>1040</last><first>1023</first></pages><author></author><title>Journal of Personality and Social Psychology</title></host><title>The structure of emotional expressivity: Each emotion counts</title></json:item><json:item><author><json:item><name>D. Watson</name></json:item><json:item><name>B. Hubbard</name></json:item><json:item><name>D. Wiese</name></json:item></author><host><volume>78</volume><pages><last>558</last><first>546</first></pages><author></author><title>Journal of Personality and Social Psychology</title></host><title>Self‐other agreement in personality and affectivity: The role of acquaintanceship, trait visibility, and assumed similarity</title></json:item><json:item><author><json:item><name>K. F. Widaman</name></json:item></author><host><volume>9</volume><pages><last>26</last><first>1</first></pages><author></author><title>Applied Psychological Measurement</title></host><title>Hierarchically nested covariance structure models for multitrait‐multimethod data</title></json:item></refBibs><genre><json:string>article</json:string></genre><host><volume>59</volume><publisherId><json:string>BMSP</json:string></publisherId><pages><total>19</total><last>213</last><first>195</first></pages><issn><json:string>0007-1102</json:string></issn><issue>1</issue><genre><json:string>journal</json:string></genre><language><json:string>unknown</json:string></language><eissn><json:string>2044-8317</json:string></eissn><title>British Journal of Mathematical and Statistical Psychology</title><doi><json:string>10.1111/(ISSN)2044-8317</json:string></doi></host><categories><wos><json:string>social science</json:string><json:string>psychology, mathematical</json:string><json:string>psychology, experimental</json:string><json:string>science</json:string><json:string>statistics & probability</json:string><json:string>mathematics, interdisciplinary applications</json:string></wos><scienceMetrix><json:string>economic & social sciences</json:string><json:string>social sciences</json:string><json:string>social sciences methods</json:string></scienceMetrix></categories><publicationDate>2006</publicationDate><copyrightDate>2006</copyrightDate><doi><json:string>10.1348/000711005X67490</json:string></doi><id>58486F3DD5F805F9F368E8D7D2B36C0BD14408A7</id><score>0.07096732</score><fulltext><json:item><extension>pdf</extension><original>true</original><mimetype>application/pdf</mimetype><uri>https://api.istex.fr/document/58486F3DD5F805F9F368E8D7D2B36C0BD14408A7/fulltext/pdf</uri></json:item><json:item><extension>zip</extension><original>false</original><mimetype>application/zip</mimetype><uri>https://api.istex.fr/document/58486F3DD5F805F9F368E8D7D2B36C0BD14408A7/fulltext/zip</uri></json:item><istex:fulltextTEI uri="https://api.istex.fr/document/58486F3DD5F805F9F368E8D7D2B36C0BD14408A7/fulltext/tei"><teiHeader><fileDesc><titleStmt><title level="a" type="main" xml:lang="en">Analysing multitrait–multimethod data with structural equation models for ordinal variables applying the WLSMV estimator: What sample size is needed for valid results?</title></titleStmt><publicationStmt><authority>ISTEX</authority><publisher>Blackwell Publishing Ltd</publisher><pubPlace>Oxford, UK</pubPlace><availability><p>2006 The British Psychological Society</p></availability><date>2006</date></publicationStmt><sourceDesc><biblStruct type="inbook"><analytic><title level="a" type="main" xml:lang="en">Analysing multitrait–multimethod data with structural equation models for ordinal variables applying the WLSMV estimator: What sample size is needed for valid results?</title><author xml:id="author-1"><persName><forename type="first">Fridtjof W.</forename><surname>Nussbeck</surname></persName><email>fridtjof.nussbeck@pse.unige.ch</email><affiliation>University of Geneva, Switzerland</affiliation></author><author xml:id="author-2"><persName><forename type="first">Michael.</forename><surname>Eid</surname></persName><affiliation>University of Geneva, Switzerland</affiliation></author><author xml:id="author-3"><persName><forename type="first">Tanja.</forename><surname>Lischetzke</surname></persName><affiliation>University of Geneva, Switzerland</affiliation></author></analytic><monogr><title level="j">British Journal of Mathematical and Statistical Psychology</title><idno type="pISSN">0007-1102</idno><idno type="eISSN">2044-8317</idno><idno type="DOI">10.1111/(ISSN)2044-8317</idno><imprint><publisher>Blackwell Publishing Ltd</publisher><pubPlace>Oxford, UK</pubPlace><date type="published" when="2006-05"></date><biblScope unit="volume">59</biblScope><biblScope unit="issue">1</biblScope><biblScope unit="page" from="195">195</biblScope><biblScope unit="page" to="213">213</biblScope></imprint></monogr><idno type="istex">58486F3DD5F805F9F368E8D7D2B36C0BD14408A7</idno><idno type="DOI">10.1348/000711005X67490</idno><idno type="ArticleID">BMSP171</idno></biblStruct></sourceDesc></fileDesc><profileDesc><creation><date>2006</date></creation><langUsage><language ident="en">en</language></langUsage><abstract xml:lang="en"><p>Convergent and discriminant validity of psychological constructs can best be examined in the framework of multitrait–multimethod (MTMM) analysis. To gain information at the level of single items, MTMM models for categorical variables have to be applied. The CTC(M−1) model is presented as an example of an MTMM model for ordinal variables. Based on an empirical application of the CTC(M−1) model, a complex simulation study was conducted to examine the sample size requirements of the robust weighted least squares mean‐ and variance‐adjusted χ2 test of model fit (WLSMV estimator) implemented in Mplus. In particular, the simulation study analysed the χ2 approximation, the parameter estimation bias, the standard error bias, and the reliability of the WLSMV estimator depending on the varying number of items per trait–method unit (ranging from 2 to 8) and varying sample sizes (250, 500, 750, and 1000 observations). The results showed that the WLSMV estimator provided a good – albeit slightly liberal – χ2 approximation and stable and reliable parameter estimates for models of reasonable complexity (2–4 items) and small sample sizes (at least 250 observations). When more complex models with 5 or more items were analysed, larger sample sizes of at least 500 observations were needed. The most complex model with 9 trait–method units and 8 items (72 observed variables) requires sample sizes of at least 1000 observations.</p></abstract></profileDesc><revisionDesc><change when="2006-05">Published</change></revisionDesc></teiHeader></istex:fulltextTEI><json:item><extension>txt</extension><original>false</original><mimetype>text/plain</mimetype><uri>https://api.istex.fr/document/58486F3DD5F805F9F368E8D7D2B36C0BD14408A7/fulltext/txt</uri></json:item></fulltext><metadata><istex:metadataXml wicri:clean="Wiley, elements deleted: body"><istex:xmlDeclaration>version="1.0" encoding="UTF-8" standalone="yes"</istex:xmlDeclaration><istex:document><component version="2.0" type="serialArticle" xml:lang="en"><header><publicationMeta level="product"><publisherInfo><publisherName>Blackwell Publishing Ltd</publisherName><publisherLoc>Oxford, UK</publisherLoc></publisherInfo><doi origin="wiley" registered="yes">10.1111/(ISSN)2044-8317</doi><issn type="print">0007-1102</issn><issn type="electronic">2044-8317</issn><idGroup><id type="product" value="BMSP"></id><id type="publisherDivision" value="ST"></id></idGroup><titleGroup><title type="main" sort="BRITISH JOURNAL OF MATHEMATICAL AND STATISTICAL PSYCHOLOGY">British Journal of Mathematical and Statistical Psychology</title></titleGroup></publicationMeta><publicationMeta level="part" position="05101"><doi origin="wiley">10.1111/bmsp.2006.59.issue-1</doi><numberingGroup><numbering type="journalVolume" number="59">59</numbering><numbering type="journalIssue" number="1">1</numbering></numberingGroup><coverDate startDate="2006-05">May 2006</coverDate></publicationMeta><publicationMeta level="unit" type="article" position="11" status="forIssue"><doi origin="wiley">10.1348/000711005X67490</doi><idGroup><id type="unit" value="BMSP171"></id></idGroup><countGroup><count type="pageTotal" number="19"></count></countGroup><titleGroup><title type="tocHeading1">Article</title></titleGroup><copyright>2006 The British Psychological Society</copyright><eventGroup><event type="xmlConverted" agent="Converter:BPG_TO_WML3G version:2.4.2 mode:FullText" date="2010-12-21"></event><event type="firstOnline" date="2010-12-24"></event><event type="publishedOnlineFinalForm" date="2010-12-24"></event><event type="xmlConverted" agent="Converter:WILEY_ML3G_TO_WILEY_ML3GV2 version:3.8.8" date="2014-01-08"></event><event type="xmlConverted" agent="Converter:WML3G_To_WML3G version:4.1.7 mode:FullText,remove_FC" date="2014-10-15"></event></eventGroup><numberingGroup><numbering type="pageFirst" number="195">195</numbering><numbering type="pageLast" number="213">213</numbering></numberingGroup><correspondenceTo> Correspondence should be addressed to Fridtjof W. Nussbeck, Faculty of Psychology and Educational Sciences, University of Geneva, 40 Boulevard du Pont d'Arve, CH‐1211 Geneva 4, Switzerland (e‐mail: <email>fridtjof.nussbeck@pse.unige.ch</email>).</correspondenceTo><linkGroup><link type="toTypesetVersion" href="file:BMSP.BMSP171.pdf"></link></linkGroup></publicationMeta><contentMeta><unparsedEditorialHistory>Received 27 May 2003; revised version received 2 June 2005</unparsedEditorialHistory><countGroup><count type="figureTotal" number="2"></count><count type="tableTotal" number="6"></count><count type="formulaTotal" number="0"></count><count type="referenceTotal" number="32"></count><count type="linksCrossRef" number="84"></count></countGroup><titleGroup><title type="main">Analysing multitrait–multimethod data with structural equation models for ordinal variables applying the WLSMV estimator: What sample size is needed for valid results?</title></titleGroup><creators><creator creatorRole="author" xml:id="cr1" affiliationRef="#a1" corresponding="yes"><personName><givenNames>Fridtjof W.</givenNames><familyName>Nussbeck</familyName></personName></creator><creator creatorRole="author" xml:id="cr2" affiliationRef="#a1"><personName><givenNames>Michael.</givenNames><familyName>Eid</familyName></personName></creator><creator creatorRole="author" xml:id="cr3" affiliationRef="#a1"><personName><givenNames>Tanja.</givenNames><familyName>Lischetzke</familyName></personName></creator></creators><affiliationGroup><affiliation xml:id="a1" countryCode="CH"><unparsedAffiliation>University of Geneva, Switzerland</unparsedAffiliation></affiliation></affiliationGroup><abstractGroup><abstract type="main" xml:lang="en"><p>Convergent and discriminant validity of psychological constructs can best be examined in the framework of multitrait–multimethod (MTMM) analysis. To gain information at the level of single items, MTMM models for categorical variables have to be applied. The CTC(M−1) model is presented as an example of an MTMM model for ordinal variables. Based on an empirical application of the CTC(M−1) model, a complex simulation study was conducted to examine the sample size requirements of the robust weighted least squares mean‐ and variance‐adjusted <i>χ</i><sup>2</sup> test of model fit (WLSMV estimator) implemented in Mplus. In particular, the simulation study analysed the <i>χ</i><sup>2</sup> approximation, the parameter estimation bias, the standard error bias, and the reliability of the WLSMV estimator depending on the varying number of items per trait–method unit (ranging from 2 to 8) and varying sample sizes (250, 500, 750, and 1000 observations). The results showed that the WLSMV estimator provided a good – albeit slightly liberal – <i>χ</i><sup>2</sup> approximation and stable and reliable parameter estimates for models of reasonable complexity (2–4 items) and small sample sizes (at least 250 observations). When more complex models with 5 or more items were analysed, larger sample sizes of at least 500 observations were needed. The most complex model with 9 trait–method units and 8 items (72 observed variables) requires sample sizes of at least 1000 observations.</p></abstract></abstractGroup></contentMeta></header></component></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>Analysing multitrait–multimethod data with structural equation models for ordinal variables applying the WLSMV estimator: What sample size is needed for valid results?</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>Analysing multitrait–multimethod data with structural equation models for ordinal variables applying the WLSMV estimator: What sample size is needed for valid results?</title></titleInfo><name type="personal"><namePart type="given">Fridtjof W.</namePart><namePart type="family">Nussbeck</namePart><affiliation>University of Geneva, Switzerland</affiliation><affiliation>E-mail: fridtjof.nussbeck@pse.unige.ch</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Michael.</namePart><namePart type="family">Eid</namePart><affiliation>University of Geneva, Switzerland</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Tanja.</namePart><namePart type="family">Lischetzke</namePart><affiliation>University of Geneva, Switzerland</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="article" displayLabel="article"></genre><originInfo><publisher>Blackwell Publishing Ltd</publisher><place><placeTerm type="text">Oxford, UK</placeTerm></place><dateIssued encoding="w3cdtf">2006-05</dateIssued><edition>Received 27 May 2003; revised version received 2 June 2005</edition><copyrightDate encoding="w3cdtf">2006</copyrightDate></originInfo><language><languageTerm type="code" authority="rfc3066">en</languageTerm><languageTerm type="code" authority="iso639-2b">eng</languageTerm></language><physicalDescription><internetMediaType>text/html</internetMediaType><extent unit="figures">2</extent><extent unit="tables">6</extent><extent unit="references">32</extent></physicalDescription><abstract lang="en">Convergent and discriminant validity of psychological constructs can best be examined in the framework of multitrait–multimethod (MTMM) analysis. To gain information at the level of single items, MTMM models for categorical variables have to be applied. The CTC(M−1) model is presented as an example of an MTMM model for ordinal variables. Based on an empirical application of the CTC(M−1) model, a complex simulation study was conducted to examine the sample size requirements of the robust weighted least squares mean‐ and variance‐adjusted χ2 test of model fit (WLSMV estimator) implemented in Mplus. In particular, the simulation study analysed the χ2 approximation, the parameter estimation bias, the standard error bias, and the reliability of the WLSMV estimator depending on the varying number of items per trait–method unit (ranging from 2 to 8) and varying sample sizes (250, 500, 750, and 1000 observations). The results showed that the WLSMV estimator provided a good – albeit slightly liberal – χ2 approximation and stable and reliable parameter estimates for models of reasonable complexity (2–4 items) and small sample sizes (at least 250 observations). When more complex models with 5 or more items were analysed, larger sample sizes of at least 500 observations were needed. The most complex model with 9 trait–method units and 8 items (72 observed variables) requires sample sizes of at least 1000 observations.</abstract><relatedItem type="host"><titleInfo><title>British Journal of Mathematical and Statistical Psychology</title></titleInfo><genre type="journal">journal</genre><identifier type="ISSN">0007-1102</identifier><identifier type="eISSN">2044-8317</identifier><identifier type="DOI">10.1111/(ISSN)2044-8317</identifier><identifier type="PublisherID">BMSP</identifier><part><date>2006</date><detail type="volume"><caption>vol.</caption><number>59</number></detail><detail type="issue"><caption>no.</caption><number>1</number></detail><extent unit="pages"><start>195</start><end>213</end><total>19</total></extent></part></relatedItem><identifier type="istex">58486F3DD5F805F9F368E8D7D2B36C0BD14408A7</identifier><identifier type="DOI">10.1348/000711005X67490</identifier><identifier type="ArticleID">BMSP171</identifier><accessCondition type="use and reproduction" contentType="copyright">2006 The British Psychological Society</accessCondition><recordInfo><recordContentSource>WILEY</recordContentSource><recordOrigin>Blackwell Publishing Ltd</recordOrigin></recordInfo></mods></metadata><serie></serie></istex></record>Pour manipuler ce document sous Unix (Dilib)
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