uu.seUppsala University Publications
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Analysis of Ordinal Variables Using Rank-Based Polychoric Correlation
Uppsala University, Disciplinary Domain of Humanities and Social Sciences. Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics.
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics.
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics.
(English)Manuscript (preprint) (Other academic)
Identifiers
URN: urn:nbn:se:uu:diva-149417OAI: oai:DiVA.org:uu-149417DiVA: diva2:404949
Available from: 2011-03-19 Created: 2011-03-19 Last updated: 2011-10-31
In thesis
1. Some Aspects on Confirmatory Factor Analysis of Ordinal Variables and Generating Non-normal Data
Open this publication in new window or tab >>Some Aspects on Confirmatory Factor Analysis of Ordinal Variables and Generating Non-normal Data
2011 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis, which consists of five papers, is concerned with various aspects of confirmatory factor analysis (CFA) of ordinal variables and the generation of non-normal data.

The first paper studies the performances of different estimation methods used in CFA when ordinal data are encountered.  To take ordinality into account the four estimation methods, i.e., maximum likelihood (ML), unweighted least squares, diagonally weighted least squares, and weighted least squares (WLS), are used in combination with polychoric correlations. The effect of model sizes and number of categories on the parameter estimates, their standard errors, and the common chi-square measure of fit when the models are both correct and misspecified are examined.

The second paper focuses on the appropriate estimator of the polychoric correlation when fitting a CFA model. A non-parametric polychoric correlation coefficient based on the discrete version of Spearman's rank correlation is proposed to contend with the situation of non-normal underlying distributions. The simulation study shows the benefits of using the non-parametric polychoric correlation under conditions of non-normality.

The third paper raises the issue of simultaneous factor analysis. We study the effect of pooling multi-group data on the estimation of factor loadings. Given the same factor loadings but different factor means and correlations, we investigate how much information is lost by pooling the groups together and only estimating the combined data set using the WLS method. The parameter estimates and their standard errors are compared with results obtained by multi-group analysis using ML.

The fourth paper uses a Monte Carlo simulation to assess the reliability of the Fleishman's power method under various conditions of skewness, kurtosis, and sample size. Based on the generated non-normal samples, the power of D'Agostino's (1986) normality test is studied.

The fifth paper extends the evaluation of algorithms to the generation of multivariate non-normal data.  Apart from the requirement of generating reliable skewness and kurtosis, the generated data also need to possess the desired correlation matrices.  Four algorithms are investigated in terms of simplicity, generality, and reliability of the technique.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2011. 21 p.
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Social Sciences, ISSN 1652-9030 ; 66
Keyword
confirmatory factor analysis, ordinal variables, maximum likelihood, weighted least squares, polychoric correlation, non-normal data, Fleishman's method, Monte Carlo simulation
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
urn:nbn:se:uu:diva-149423 (URN)978-91-554-8035-6 (ISBN)
Public defence
2011-05-06, Hörsal 2, Ekonomikum, Kyrkogårdsgatan 10, Uppsala, 13:00 (English)
Opponent
Supervisors
Available from: 2011-04-14 Created: 2011-03-19 Last updated: 2011-05-05Bibliographically approved

Open Access in DiVA

No full text

Authority records BETA

Lyhagen, Johan

Search in DiVA

By author/editor
Lyhagen, Johan
By organisation
Disciplinary Domain of Humanities and Social SciencesDepartment of Statistics

Search outside of DiVA

GoogleGoogle Scholar

urn-nbn

Altmetric score

urn-nbn
Total: 530 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf