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Some Aspects on Confirmatory Factor Analysis of Ordinal Variables and Generating Non-normal Data
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics.
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 [en]
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: urn:nbn:se:uu:diva-149423ISBN: 978-91-554-8035-6OAI: oai:DiVA.org:uu-149423DiVA: diva2:405108
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
List of papers
1. Confirmatory Factor Analysis of Ordinal Variables With Misspecified Models
Open this publication in new window or tab >>Confirmatory Factor Analysis of Ordinal Variables With Misspecified Models
2010 (English)In: Structural Equation Modeling, ISSN 1070-5511, E-ISSN 1532-8007, Vol. 17, no 3, 392-423 p.Article in journal (Refereed) Published
Abstract [en]

Ordinal variables are common in many empirical investigations in the social and behavioral sciences. Researchers often apply the maximum likelihood method to fit structural equation models to ordinal data. This assumes that the observed measures have normal distributions, which is not the case when the variables are ordinal. A better approach is to use polychoric correlations and fit the models using methods such as unweighted least squares (ULS), maximum likelihood (ML), weighted least squares (WLS), or diagonally weighted least squares (DWLS). In this simulation evaluation we study the behavior of these methods in combination with polychoric correlations when the models are misspecified. We also study the effect of model size and number of categories on the parameter estimates, their standard errors, and the common chi-square measures of fit when the models are both correct and misspecified. When used routinely, these methods give consistent parameter estimates but ULS, ML, and DWLS give incorrect standard errors. Correct standard errors can be obtained for these methods by robustification using an estimate of the asymptotic covariance matrix W of the polychoric correlations. When used in this way the methods are here called RULS, RML, and RDWLS.

Place, publisher, year, edition, pages
Taylor&Francis Group, 2010
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
urn:nbn:se:uu:diva-131973 (URN)10.1080/10705511.2010.489003 (DOI)000279721100003 ()
Available from: 2010-10-13 Created: 2010-10-12 Last updated: 2011-05-05Bibliographically approved
2. Analysis of Ordinal Variables Using Rank-Based Polychoric Correlation
Open this publication in new window or tab >>Analysis of Ordinal Variables Using Rank-Based Polychoric Correlation
(English)Manuscript (preprint) (Other academic)
Identifiers
urn:nbn:se:uu:diva-149417 (URN)
Available from: 2011-03-19 Created: 2011-03-19 Last updated: 2011-10-31
3. The Effect of Pooling Multi-Group Data on the Estimation of Factor Loadings
Open this publication in new window or tab >>The Effect of Pooling Multi-Group Data on the Estimation of Factor Loadings
(English)Manuscript (preprint) (Other academic)
Identifiers
urn:nbn:se:uu:diva-149418 (URN)
Available from: 2011-03-19 Created: 2011-03-19 Last updated: 2011-05-05
4.
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5. An Evaluation of Algorithms on Generating Multivariate Non-normal Data
Open this publication in new window or tab >>An Evaluation of Algorithms on Generating Multivariate Non-normal Data
(English)Manuscript (preprint) (Other academic)
Identifiers
urn:nbn:se:uu:diva-149420 (URN)
Available from: 2011-03-19 Created: 2011-03-19 Last updated: 2011-05-05

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