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Approximated Penalized Maximum Likelihood for Exploratory Factor Analysis: A Simulation Study of an Orthogonal Case
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)
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:uu:diva-247288OAI: oai:DiVA.org:uu-247288DiVA: diva2:795660
Available from: 2015-03-17 Created: 2015-03-17 Last updated: 2015-07-07
In thesis
1. Essays on Estimation Methods for Factor Models and Structural Equation Models
Open this publication in new window or tab >>Essays on Estimation Methods for Factor Models and Structural Equation Models
2015 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis which consists of four papers is concerned with estimation methods in factor analysis and structural equation models. New estimation methods are proposed and investigated.

In paper I an approximation of the penalized maximum likelihood (ML) is introduced to fit an exploratory factor analysis model. Approximated penalized ML continuously and efficiently shrinks the factor loadings towards zero. It naturally factorizes a covariance matrix or a correlation matrix. It is also applicable to an orthogonal or an oblique structure.

Paper II, a simulation study, investigates the properties of approximated penalized ML with an orthogonal factor model. Different combinations of penalty terms and tuning parameter selection methods are examined. Differences in factorizing a covariance matrix and factorizing a correlation matrix are also explored. It is shown that the approximated penalized ML frequently improves the traditional estimation-rotation procedure.

In Paper III we focus on pseudo ML for multi-group data. Data from different groups are pooled and normal theory is used to fit the model. It is shown that pseudo ML produces consistent estimators of factor loadings and that it is numerically easier than multi-group ML. In addition, normal theory is not applicable to estimate standard errors. A sandwich-type estimator of standard errors is derived.

Paper IV examines properties of the recently proposed polychoric instrumental variable (PIV) estimators for ordinal data through a simulation study. PIV is compared with conventional estimation methods (unweighted least squares and diagonally weighted least squares). PIV produces accurate estimates of factor loadings and factor covariances in the correctly specified confirmatory factor analysis model and accurate estimates of loadings and coefficient matrices in the correctly specified structure equation model. If the model is misspecified, robustness of PIV depends on model complexity, underlying distribution, and instrumental variables.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2015. 29 p.
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Social Sciences, ISSN 1652-9030 ; 111
Keyword
shrinkage, factor rotation, penalized maximum likelihood, pseudo-maximum likelihood, multi-group analysis, ordinal data, robustness
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
urn:nbn:se:uu:diva-247292 (URN)978-91-554-9199-4 (ISBN)
Public defence
2015-05-08, Hörsal 2, Ekonomikum, Kyrkogårdsgatan 10, Uppsala, 10:15 (English)
Opponent
Supervisors
Available from: 2015-04-16 Created: 2015-03-17 Last updated: 2015-07-07

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