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ERIC Number: EJ901767
Record Type: Journal
Publication Date: 2010-Jun
Pages: 29
Abstractor: As Provided
Reference Count: 70
ISSN: ISSN-1076-9986
Metropolis-Hastings Robbins-Monro Algorithm for Confirmatory Item Factor Analysis
Cai, Li
Journal of Educational and Behavioral Statistics, v35 n3 p307-335 Jun 2010
Item factor analysis (IFA), already well established in educational measurement, is increasingly applied to psychological measurement in research settings. However, high-dimensional confirmatory IFA remains a numerical challenge. The current research extends the Metropolis-Hastings Robbins-Monro (MH-RM) algorithm, initially proposed for exploratory IFA, to the case of maximum likelihood estimation under user-defined linear restrictions for confirmatory IFA. MH-RM naturally integrates concepts such as the missing data formulation, data augmentation, the Metropolis algorithm, and stochastic approximation. In a limited simulation study, the accuracy of the MH-RM algorithm is checked against the standard Bock-Aitkin expectation-maximization (EM) algorithm. To demonstrate the efficiency and flexibility of the MH-RM algorithm, it is applied to the IFA of real data from pediatric quality-of-life (QOL) research in comparison with adaptive quadrature-based EM algorithm. The particular data set required a confirmatory item factor model with eight factors and a variety of equality and fixing constraints to implement the hypothesized factor pattern. MH-RM converged in less than 3 minutes to the maximum likelihood solution while the EM algorithm spent well over 4 hours. (Contains 7 tables and 1 figure.)
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Publication Type: Journal Articles; Reports - Research
Education Level: Elementary Secondary Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A