A Note on Exploratory Item Factor Analysis by Singular Value Decomposition.
Psychometrika
; 85(2): 358-372, 2020 06.
Article
in En
| MEDLINE
| ID: mdl-32451743
ABSTRACT
We revisit a singular value decomposition (SVD) algorithm given in Chen et al. (Psychometrika 84124-146, 2019b) for exploratory item factor analysis (IFA). This algorithm estimates a multidimensional IFA model by SVD and was used to obtain a starting point for joint maximum likelihood estimation in Chen et al. (2019b). Thanks to the analytic and computational properties of SVD, this algorithm guarantees a unique solution and has computational advantage over other exploratory IFA methods. Its computational advantage becomes significant when the numbers of respondents, items, and factors are all large. This algorithm can be viewed as a generalization of principal component analysis to binary data. In this note, we provide the statistical underpinning of the algorithm. In particular, we show its statistical consistency under the same double asymptotic setting as in Chen et al. (2019b). We also demonstrate how this algorithm provides a scree plot for investigating the number of factors and provide its asymptotic theory. Further extensions of the algorithm are discussed. Finally, simulation studies suggest that the algorithm has good finite sample performance.
Key words
Full text:
1
Collection:
01-internacional
Database:
MEDLINE
Main subject:
Algorithms
Type of study:
Prognostic_studies
Language:
En
Journal:
Psychometrika
Year:
2020
Document type:
Article
Affiliation country:
China
Publication country:
EEUU
/
ESTADOS UNIDOS
/
ESTADOS UNIDOS DA AMERICA
/
EUA
/
UNITED STATES
/
UNITED STATES OF AMERICA
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US
/
USA