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Factor Analysis for Categorical Data
Abstract
Summary: The method of factor analysis is widely used as an exploratory tool to reduce the dimensionality of multivariate data. The fact that the standard model is strictly applicable only when the manifest variables are scaled is a serious limitation in social science where the variables are often categorical. In this paper we aim to provide a theoretical framework within which methods for the factor analysis of categorical data can be devised and compared. Discussion is restricted to the case of ordered categories where the latent variables are continuous. It is argued that the choice of model should be made from a restricted set which includes two existing models as special cases. A new method is proposed together with a simple approximate technique of fitting for the one-factor model. The paper concludes with an evaluation of existing methods and makes some suggestions about the direction which future research should take.
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Citations
Cited by
A Beginner’s Guide to Factor Analysis: Focusing on Exploratory Factor Analysis
Yong, A. G., & Pearce, S. (2013) · Tutorials in Quantitative Methods for Psychology · doi:10.20982/tqmp.09.2.p079 · Cited by 3,304
“Analysis for Categorical Data’ by Bartholomew (1980) for further explanation.”
MethodMarginal Maximum Likelihood Estimation of Item Parameters: Application of an EM Algorithm
Bock, R. D., & Aitkin, M. (1981) · Psychometrika · doi:10.1007/bf02293801 · Cited by 2,339
Regression and ordered categorical variables
Anderson, J. A. (1984) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1984.tb01270.x · Cited by 574
TECHNICAL GUIDELINES FOR ASSESSING COMPUTERIZED ADAPTIVE TESTS
GREEN, B. F., BOCK, R. D., HUMPHREYS, L. G., LINN, R. L., & RECKASE, M. D. (1984) · Journal of Educational Measurement · doi:10.1111/j.1745-3984.1984.tb01039.x · Cited by 383
Full-Information Item Bifactor Analysis of Graded Response Data
Gibbons, R. D., Bock, R. D., Hedeker, D., Weiss, D. J., Segawa, E., Bhaumik, D. K., Kupfer, D. J., Frank, E., Grochocinski, V. J., & Stover, A. (2007) · Applied Psychological Measurement · doi:10.1177/0146621606289485 · Cited by 269
Metadata
- Authors
- Bartholomew, D. J.
- Venue
- Journal of the Royal Statistical Society Series B: Statistical Methodology
- Publisher
- Oxford University Press (OUP)
- Published
- 1980-07-01
- Volume
- 42
- Issue
- 3
- Pages
- 293-312
- ISSN
- 1369-7412 (ISSN-L)
- 1467-9868
- OpenAlex
- W2904926823
- Cited by
- 192
- References
- 0
- FWCI
- 6.38
- Type
- journal article
- Language
- en
- Open access
- closed
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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