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Limited information estimation in binary factor analysis: A review and extension

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  • Wu, Jianmin
  • Bentler, Peter M.
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    Abstract

    Based on the Bayes modal estimate of factor scores in binary latent variable models, this paper proposes two new limited information estimators for the factor analysis model with a logistic link function for binary data based on Bernoulli distributions up to the second and the third order with maximum likelihood estimation and Laplace approximations to required integrals. These estimators and two existing limited information weighted least squares estimators are studied empirically. The limited information estimators compare favorably to full information estimators based on marginal maximum likelihood, MCMC, and multinomial distribution with a Laplace approximation methodology. Among the various estimators, Maydeu-Olivares and Joe’s (2005) weighted least squares limited information estimators implemented with Laplace approximations for probabilities are shown in a simulation to have the best root mean square errors.

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    Bibliographic Info

    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 57 (2013)
    Issue (Month): 1 ()
    Pages: 392-403

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    Handle: RePEc:eee:csdana:v:57:y:2013:i:1:p:392-403

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    Web page: http://www.elsevier.com/locate/csda

    Related research

    Keywords: Limited information; Laplace approximation; Binary response; Marginal likelihood; Factor scores;

    References

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    1. Anders Christoffersson, 1975. "Factor analysis of dichotomized variables," Psychometrika, Springer, vol. 40(1), pages 5-32, March.
    2. Anders Skrondal & Petter Laake, 2001. "Regression among factor scores," Psychometrika, Springer, vol. 66(4), pages 563-575, December.
    3. Mark Reiser, 1996. "Analysis of residuals for the multionmial item response model," Psychometrika, Springer, vol. 61(3), pages 509-528, September.
    4. Youngjo Lee & John A. Nelder, 2006. "Double hierarchical generalized linear models (with discussion)," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 55(2), pages 139-185.
    5. R. Bock & Murray Aitkin, 1981. "Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm," Psychometrika, Springer, vol. 46(4), pages 443-459, December.
    6. Joe, Harry, 2008. "Accuracy of Laplace approximation for discrete response mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5066-5074, August.
    7. Wu, Jianmin & Bentler, Peter M., 2012. "Application of H-likelihood to factor analysis models with binary response data," Journal of Multivariate Analysis, Elsevier, vol. 106(C), pages 72-79.
    8. Teugels, Jozef L, 1990. "Some representations of the multivariate Bernoulli and binomial distributions," Journal of Multivariate Analysis, Elsevier, vol. 32(2), pages 256-268, February.
    9. Harry Joe & Alberto Maydeu-Olivares, 2010. "A General Family of Limited Information Goodness-of-Fit Statistics for Multinomial Data," Psychometrika, Springer, vol. 75(3), pages 393-419, September.
    10. An, Xinming & Bentler, Peter M., 2012. "Efficient direct sampling MCEM algorithm for latent variable models with binary responses," Computational Statistics & Data Analysis, Elsevier, vol. 56(2), pages 231-244.
    11. Stephen Schilling & R. Bock, 2005. "High-dimensional maximum marginal likelihood item factor analysis by adaptive quadrature," Psychometrika, Springer, vol. 70(3), pages 533-555, September.
    12. Philippe Huber & Elvezio Ronchetti & Maria-Pia Victoria-Feser, 2004. "Estimation of generalized linear latent variable models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(4), pages 893-908.
    13. Yun, Sungcheol & Lee, Youngjo, 2004. "Comparison of hierarchical and marginal likelihood estimators for binary outcomes," Computational Statistics & Data Analysis, Elsevier, vol. 45(3), pages 639-650, April.
    14. Alberto Maydeu, 2003. "Limited Information Estimation and Testing of Discretized Multivariate Normal Structural Models," Working Papers Economia wp03-03, Instituto de Empresa, Area of Economic Environment.
    15. Maydeu-Olivares, Albert & Joe, Harry, 2005. "Limited- and Full-Information Estimation and Goodness-of-Fit Testing in 2n Contingency Tables: A Unified Framework," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1009-1020, September.
    16. Roderick McDonald & E. Burr, 1967. "A comparison of four methods of constructing factor scores," Psychometrika, Springer, vol. 32(4), pages 381-401, December.
    17. Yanyan Sheng, . "A MATLAB Package for Markov Chain Monte Carlo with a Multi-Unidimensional IRT Model," Journal of Statistical Software, American Statistical Association, vol. 28(i10).
    18. Albert Maydeu-Olivares, 2001. "Limited information estimation and testing of Thurstonian models for paired comparison data under multiple judgment sampling," Psychometrika, Springer, vol. 66(2), pages 209-227, June.
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