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ML Estimation of Mean and Covariance Structures with Missing Data Using Complete Data Routines

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  • Mortaza Jamshidian
  • Peter M. Bentler

Abstract

We consider maximum likelihood (ML) estimation of mean and covariance structure models when data are missing. Expectation maximization (EM), generalized expectation maximization (GEM), Fletcher-Powell, and Fisher-scoring algorithms are described for parameter estimation. It is shown how the machinery within a software that handles the complete data problem can be utilized to implement each algorithm. A numerical differentiation method for obtaining the observed information matrix and the standard errors is given. This method also uses the complete data program machinery. The likelihood ratio test is discussed for testing hypotheses. Three examples are used to compare the cost of the four algorithms mentioned above, as well as to illustrate the standard error estimation and the test of hypothesis considered. The sensitivity of the ML estimates as well as the mean imputed and listwise deletion estimates to missing data mechanisms is investigated using three artificial data sets that are missing completely at random (MCAR), missing at random (MAR), and neither MCAR nor MAR.

Suggested Citation

  • Mortaza Jamshidian & Peter M. Bentler, 1999. "ML Estimation of Mean and Covariance Structures with Missing Data Using Complete Data Routines," Journal of Educational and Behavioral Statistics, , vol. 24(1), pages 21-24, March.
    • Handle: RePEc:sae:jedbes:v:24:y:1999:i:1:p:21-24
    DOI: 10.3102/10769986024001021
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    Cited by:

    1. Sik-Yum Lee, 2006. "Bayesian Analysis of Nonlinear Structural Equation Models with Nonignorable Missing Data," Psychometrika, Springer;The Psychometric Society, vol. 71(3), pages 541-564, September.
    2. Mortaza Jamshidian & Siavash Jalal, 2010. "Tests of Homoscedasticity, Normality, and Missing Completely at Random for Incomplete Multivariate Data," Psychometrika, Springer;The Psychometric Society, vol. 75(4), pages 649-674, December.
    3. Xin-Yuan Song & Sik-Yum Lee, 2002. "Analysis of structural equation model with ignorable missing continuous and polytomous data," Psychometrika, Springer;The Psychometric Society, vol. 67(2), pages 261-288, June.
    4. Erik Meijer & Arie Kapteyn & Tatiana Andreyeva, 2008. "Health Indexes and Retirement Modeling in International Comparisons," Working Papers 614, RAND Corporation.
    5. Jamshidian, Mortaza & Jalal, Siavash & Jansen, Camden, 2014. "MissMech: An R Package for Testing Homoscedasticity, Multivariate Normality, and Missing Completely at Random (MCAR)," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 56(i06).
    6. Erik Meijer & Arie Kapteyn & Tatiana Andreyeva, 2008. "Health Indexes and Retirement Modeling in International Comparisons," Working Papers WR-614, RAND Corporation.

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