5. Three Likelihood-Based Methods for Mean and Covariance Structure Analysis with Nonnormal Missing Data

Sociological Methodology - Tập 30 Số 1 - Trang 165-200 - 2000
Ke‐Hai Yuan1, Peter M. Bentler2
1University of North Texas,
2University of California, Los Angeles

Tóm tắt

Survey and longitudinal studies in the social and behavioral sciences generally contain missing data. Mean and covariance structure models play an important role in analyzing such data. Two promising methods for dealing with missing data are a direct maximum-likelihood and a two-stage approach based on the unstructured mean and covariance estimates obtained by the EM-algorithm. Typical assumptions under these two methods are ignorable nonresponse and normality of data. However, data sets in social and behavioral sciences are seldom normal, and experience with these procedures indicates that normal theory based methods for nonnormal data very often lead to incorrect model evaluations. By dropping the normal distribution assumption, we develop more accurate procedures for model inference. Based on the theory of generalized estimating equations, a way to obtain consistent standard errors of the two-stage estimates is given. The asymptotic efficiencies of different estimators are compared under various assumptions. We also propose a minimum chi-square approach and show that the estimator obtained by this approach is asymptotically at least as efficient as the two likelihood-based estimators for either normal or nonnormal data. The major contribution of this paper is that for each estimator, we give a test statistic whose asymptotic distribution is chisquare as long as the underlying sampling distribution enjoys finite fourth-order moments. We also give a characterization for each of the two likelihood ratio test statistics when the underlying distribution is nonnormal. Modifications to the likelihood ratio statistics are also given. Our working assumption is that the missing data mechanism is missing completely at random. Examples and Monte Carlo studies indicate that, for commonly encountered nonnormal distributions, the procedures developed in this paper are quite reliable even for samples with missing data that are missing at random.

Từ khóa


Tài liệu tham khảo

10.2307/271029

10.1214/aos/1176347760

10.1080/01621459.1957.10501379

10.1214/aos/1176350834

Arbuckle James L., 1996, Advanced Structural Equation Modeling: Issues and Techniques, 243

10.1007/BF02294626

10.1080/01621459.1990.10475326

10.1111/j.2517-6161.1975.tb01037.x

10.1007/BF02293875

Bentler Peter M., 1995, EQS Structural Equations Program Manual

Bentler Peter M., EQS 6 Structural Equations Program Manual

Bentler Peter M., 1985, Multivariate Analysis VI, 9

10.1207/S15327906Mb340203

10.1002/9781118619179

Bollen Kenneth A., 1993, Testing Structural Equation Models, 111

10.1007/BF02294022

10.1080/10705519409539983

10.1111/j.2044-8317.1984.tb00789.x

10.1093/biomet/74.2.375

10.1007/978-1-4899-1292-3_4

10.1111/j.2044-8317.1988.tb00896.x

10.1037/1082-989X.1.1.16

10.1111/j.2517-6161.1977.tb01600.x

Dijkstra Theo K., 1981, Latent Variables in Linear Stochastic Models: Reflections on “Maximum Likelihood” and “Partial Least Squares” Methods

10.1007/978-1-4899-2937-2

10.1007/978-1-4899-4549-5

10.1007/BF02296204

10.1093/oso/9780198522287.003.0001

10.2307/1913471

10.1037/0033-2909.112.2.351

10.3102/10769986024001021

Jöreskog Karl G., 1993, LISREL 8 User's Reference Guide

10.1007/BF02869518

Kline Rex B., 1998, Principles and Practice of Structural Equation Modeling

10.1002/sim.4780070131

Lange Kenneth L., 1989, Journal of the American Statistical Association, 84, 881

10.1007/BF02294002

10.1093/biomet/73.1.13

10.2307/2347491

Little Roderick J.A., 1987, Statistical Analysis with Missing Data

10.2307/2531754

Mardia Kanti V., 1979, Multivariate Analysis

10.1080/10705519809540087

10.1214/ss/1177010269

Meng Xiao-Li, Pedlow Steven. 1992. “EM: A Bibliographic Review with Missing Articles.” Pp. 24–27 in Statistical Computing Section, Proceedings of the American Statistical Association.

10.1037/0033-2909.105.1.156

10.1111/j.1467-9574.1991.tb01301.x

10.1007/978-1-4612-3974-1

10.1002/9780470316559

10.1093/biomet/67.1.31

10.1007/BF02294365

Muthén Linda, 1998, Mplus User's Guide

Neale Michael C., 1994, “Mx: Statistical Modeling,”, 2

10.1214/lnms/1215463784

10.2307/2533454

Rovine Michael J., 1994, Latent Variables Analysis: Applications for Developmental Research, 181

10.1002/9780470316696

10.1080/01621459.1996.10476908

Satorra Albert, Bentler Peter M. 1988. “Scaling Corrections for Chi-Square Statistics in Covariance Structure Analysis.” Pp. 308–13 in American Statistical Association 1988 Proceedings of Business and Economics Sections. Alexandria, VA: American Statistical Association.

10.1016/0167-9473(90)90004-2

Satorra Albert, 1991, Applied Stochastic Models and Data Analysis, 555

Satorra Albert, 1994, Latent Variables Analysis: Applications for Developmental Research, 399

10.1201/9781439821862

Schoenberg Ronald, 1989, LINCS: Linear Covariance Structure Analysis. User's Guide

Shapiro Alexander, 1983, South African Statistical Journal, 17, 33

Shapiro Alexander, 1987, South African Statistical Journal, 21, 39

10.1080/01621459.1987.10478544

10.1080/03610929108830742

10.1515/9783110916690-024

10.1080/01621459.1997.10474029

10.1016/S0167-9473(97)00025-X

10.1111/j.2044-8317.1998.tb00682.x

Yuan Ke-Hai, 1999, Statistica Sinica, 9, 831

10.1006/jmva.1997.1731

Yung Yiu-Fai, 1996, Advanced Structural Equation Modeling Techniques, 195

Thông tin
Thông tin xuất bản

Sociological Methodology

Tập 30 Số 1

165-200

Thông tin tác giả