×

Maximum likelihood and generalized least squares analyses of two level structural equation models. (English) Zbl 0761.62102

Summary: A two-level structural equation model with small level-one samples and unbalanced designs is treated. Under the assumption of normality, the maximum likelihood and generalized least squares methods are employed to analyze the model. Asymptotic properties of the estimators are discussed. Results of a Monte Carlo study investigating the performance of the estimators are reported.

MSC:

62J99 Linear inference, regression
62F12 Asymptotic properties of parametric estimators
62H12 Estimation in multivariate analysis
Full Text: DOI

References:

[1] Afifi, A. A.; Elashoff, R. M., Missing observations in multivariate statistics - III: Large sample analysis of simple linear regression, J. Amer. Statist. Assoc., 64, 359-365 (1969) · Zbl 0175.17103
[2] Aitkin, M.; Anderson, D.; Hinde, J., Statistical modelling of data on teaching styles (with discussion), J. Roy. Statist. Soc. Ser. A, 144, 419-461 (1981)
[3] Aitkin, M.; Longford, N., Statistical modelling issues in school effectiveness studies, J. Roy. Statist. Soc. Ser. A, 149, 1-43 (1986)
[4] Bentler, P. M., Multivariate analysis with latent variables: Causal modeling, Ann. Rev. Psych., 31, 419-456 (1980)
[5] Bentler, P. M.; Lee, S. Y., Matrix derivatives with chain rule and rules for simple, Hadamand, and Kronecker products, J. Math. Psych., 17, 255-262 (1978) · Zbl 0382.62092
[6] Bock, D., Multilevel Analysis of Educational Data (1989), Academic Press: Academic Press New York
[7] Browne, M. W., Generalized least squares estimators in the analysis of covariance structures, South African Statist. J., 8, 1-24 (1974) · Zbl 0281.62071
[8] Goldstein, H. I., Multilevel Models in Educational and Social Research (1987), Oxford University Press: Oxford University Press Oxford
[9] Goldstein, H.; McDonald, R. P., A general model for analysis of multilevel data, Psychometrika, 53, 455-468 (1988) · Zbl 0718.62158
[10] FORTRAN Subroutines for Statistical Analysis (1987), (Houston, TX)
[11] Jöreskog, K. G., A general method for analysis of covariance structures, Biometrika, 57, 239-251 (1970) · Zbl 0195.48801
[12] Jöreskog, K. G., Structural analysis of covariance and correlation matrices, Psychometrika, 43, 443-447 (1978) · Zbl 0392.62043
[13] Lawley, D. N.; Maxwell, A. E., Factor Analysis as a Statistical Method (1971), Butterworths: Butterworths London · Zbl 0251.62042
[14] Lee, S. Y., Multilevel analysis of structural equation models, Biometrika, 77, 763-772 (1990) · Zbl 0711.62045
[15] Lee, S. Y.; Jennrich, R. I., A study of algorithms for covariance structure analysis with specific comparisons using factor analysis, Psychometrika, 43, 99-113 (1979) · Zbl 0419.62052
[16] McDonald, R. P., A simple comprehensive model for the analysis of covariance structures: Some remarks on applications, British J. Math. Statist. Psych., 33, 161-183 (1980) · Zbl 0439.62054
[17] McDonald, R. P.; Goldstein, H., Balanced versus unbalanced designs for linear structural relations in two-level data, British J. Math. Statist. Psych., 42, 215-232 (1989) · Zbl 0718.62168
[18] McDonald, R. P.; Swaminathan, H. A., A simple matrix calculus with application to multivariate analysis, Gen. Syst., 18, 37-54 (1973)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.