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Volumn 22, Issue 1, 1997, Pages 77-108

Hierarchical Linear Models for Multivariate Outcomes

Author keywords

Empirical Bayes; Hierarchical linear models; Individual differences; Maximum likelihood; Missing outcomes; Multilevel data; Multivariate repeated measures; Multivariate two stage models; Quasi Newton; Random effects; Sensitivity; t prior

Indexed keywords


EID: 0642373832     PISSN: 10769986     EISSN: None     Source Type: Journal    
DOI: 10.3102/10769986022001077     Document Type: Article
Times cited : (56)

References (52)
  • 3
    • 0002807578 scopus 로고
    • Addendum - Measurement of human variation: A two-stage model
    • R. D. Bock (Ed.). New York: Academic Press
    • Bock, R. D. (1989). Addendum - Measurement of human variation: A two-stage model. In R. D. Bock (Ed.), Multilevel analysis of educational data (pp. 319-342). New York: Academic Press.
    • (1989) Multilevel Analysis of Educational Data , pp. 319-342
    • Bock, R.D.1
  • 8
    • 0001613054 scopus 로고
    • The multivariate t-distribution associated with a set of normal standard deviates
    • Cornish, E. A. (1954). The multivariate t-distribution associated with a set of normal standard deviates. Australian Journal of Physics, 7, 531-542.
    • (1954) Australian Journal of Physics , vol.7 , pp. 531-542
    • Cornish, E.A.1
  • 9
  • 10
    • 0002428888 scopus 로고
    • Random coefficient models for multilevel analysis
    • de Leeuw, J., & Kreft, I. (1986). Random coefficient models for multilevel analysis. Journal of Educational Statistics, 11, 57-85.
    • (1986) Journal of Educational Statistics , vol.11 , pp. 57-85
    • De Leeuw, J.1    Kreft, I.2
  • 12
    • 0000777364 scopus 로고
    • A bivariate generalization of Student's t-distribution with tables for certain special cases
    • Dunnett, C. W., & Sobel, M. (1954). A bivariate generalization of Student's t-distribution with tables for certain special cases. Biometrika, 41, 153-169.
    • (1954) Biometrika , vol.41 , pp. 153-169
    • Dunnett, C.W.1    Sobel, M.2
  • 13
    • 0000115992 scopus 로고
    • Some applications of matrix derivatives in multivariate analysis
    • Dwyer, P. S. (1967). Some applications of matrix derivatives in multivariate analysis. Journal of the American Statistical Association, 62, 607-625.
    • (1967) Journal of the American Statistical Association , vol.62 , pp. 607-625
    • Dwyer, P.S.1
  • 14
    • 0014825610 scopus 로고
    • A new approach to variable metric algorithms
    • Fletcher, R. (1970). A new approach to variable metric algorithms. Computer Journal, 13, 317-322.
    • (1970) Computer Journal , vol.13 , pp. 317-322
    • Fletcher, R.1
  • 15
    • 0000387235 scopus 로고
    • A rapidly convergent descent method for minimization
    • Fletcher, R., & Powell, M. J. D. (1963). A rapidly convergent descent method for minimization. Computer Journal, 6, 163-168.
    • (1963) Computer Journal , vol.6 , pp. 163-168
    • Fletcher, R.1    Powell, M.J.D.2
  • 19
    • 0000429066 scopus 로고
    • A general model for the analysis of multilevel data
    • Goldstein, H., & McDonald, R. P. (1988). A general model for the analysis of multilevel data. Psychometrika, 53, 455-467.
    • (1988) Psychometrika , vol.53 , pp. 455-467
    • Goldstein, H.1    McDonald, R.P.2
  • 20
    • 84890913931 scopus 로고
    • Maximum likelihood approaches to variance component estimation and to related problems
    • Harville, D. A. (1977). Maximum likelihood approaches to variance component estimation and to related problems. Journal of the American Statistical Association, 72, 320-340.
    • (1977) Journal of the American Statistical Association , vol.72 , pp. 320-340
    • Harville, D.A.1
  • 21
    • 0019920786 scopus 로고
    • Extensions of the multivariate normal models for pedigree analysis
    • Hopper, J. L., & Mathews, J. D. (1982). Extensions of the multivariate normal models for pedigree analysis. Annals of Human Genetics, 46, 373-383.
    • (1982) Annals of Human Genetics , vol.46 , pp. 373-383
    • Hopper, J.L.1    Mathews, J.D.2
  • 22
    • 0014794877 scopus 로고
    • Unified approach to quadratically convergent algorithms for function minimization
    • Huang, H. Y. (1970). Unified approach to quadratically convergent algorithms for function minimization. Journal of Optimization Theory and Applications, 5, 405-423.
    • (1970) Journal of Optimization Theory and Applications , vol.5 , pp. 405-423
    • Huang, H.Y.1
  • 24
    • 0022966316 scopus 로고
    • Unbalanced repeated-measures models with structured covariance matrices
    • Jennrich, R. J., & Schlucter, M. D. (1986). Unbalanced repeated-measures models with structured covariance matrices. Biometrics, 42, 805-820.
    • (1986) Biometrics , vol.42 , pp. 805-820
    • Jennrich, R.J.1    Schlucter, M.D.2
  • 28
    • 84950419603 scopus 로고
    • Newton-Raphson and EM algorithms for linear mixed-effects models of repeated-measures data
    • Lindstrom, M. J., & Bates, D. M. (1988). Newton-Raphson and EM algorithms for linear mixed-effects models of repeated-measures data. Journal of the American Statistical Association. 83, 1014-1022.
    • (1988) Journal of the American Statistical Association , vol.83 , pp. 1014-1022
    • Lindstrom, M.J.1    Bates, D.M.2
  • 30
    • 77956887650 scopus 로고
    • A fast scoring algorithm for maximum likelihood estimation in unbalanced mixed models with nested effects
    • Longford, N. T. (1987). A fast scoring algorithm for maximum likelihood estimation in unbalanced mixed models with nested effects. Biometrika, 74, 817-827.
    • (1987) Biometrika , vol.74 , pp. 817-827
    • Longford, N.T.1
  • 32
    • 21144481043 scopus 로고
    • Factor analysis for clustered observations
    • Longford, N. T., & Muthén, B. O. (1992). Factor analysis for clustered observations. Psychometrika, 57, 581-597.
    • (1992) Psychometrika , vol.57 , pp. 581-597
    • Longford, N.T.1    Muthén, B.O.2
  • 33
    • 0000387723 scopus 로고
    • Matrix derivatives with an application to an adaptive linear decision problem
    • MacRae, E. C. (1974). Matrix derivatives with an application to an adaptive linear decision problem. Annals of Statistics, 2, 337-346.
    • (1974) Annals of Statistics , vol.2 , pp. 337-346
    • MacRae, E.C.1
  • 34
    • 0000489758 scopus 로고
    • The commutation matrix: Some properties and applications
    • Magnus, J. R., & Neudecker, H. (1979). The commutation matrix: Some properties and applications. Annals of Statistics, 7, 381-394.
    • (1979) Annals of Statistics , vol.7 , pp. 381-394
    • Magnus, J.R.1    Neudecker, H.2
  • 37
    • 0001411838 scopus 로고
    • Latent variable modelling in heterogeneous populations
    • Muthén, B. (1989). Latent variable modelling in heterogeneous populations. Psychometrika, 54, 557-585.
    • (1989) Psychometrika , vol.54 , pp. 557-585
    • Muthén, B.1
  • 38
    • 0000661332 scopus 로고
    • A generalized multivariate of variance model useful especially for growth curve problems
    • Potthoff, R. F., & Roy, S. N. (1964). A generalized multivariate of variance model useful especially for growth curve problems. Biometrika, 69, 657-660.
    • (1964) Biometrika , vol.69 , pp. 657-660
    • Potthoff, R.F.1    Roy, S.N.2
  • 39
    • 0002007029 scopus 로고
    • Educational applications of hierarchical models: A review
    • Raudenbush, S. W. (1988). Educational applications of hierarchical models: A review. Journal of Educational Statistics, 13, 85-116.
    • (1988) Journal of Educational Statistics , vol.13 , pp. 85-116
    • Raudenbush, S.W.1
  • 40
    • 84936526615 scopus 로고
    • A hierarchical model for studying school effects
    • Raudenbush, S. W., & Bryk, A. S. (1986). A hierarchical model for studying school effects. Sociology of Education, 59, 1-17.
    • (1986) Sociology of Education , vol.59 , pp. 1-17
    • Raudenbush, S.W.1    Bryk, A.S.2
  • 41
    • 0001210798 scopus 로고
    • A multilevel, multivariate model for studying school climate with estimation via the EM algorithm and application to U.S. high-school data
    • Raudenbush, S. W., Rowan, B., & Kang, S. J. (1991). A multilevel, multivariate model for studying school climate with estimation via the EM algorithm and application to U.S. high-school data. Journal of Educational Statistics, 16, 295-330.
    • (1991) Journal of Educational Statistics , vol.16 , pp. 295-330
    • Raudenbush, S.W.1    Rowan, B.2    Kang, S.J.3
  • 42
    • 8644235937 scopus 로고
    • Understanding correlates of change by modelling individual differences in growth
    • Rogosa, D. R., & Willett, J. B. (1985). Understanding correlates of change by modelling individual differences in growth. Psychometrika, 50, 203-228.
    • (1985) Psychometrika , vol.50 , pp. 203-228
    • Rogosa, D.R.1    Willett, J.B.2
  • 43
    • 0642346421 scopus 로고
    • A note on Bayesian, likelihood, and sampling distribution inferences
    • Rubin, D. B. (1978). A note on Bayesian, likelihood, and sampling distribution inferences. Journal of Educational Statistics, 3, 189-201.
    • (1978) Journal of Educational Statistics , vol.3 , pp. 189-201
    • Rubin, D.B.1
  • 44
    • 0023675408 scopus 로고
    • Analysis of incomplete multivariate data using linear models with structured covariance matrices
    • Schlucter, M. D. (1988). Analysis of incomplete multivariate data using linear models with structured covariance matrices. Statistics in Medicine, 7, 317-324.
    • (1988) Statistics in Medicine , vol.7 , pp. 317-324
    • Schlucter, M.D.1
  • 47
    • 0000812928 scopus 로고
    • Sensitivity analysis for fixed effects in hierarchical models: A Gibbs sampling approach
    • Seltzer, M. H. (1993). Sensitivity analysis for fixed effects in hierarchical models: A Gibbs sampling approach. Journal of Educational Statistics, 18, 207-235.
    • (1993) Journal of Educational Statistics , vol.18 , pp. 207-235
    • Seltzer, M.H.1
  • 49
    • 0016926995 scopus 로고
    • Algorithm 500: Minimization of unconstrained multivariate functions
    • Shanno, D. F., & Phua, K. H. (1974). Algorithm 500: Minimization of unconstrained multivariate functions. ACM Transactions on Mathematical Software, 2, 87-94.
    • (1974) ACM Transactions on Mathematical Software , vol.2 , pp. 87-94
    • Shanno, D.F.1    Phua, K.H.2


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