메뉴 건너뛰기




Volumn 69, Issue 3, 2004, Pages 437-457

On the asymptotic distributions of two statistics for two-level covariance structure models within the class of elliptical distributions

Author keywords

Asymptotics; Elliptical distribution; Likelihood ratio statistic; Rescaled statistic

Indexed keywords


EID: 12344302064     PISSN: 00333123     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02295645     Document Type: Article
Times cited : (7)

References (61)
  • 1
    • 84988090494 scopus 로고
    • Distribution of the correlation coefficient for the class of bivariate elliptical models
    • Ali, M.M., & Joarder, A.H. (1991). Distribution of the correlation coefficient for the class of bivariate elliptical models. Canadian Journal of Statistics, 19, 447-452.
    • (1991) Canadian Journal of Statistics , vol.19 , pp. 447-452
    • Ali, M.M.1    Joarder, A.H.2
  • 2
    • 0001428349 scopus 로고
    • Cochran's theorem for elliptically contoured distributions
    • Anderson, T W., & Fang, K.-T. ( 1987). Cochran's theorem for elliptically contoured distributions. Sankhy = a A, 49, 305-315.
    • (1987) Sankhy = a A , vol.49 , pp. 305-315
    • Anderson, T.W.1    Fang, K.-T.2
  • 3
    • 0033416774 scopus 로고    scopus 로고
    • Structural equation modeling with small samples: Test statistics
    • Bentler, P.M., & Yuan, K.-H. (1999). Structural equation modeling with small samples: Test statistics. Multivariate Behavioral Research, 34, 181-197.
    • (1999) Multivariate Behavioral Research , vol.34 , pp. 181-197
    • Bentler, P.M.1    Yuan, K.-H.2
  • 6
    • 0011703342 scopus 로고    scopus 로고
    • The robustness of LISREL modeling revisited
    • R. Cudeck. S. du Toit, & D. S örbom (Eds.). Lincolnwood, IL: Scientific Software International
    • Boomsma. A., & Hoogland, J.J. (2001). The robustness of LISREL modeling revisited. In R. Cudeck. S. du Toit, & D. S örbom (Eds.), Structural equation modeling: Present and future (pp. 139-168). Lincolnwood, IL: Scientific Software International.
    • (2001) Structural Equation Modeling: Present and Future , pp. 139-168
    • Boomsma, A.1    Hoogland, J.J.2
  • 7
    • 85004870441 scopus 로고
    • Asymptotic distribution-free methods for the analysis of covariance structures
    • Browne, M.W. ( 1984). Asymptotic distribution-free methods for the analysis of covariance structures. British Journal of Mathematical and Statistical Psychology, 37, 62-83.
    • (1984) British Journal of Mathematical and Statistical Psychology , vol.37 , pp. 62-83
    • Browne, M.W.1
  • 8
    • 0007884968 scopus 로고
    • Adjustments for kurtosis in factor analysis with elliptically distributed errors
    • Browne, M.W., & Shapiro, A. (1987). Adjustments for kurtosis in factor analysis with elliptically distributed errors. Journal of the Royal Statistical Society B, 49, 346-352.
    • (1987) Journal of the Royal Statistical Society B , vol.49 , pp. 346-352
    • Browne, M.W.1    Shapiro, A.2
  • 9
    • 0039435059 scopus 로고    scopus 로고
    • Efficiency and robustness of alternative estimators for two- And three-level models: The case of NAEP
    • Cheong, Y.F., Fotiu, R.P., & Raudenbush, S.W. (2001). Efficiency and robustness of alternative estimators for two- and three-level models: The case of NAEP. Journal of Educational and Behavioral Statistics, 26, 411-429.
    • (2001) Journal of Educational and Behavioral Statistics , vol.26 , pp. 411-429
    • Cheong, Y.F.1    Fotiu, R.P.2    Raudenbush, S.W.3
  • 10
    • 0001922927 scopus 로고    scopus 로고
    • The robustness of test statistics to nonnormality and specification error in confirmatory factor analysis
    • Curran. P.J., West. S.G., & Finch, J.F. (1996). The robustness of test statistics to nonnormality and specification error in confirmatory factor analysis. Psychological Methods, 1, 16-29.
    • (1996) Psychological Methods , vol.1 , pp. 16-29
    • Curran, P.J.1    West, S.G.2    Finch, J.F.3
  • 11
    • 0002828494 scopus 로고
    • Some multivariate applications of elliptical distributions
    • S. Ikeda (Ed.). Tokyo: Shinko Tsusho.
    • Devlin, S.J., Gnanadesikan, R., & Kettenring, J.R. (1976). Some multivariate applications of elliptical distributions. In S. Ikeda (Ed.), Essays in Probability and Statistics (pp. 365-93). Tokyo: Shinko Tsusho.
    • (1976) Essays in Probability and Statistics , pp. 365-393
    • Devlin, S.J.1    Gnanadesikan, R.2    Kettenring, J.R.3
  • 12
    • 0142227400 scopus 로고    scopus 로고
    • Multilevel structural equation modeling
    • (in press). J. de Leeuw & I. Kreft (Eds.). New York: Kluwer
    • du Toit. S., & du Toit, M. (in press). Multilevel structural equation modeling. In J. de Leeuw & I. Kreft (Eds.). Handbook of quantitative multilevel analysis. New York: Kluwer.
    • Handbook of Quantitative Multilevel Analysis
    • Du Toit, S.1    Du Toit, M.2
  • 14
    • 0010033533 scopus 로고    scopus 로고
    • Performance of modified test statistics in covariance and correlation structure analysis under conditions of multivariate nonnormality
    • Fouladi, R.T. (2000). Performance of modified test statistics in covariance and correlation structure analysis under conditions of multivariate nonnormality. Structural Equation Modeling, 7, 356-410.
    • (2000) Structural Equation Modeling , vol.7 , pp. 356-410
    • Fouladi, R.T.1
  • 16
    • 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, 435-467.
    • (1988) Psychometrika , vol.53 , pp. 435-467
    • Goldstein, H.1    McDonald, R.P.2
  • 18
    • 51249178485 scopus 로고
    • Normalizing and variance stabilizing transformations of multivariate statistics under an elliptical population
    • Hayakawa, T. (1987). Normalizing and variance stabilizing transformations of multivariate statistics under an elliptical population. Annals of the Institute of Statistical Mathematics, 39, 299-306.
    • (1987) Annals of the Institute of Statistical Mathematics , vol.39 , pp. 299-306
    • Hayakawa, T.1
  • 22
    • 38249010845 scopus 로고
    • Robust statistics for test-of-independence and related structural models
    • Kano, Y. (1992). Robust statistics for test-of-independence and related structural models. Statistics & Probability Letters, 15, 21-26.
    • (1992) Statistics & Probability Letters , vol.15 , pp. 21-26
    • Kano, Y.1
  • 23
    • 0001107419 scopus 로고
    • Consistency property of elliptical probability density functions
    • Kano, Y. (1994). Consistency property of elliptical probability density functions. Journal of Multivariate Analysis, 51, 343-350.
    • (1994) Journal of Multivariate Analysis , vol.51 , pp. 343-350
    • Kano, Y.1
  • 24
    • 0011523365 scopus 로고
    • Covariance structure analysis with heterogeneous kurtosis parameters
    • Kano, Y., Berkane, M., & Bentler, P.M. (1990). Covariance structure analysis with heterogeneous kurtosis parameters. Biometrika, 77, 575-585.
    • (1990) Biometrika , vol.77 , pp. 575-585
    • Kano, Y.1    Berkane, M.2    Bentler, P.M.3
  • 25
    • 21144468815 scopus 로고
    • Statistical inference based on pseudo-maximum likelihood estimators in elliptical populations
    • Kano, Y., Berkane, M., & Bentler, P.M. (1993). Statistical inference based on pseudo-maximum likelihood estimators in elliptical populations. Journal of the American Statistical Association, 88, 135-143.
    • (1993) Journal of the American Statistical Association , vol.88 , pp. 135-143
    • Kano, Y.1    Berkane, M.2    Bentler, P.M.3
  • 27
    • 0000564847 scopus 로고
    • Multilevel analysis of structural equation models
    • Lee, S.-Y. (1990). Multilevel analysis of structural equation models. Biometrika, 77, 763-772.
    • (1990) Biometrika , vol.77 , pp. 763-772
    • Lee, S.-Y.1
  • 28
    • 0032375617 scopus 로고    scopus 로고
    • Analysis of two-level structural equation models via EM type algorithms
    • Lee, S.Y., & Poon, W.Y. (1998). Analysis of two-level structural equation models via EM type algorithms. Statistica Sinica, 8, 749-766.
    • (1998) Statistica Sinica , vol.8 , pp. 749-766
    • Lee, S.Y.1    Poon, W.Y.2
  • 29
    • 7244238417 scopus 로고    scopus 로고
    • An EM algorithm for fitting two-level structural equation models
    • Liang, J., & Bentler, P.M. (2004). An EM algorithm for fitting two-level structural equation models. Psychometrika, 69, 101-122.
    • (2004) Psychometrika , vol.69 , pp. 101-122
    • Liang, J.1    Bentler, P.M.2
  • 30
    • 77956887650 scopus 로고
    • A fast scoring algorithm for maximum likelihood estimation in unbalanced mixed models with nested random effects
    • Longford, N.T. (1987). A fast scoring algorithm for maximum likelihood estimation in unbalanced mixed models with nested random 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., & Muth én, B.O. (1992). Factor analysis for clustered observations. Psychometrika, 57, 581-597.
    • (1992) Psychometrika , vol.57 , pp. 581-597
    • Longford, N.T.1    Muth Én, B.O.2
  • 36
    • 0018904089 scopus 로고
    • Asymptotic distributions in canonical correlation analysis and other multi-variate procedures for nonnormal populations
    • Muirhead, R.J., & Waternaux, C.M. (1980). Asymptotic distributions in canonical correlation analysis and other multi-variate procedures for nonnormal populations. Biometrika, 67, 31-43.
    • (1980) Biometrika , vol.67 , pp. 31-43
    • Muirhead, R.J.1    Waternaux, C.M.2
  • 37
    • 84965569319 scopus 로고
    • Multilevel covariance structure analysis
    • Muthén, B. (1994). Multilevel covariance structure analysis. Sociological Methods & Research, 22, 376-398.
    • (1994) Sociological Methods & Research , vol.22 , pp. 376-398
    • Muthén, B.1
  • 38
    • 0031526569 scopus 로고    scopus 로고
    • Latent variable modeling of longitudinal and multilevel data
    • A. Raftery (ed.). Boston: Blackwell Publishers
    • Muthén, B. (1997). Latent variable modeling of longitudinal and multilevel data. In A. Raftery (ed.), Sociological methodology 1997 (pp. 453-480). Boston: Blackwell Publishers.
    • (1997) Sociological Methodology 1997 , pp. 453-480
    • Muthén, B.1
  • 39
    • 84886337777 scopus 로고
    • Complex sample data in structural equation modeling
    • P. V. Marsden (E.). Cambridge, MA: Blackwell Publishers
    • Muthén, B., & Satorra, A. (1995). Complex sample data in structural equation modeling. In P. V. Marsden (E.), Sociological methodology 1995 (pp. 267-316). Cambridge, MA: Blackwell Publishers.
    • (1995) Sociological Methodology 1995 , pp. 267-316
    • Muthén, B.1    Satorra, A.2
  • 41
    • 38149148060 scopus 로고
    • A distribution free approach for analysis of two-level structural equation model
    • Poon, W.-Y, & Lee, S.-Y. (1994). A distribution free approach for analysis of two-level structural equation model. Computational Statistics & Data Analysis, 17, 265-275.
    • (1994) Computational Statistics & Data Analysis , vol.17 , pp. 265-275
    • Poon, W.-Y.1    Lee, S.-Y.2
  • 42
    • 9944230216 scopus 로고
    • Asymptotic distributions of some test criteria for the covariance matrix in elliptical distributions under local alternatives
    • Purkayastha, S., & Srivastava, M.S. (1995). Asymptotic distributions of some test criteria for the covariance matrix in elliptical distributions under local alternatives. Journal of Multivariate Analysis, 55, 165-186.
    • (1995) Journal of Multivariate Analysis , vol.55 , pp. 165-186
    • Purkayastha, S.1    Srivastava, M.S.2
  • 43
    • 85004720677 scopus 로고
    • Maximum likelihood estimation for unbalanced multilevel covariance structure models via the EM algorithm
    • Raudenbush, S.W. (1995). Maximum likelihood estimation for unbalanced multilevel covariance structure models via the EM algorithm. British Journal of Mathematical and Statistical Psychology, 48, 359-370.
    • (1995) British Journal of Mathematical and Statistical Psychology , vol.48 , pp. 359-370
    • Raudenbush, S.W.1
  • 45
    • 0036004225 scopus 로고    scopus 로고
    • Asymptotic robustness in multiple group linear-latent variable models
    • Satorra, A. (2002). Asymptotic robustness in multiple group linear-latent variable models. Econometric Theory, 18, 297-312.
    • (2002) Econometric Theory , vol.18 , pp. 297-312
    • Satorra, A.1
  • 48
    • 38249018457 scopus 로고
    • Model conditions for asymptotic robustness in the analysis of linear relations
    • Satorra, A., & Bentler, P.M. (1990). Model conditions for asymptotic robustness in the analysis of linear relations. Computational Statistics & Data Analysis, 10, 235-249.
    • (1990) Computational Statistics & Data Analysis , vol.10 , pp. 235-249
    • Satorra, A.1    Bentler, P.M.2
  • 49
    • 0003217529 scopus 로고
    • Corrections to test statistics and standard errors in covariance structure analysis
    • A. von Eye & C. C. Clogg (Es.). Thousand Oaks, CA: Sage
    • Satorra, A., & Bentler, P.M. (1994). Corrections to test statistics and standard errors in covariance structure analysis. In A. von Eye & C. C. Clogg (Es.), Latent variables analysis: Applications for developmental research (pp. 399-419). Thousand Oaks, CA: Sage.
    • (1994) Latent Variables Analysis: Applications for Developmental Research , pp. 399-419
    • Satorra, A.1    Bentler, P.M.2
  • 50
  • 52
    • 38249005332 scopus 로고
    • On the problem of more than one kurtosis parameter in multivariate analysis
    • Steyn, H.S. (1993). On the problem of more than one kurtosis parameter in multivariate analysis. Journal of Multivariate Analysis, 44, 1-22.
    • (1993) Journal of Multivariate Analysis , vol.44 , pp. 1-22
    • Steyn, H.S.1
  • 53
    • 0030187090 scopus 로고    scopus 로고
    • The distribution of the covariance matrix for a subset of elliptical distributions with extension to two kurtosis parameters
    • Steyn, H.S. (1996). The distribution of the covariance matrix for a subset of elliptical distributions with extension to two kurtosis parameters. Journal of Multivariate Analysis, 55, 96-106.
    • (1996) Journal of Multivariate Analysis , vol.55 , pp. 96-106
    • Steyn, H.S.1
  • 54
    • 0001584323 scopus 로고
    • Radial estimates and the test for sphericity
    • Tyler, D.E. (1982). Radial estimates and the test for sphericity. Biometrika, 69, 429-36.
    • (1982) Biometrika , vol.69 , pp. 429-436
    • Tyler, D.E.1
  • 55
    • 0001076947 scopus 로고
    • Robustness and efficiency properties of scatter matrices
    • Tyler, D.E. (1983). Robustness and efficiency properties of scatter matrices. Biometrika, 70, 411-420.
    • (1983) Biometrika , vol.70 , pp. 411-420
    • Tyler, D.E.1
  • 56
    • 0011089869 scopus 로고    scopus 로고
    • Asymptotic expansion of the joint distribution of sample mean vector and sample covariance matrix from an elliptical population
    • Wakaki, H. ( 1997). Asymptotic expansion of the joint distribution of sample mean vector and sample covariance matrix from an elliptical population. Hiroshima Mathematics Journal, 27, 295-305.
    • (1997) Hiroshima Mathematics Journal , vol.27 , pp. 295-305
    • Wakaki, H.1
  • 57
    • 0033418689 scopus 로고    scopus 로고
    • On normal theory and associated test statistics in covariance structure analysis under two classes of nonnormal distributions
    • Yuan, K.-H., & Bentler, P.M. (1999). On normal theory and associated test statistics in covariance structure analysis under two classes of nonnormal distributions. Statistica Sinica, 9, 831-853.
    • (1999) Statistica Sinica , vol.9 , pp. 831-853
    • Yuan, K.-H.1    Bentler, P.M.2
  • 58
    • 0000605350 scopus 로고    scopus 로고
    • Inferences on correlation coefficients in some classes of nonnormal distributions
    • Yuan, K.-H., & Bentler, P.M. (2000). Inferences on correlation coefficients in some classes of nonnormal distributions. Journal of Multivariate Analysis, 72, 230-248.
    • (2000) Journal of Multivariate Analysis , vol.72 , pp. 230-248
    • Yuan, K.-H.1    Bentler, P.M.2
  • 59
    • 0037004494 scopus 로고    scopus 로고
    • On normal theory based inference for multilevel models with distributional violations
    • Yuan, K.-H., & Bentler, P.M. (2002). On normal theory based inference for multilevel models with distributional violations. Psychometrika, 67, 539-561.
    • (2002) Psychometrika , vol.67 , pp. 539-561
    • Yuan, K.-H.1    Bentler, P.M.2
  • 60
    • 0141924118 scopus 로고    scopus 로고
    • Eight test statistics for multilevel structural equation models
    • Yuan, K.-H., & Bentler, P.M. (2003). Eight test statistics for multilevel structural equation models. Computational Statistics & Data Analysis, 44, 89-107.
    • (2003) Computational Statistics & Data Analysis , vol.44 , pp. 89-107
    • Yuan, K.-H.1    Bentler, P.M.2
  • 61
    • 18644379651 scopus 로고    scopus 로고
    • Asymptotic robustness of the normal theory likelihood ratio statistic for two-level covariance structure models
    • (in press)
    • Yuan, K.-H., & Bentler, P.M. (in press). Asymptotic robustness of the normal theory likelihood ratio statistic for two-level covariance structure models. Journal of Multivariate Analysis.
    • Journal of Multivariate Analysis
    • Yuan, K.-H.1    Bentler, P.M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.