메뉴 건너뛰기




Volumn 52, Issue 5, 2017, Pages 661-670

Small Sample Methods for Multilevel Modeling: A Colloquial Elucidation of REML and the Kenward-Roger Correction

Author keywords

explanation; Kenward Roger; mixed model; Restricted maximum likelihood; tutorial

Indexed keywords

DOCUMENTATION; HUMAN; MAXIMUM LIKELIHOOD METHOD; MULTILEVEL ANALYSIS; SAMPLING BIAS; SCIENTIST; SIMULATION; REPRODUCIBILITY; SAMPLE SIZE; STATISTICAL BIAS; STATISTICAL MODEL;

EID: 85024407861     PISSN: 00273171     EISSN: None     Source Type: Journal    
DOI: 10.1080/00273171.2017.1344538     Document Type: Article
Times cited : (182)

References (28)
  • 1
    • 84922259964 scopus 로고    scopus 로고
    • Explaining fixed effects: Random effects modeling of time-series cross-sectional and panel data
    • Bell, A., & Jones, K. (2015). Explaining fixed effects: Random effects modeling of time-series cross-sectional and panel data. Political Science Research and Methods, 3, 133–153. doi:10.1017/psrm.2014.7
    • (2015) Political Science Research and Methods , vol.3 , pp. 133-153
    • Bell, A.1    Jones, K.2
  • 3
    • 33847083094 scopus 로고    scopus 로고
    • A comparison of Bayesian and likelihood-based methods for fitting multilevel models
    • Browne, W. J., & Draper, D. (2006). A comparison of Bayesian and likelihood-based methods for fitting multilevel models. Bayesian Analysis, 1, 473–514. doi:10.1214/06-BA117
    • (2006) Bayesian Analysis , vol.1 , pp. 473-514
    • Browne, W.J.1    Draper, D.2
  • 4
    • 0018115641 scopus 로고
    • Assessing the accuracy of the maximum likelihood estimator: Observed versus expected Fisher information
    • Efron, B., & Hinkley, D. V. (1978). Assessing the accuracy of the maximum likelihood estimator: Observed versus expected Fisher information. Biometrika, 65, 457–482. doi:10.1093/biomet/65.3.457
    • (1978) Biometrika , vol.65 , pp. 457-482
    • Efron, B.1    Hinkley, D.V.2
  • 6
    • 66149144783 scopus 로고    scopus 로고
    • Making treatment effect inferences from multiple-baseline data: The utility of multilevel modeling approaches
    • Ferron, J. M., Bell, B. A., Hess, M. R., Rendina-Gobioff, G., & Hibbard, S. T. (2009). Making treatment effect inferences from multiple-baseline data: The utility of multilevel modeling approaches. Behavior Research Methods, 41, 372–384. doi:10.3758/BRM.41.2.372
    • (2009) Behavior Research Methods , vol.41 , pp. 372-384
    • Ferron, J.M.1    Bell, B.A.2    Hess, M.R.3    Rendina-Gobioff, G.4    Hibbard, S.T.5
  • 7
    • 70350471314 scopus 로고
    • Multilevel mixed linear model analysis using iterative generalized least squares
    • Goldstein, H. (1986). Multilevel mixed linear model analysis using iterative generalized least squares. Biometrika, 73, 43–56. doi:10.1093/biomet/73.1.43
    • (1986) Biometrika , vol.73 , pp. 43-56
    • Goldstein, H.1
  • 8
    • 0000655117 scopus 로고
    • Mean squared error of estimation or prediction under a general linear model
    • Harville, D. A., & Jeske, D. R. (1992). Mean squared error of estimation or prediction under a general linear model. Journal of the American Statistical Association, 87, 724–731. doi:10.1080/01621459.1992.10475274
    • (1992) Journal of the American Statistical Association , vol.87 , pp. 724-731
    • Harville, D.A.1    Jeske, D.R.2
  • 9
    • 84883641307 scopus 로고    scopus 로고
    • How few countries will do? Comparative survey analysis from a Bayesian perspective
    • July
    • Hox, J. J., van de Schoot, R., & Matthijsse, S. (2012, July). How few countries will do? Comparative survey analysis from a Bayesian perspective. Survey Research Methods, 6, 87–93.
    • (2012) Survey Research Methods , vol.6 , pp. 87-93
    • Hox, J.J.1    van de Schoot, R.2    Matthijsse, S.3
  • 10
    • 85041022610 scopus 로고    scopus 로고
    • Using cluster bootstrapping to analyze nested data with a few clusters
    • Advance online publication
    • Huang, F. L. (2017). Using cluster bootstrapping to analyze nested data with a few clusters. Educational and Psychological Measurement. Advance online publication. doi:10.1177/0013164416678980.
    • (2017) Educational and Psychological Measurement
    • Huang, F.L.1
  • 11
    • 0001089821 scopus 로고
    • Unbiasedness of two-stage estimation and prediction procedures for mixed linear models
    • Kackar, R. N., & Harville, D. A. (1981). Unbiasedness of two-stage estimation and prediction procedures for mixed linear models. Communications in Statistics-Theory and Methods, 10, 1249–1261. doi:10.1080/03610928108828108
    • (1981) Communications in Statistics-Theory and Methods , vol.10 , pp. 1249-1261
    • Kackar, R.N.1    Harville, D.A.2
  • 12
    • 70350184453 scopus 로고
    • Approximations for standard errors of estimators of fixed and random effects in mixed linear models
    • Kackar, R. N., & Harville, D. A. (1984). Approximations for standard errors of estimators of fixed and random effects in mixed linear models. Journal of the American Statistical Association, 79, 853–862. doi:10.2307/2288715
    • (1984) Journal of the American Statistical Association , vol.79 , pp. 853-862
    • Kackar, R.N.1    Harville, D.A.2
  • 13
    • 61849100484 scopus 로고    scopus 로고
    • An improved approximation to the precision of fixed effects from restricted maximum likelihood
    • Kenward, M. G., & Roger, J. H. (2009). An improved approximation to the precision of fixed effects from restricted maximum likelihood. Computational Statistics and Data Analysis, 53, 2583–2595. doi:10.1016/j.csda.2008.12.013
    • (2009) Computational Statistics and Data Analysis , vol.53 , pp. 2583-2595
    • Kenward, M.G.1    Roger, J.H.2
  • 14
    • 0030880605 scopus 로고    scopus 로고
    • Small sample inference for fixed effects from restricted maximum likelihood
    • Kenward, M. G., & Roger, J. H. (1997). Small sample inference for fixed effects from restricted maximum likelihood. Biometrics, 53, 983–997. doi:10.2307/2533558
    • (1997) Biometrics , vol.53 , pp. 983-997
    • Kenward, M.G.1    Roger, J.H.2
  • 15
    • 0007019292 scopus 로고    scopus 로고
    • The analysis of repeated measurements: A comparison of mixed-model Satterthwaite F tests and a nonpooled adjusted degrees of freedom multivariate test
    • Keselman, H. J., Algina, J., Kowalchuk, R. K., & Wolfinger, R. D. (1999). The analysis of repeated measurements: A comparison of mixed-model Satterthwaite F tests and a nonpooled adjusted degrees of freedom multivariate test. Communications in Statistics-Theory and Methods, 28, 2967–2999. doi:10.1080/03610929908832460
    • (1999) Communications in Statistics-Theory and Methods , vol.28 , pp. 2967-2999
    • Keselman, H.J.1    Algina, J.2    Kowalchuk, R.K.3    Wolfinger, R.D.4
  • 16
    • 69949190053 scopus 로고    scopus 로고
    • Sufficient sample sizes for multilevel modeling
    • Maas, C. J., & Hox, J. J. (2005). Sufficient sample sizes for multilevel modeling. Methodology, 1, 86–92. doi:10.1027/1614-2241.1.3.86
    • (2005) Methodology , vol.1 , pp. 86-92
    • Maas, C.J.1    Hox, J.J.2
  • 17
    • 84974808077 scopus 로고    scopus 로고
    • On using Bayesian methods to address small sample problems
    • McNeish, D. (2016). On using Bayesian methods to address small sample problems. Structural Equation Modeling, 23, 750–773. doi:10.1080/10705511.2016.1186549
    • (2016) Structural Equation Modeling , vol.23 , pp. 750-773
    • McNeish, D.1
  • 18
    • 84973596359 scopus 로고    scopus 로고
    • Modeling clustered data with very few clusters
    • McNeish, D., & Stapleton, L. M. (2016a). Modeling clustered data with very few clusters. Multivariate Behavioral Research, 51, 495–518. doi:10.1080/00273171.2016.1167008
    • (2016) Multivariate Behavioral Research , vol.51 , pp. 495-518
    • McNeish, D.1    Stapleton, L.M.2
  • 19
    • 84908298355 scopus 로고    scopus 로고
    • The effect of small sample size on two-level model estimates: A review and illustration
    • McNeish, D., & Stapleton, L. M. (2016b). The effect of small sample size on two-level model estimates: A review and illustration. Educational Psychology Review, 28, 295–314. doi:10.1007/s10648-014-9287-x
    • (2016) Educational Psychology Review , vol.28 , pp. 295-314
    • McNeish, D.1    Stapleton, L.M.2
  • 20
    • 84873047637 scopus 로고    scopus 로고
    • Bayesian structural equation modeling: a more flexible representation of substantive theory
    • Muthén, B., & Asparouhov, T. (2012). Bayesian structural equation modeling: a more flexible representation of substantive theory. Psychological Methods, 17, 313–335. doi:10.1037/a0026802
    • (2012) Psychological Methods , vol.17 , pp. 313-335
    • Muthén, B.1    Asparouhov, T.2
  • 21
    • 84900529999 scopus 로고
    • The estimation of the mean squared error of small-area estimators
    • Prasad, N. G. N., & Rao, J. N. (1990). The estimation of the mean squared error of small-area estimators. Journal of the American Statistical Association, 85, 163–171. doi:10.1080/01621459.1990.10475320
    • (1990) Journal of the American Statistical Association , vol.85 , pp. 163-171
    • Prasad, N.G.N.1    Rao, J.N.2
  • 23
    • 84872636119 scopus 로고
    • An approximate distribution of estimates of variance components
    • Satterthwaite, F. E. (1946). An approximate distribution of estimates of variance components. Biometrics Bulletin, 2, 110–114. doi:10.2307/3002019
    • (1946) Biometrics Bulletin , vol.2 , pp. 110-114
    • Satterthwaite, F.E.1
  • 25
    • 0000935535 scopus 로고
    • Standard errors and sample sizes for two-level research
    • Snijders, T. A., & Bosker, R. J. (1993). Standard errors and sample sizes for two-level research. Journal of Educational Statistics, 18, 237–259. doi:10.2307/1165134
    • (1993) Journal of Educational Statistics , vol.18 , pp. 237-259
    • Snijders, T.A.1    Bosker, R.J.2
  • 26
    • 84938968883 scopus 로고    scopus 로고
    • Standardized effect size measures for mediation analysis in cluster-randomized trials
    • Stapleton, L. M., Pituch, K. A., & Dion, E. (2015). Standardized effect size measures for mediation analysis in cluster-randomized trials. The Journal of Experimental Education, 83, 547–582. doi:10.1080/00220973.2014.919569
    • (2015) The Journal of Experimental Education , vol.83 , pp. 547-582
    • Stapleton, L.M.1    Pituch, K.A.2    Dion, E.3
  • 27
    • 84977106631 scopus 로고    scopus 로고
    • Analyzing small data sets using Bayesian estimation: the case of posttraumatic stress symptoms following mechanical ventilation in burn survivors
    • van de Schoot, R., Broere, J. J., Perryck, K. H., Zondervan-Zwijnenburg, M., & van Loey, N. E. (2015). Analyzing small data sets using Bayesian estimation: the case of posttraumatic stress symptoms following mechanical ventilation in burn survivors. European Journal of Psychotraumatology, 6. doi:10.3402/ejpt.v6.25216
    • (2015) European Journal of Psychotraumatology , vol.6
    • van de Schoot, R.1    Broere, J.J.2    Perryck, K.H.3    Zondervan-Zwijnenburg, M.4    van Loey, N.E.5
  • 28
    • 84899945186 scopus 로고    scopus 로고
    • A gentle introduction to Bayesian analysis: Applications to developmental research
    • van de Schoot, R., Kaplan, D., Denissen, J., Asendorpf, J. B., Neyer, F. J., & Aken, M. A. (2014). A gentle introduction to Bayesian analysis: Applications to developmental research. Child Development, 85, 842–860. doi:10.1111/cdev.12169
    • (2014) Child Development , vol.85 , pp. 842-860
    • van de Schoot, R.1    Kaplan, D.2    Denissen, J.3    Asendorpf, J.B.4    Neyer, F.J.5    Aken, M.A.6


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.