Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aptech Systems. Gauss. Aptech Systems, Maple Valley, WA, 1994.
A. C. Atkinson. Plots, Transformations, and Regression. Clarendon Press, Oxford, UK, 1985.
B. H. Baltagi. Econometric Analysis of Panel Data. Wiley, New York, 1995.
M. S. Bartlett and D. G. Kendall. The statistical analysis of variance-hetero-geneity and the logarithmic transformation. Supplement to the Journal of the Royal Statistical Society, 8:128–138, 1946.
C. S. Berkey and R. L. Kent Jr. Longitudinal principal components and non-linear regression models of early childhood growth. Annals of Human Biology, 10:523–536, 1983.
J. Berkhof and T. A. B. Snijders. Variance component testing in multilevel models. Journal of Educational and Behavioral Statistics, 26:133–152, 2002.
B. A. Brumback and J. A. Rice. Smoothing spline models for the analysis of nested and crossed samples of curves. Journal of the American Statistical Association, 93: 961–994, 1998. (with discussion).
A. S. Bryk and S. W. Raudenbush. Application of hierarchical linear models to assessing change. Psychological Bulletin, 101:147–158, 1987.
E. Cantoni and T. Hastie. Degrees-of-freedom tests for smoothing splines. Biometrika, 89:251–263, 2002.
C.-T. Chiang, J. A. Rice, and C. O. Wu. Smoothing spline estimation for varying coefficient models with repeatedly measured dependent variables. Journal of the American Statistical Association, 96:605–619, 2001.
R. D. Cook and S. Weisberg. Residuals and Influence in Regression. Chapman & Hall, London, 1982.
C. De Boor. A Practical Guide to Splines. Springer, New York, 1978.
L. E. Eberly and L. M. Thackeray. On Lange and Ryan's plotting technique for diagnosing non-normality of random effects. Statistics & Probability Letters, 75:77–85, 2005.
P. H. C. Eilers and B. D. Marx. Flexible smoothing with splines and penalties. Statistical Science, 11:89–121, 1996. (with discussion).
J. Fan and J. T. Zhang. Two-step estimation of functional linear models with applications to longitudinal data. Journal of the Royal Statistical Society, Series B, 62:303–322, 2000.
A. Fielding. Role of the Hausman test and whether higher level effects should be treated as random or fixed. Multilevel Modelling Newsletter, 16(2): 3–9, 2004.
H. Goldstein. Efficient statistical modelling of longitudinal data. Annals of Human Biology, 13:129–141, 1986.
H. Goldstein. Multilevel Statistical Models, 3rd edition. Edward Arnold, London, 2003.
H. Goldstein, J. Rasbash, I. Plewis, D. Draper, W. Browne, M. Yang, G. Woodhouse, and M. Healy. A User's Guide to MLwiN. Multilevel Models Project, Institute of Education, University of London, London, 1998.
P. J. Green. Penalized likelihood for general semi-parametric regression models. International Statistical Review, 55:245–259, 1987.
P. J. Green and B. W. Silverman. Nonparametric Regression and Generalized Linear Models. Chapman & Hall, London, 1994.
W. Guo. Functional mixed effects model. Biometrics, 58:121–128, 2002.
J. Haslett and D. Dillane. Application of ‘delete = replace’ to deletion diagnostics for variance component estimation in the linear mixed model. Journal of the Royal Statistical Society, Series B, 66:131–143, 2004.
T. Hastie and R. Tibshirani. Generalized Additive Models. Chapman & Hall, London, 1990.
T. Hastie and R. Tibshirani. Varying-coefficient models. Journal of the Royal Statistical Society, Series B, 55:757–796, 1993. (with discussion).
J. A. Hausman. Specification tests in econometrics. Econometrica, 46:1251–1271, 1978.
J. A. Hilden-Minton. Multilevel Diagnostics for Mixed and Hierarchical Linear Models. PhD thesis, Department of Mathematics, University of California, Los Angeles, 1995.
J. S. Hodges. Some algebra and geometry for hierarchical linear models, applied to diagnostics. Journal of the Royal Statistical Society, Series B, 60:497–536, 1998.
D. R. Hoover, J. A. Rice, C. O. Wu, and L.-P. Yang. Nonparametric smoothing estimates of time-varying coefficient models with longitudinal data. Biometrika, 85:809–822, 1998.
C. Hsiao. Random coefficient models. In L. Mátyás and P. Sevestre, editors, The Econometrics of Panel Data, 2nd edition, pages 77–99. Kluwer, Dordrecht, The Netherlands, 1996.
G. James, T. Hastie, and C. A. Sugar. Principal component models for sparse functional data. Biometrika, 87:587–602, 2000.
J.-S. Kim and E. W. Frees. Omitted variables in multilevel models. Psychometrika, 71:659–690, 2006.
R. Kohn, C. F. Ansley, and D. Tharm. The performance of cross-validation and maximum likelihood estimators of spline smoothing parameters. Journal of the American Statistical Association, 86:1042–1050, 1991.
N. Lange and L. Ryan. Assessing normality in random effects models. Annals of Statistics, 17:624–642, 1989.
I. H. Langford and T. Lewis. Outliers in multilevel data. Journal of the Royal Statistical Society, Series A, 161:121–160, 1998.
E. Lesaffre and G. Verbeke. Local influence in linear mixed models. Biometrics, 54:570–582, 1998.
T. Lewis and I. H. Langford. Outliers, robustness and the detection of discrepant data. In A. H. Leyland and H. Goldstein, editors, Multilevel Modelling of Health Statistics, pages 75–91. Wiley, New York, 2001.
X. Lin and D. Zhang. Inference in generalized additive mixed models by using smoothing splines. Journal of the Royal Statistical Society, Series B, 61:381–400, 1999.
R. C. Littell, G. A. Milliken, W. W. Stroup, and R. D. Wolfinger. SAS System for Mixed Models. SAS Institute, Cary, NC, 1996.
N. T. Longford. A fast scoring algorithm for maximum likelihood estimation in unbalanced mixed models with nested random effects. Biometrika, 74:817–827, 1987.
N. T. Longford. Random Coefficient Models. Oxford University Press, Oxford, UK, 1993.
N. T. Longford. Simulation-based diagnostics in random-coefficient models. Journal of the Royal Statistical Society, Series A, 164:259–273, 2001.
X. L. Meng and D. B. Rubin. Maximum likelihood estimation via the ECM algorithm: A general framework. Biometrika, 80:267–278, 1993.
C. R. Rao. Linear Statistical Inference and its Applications, 2nd edition. Wiley, New York, 1973.
S. W. Raudenbush and A. S. Bryk. Hierarchical Linear Models: Applications and Data Analysis Methods, 2nd edition. Sage, Thousand Oaks, CA, 2002.
J. A. Rice and B. W. Silverman. Estimating the mean and covariance structure nonparametrically when the data are curves. Journal of the Royal Statistical Society, Series B, 53:233–243, 1991.
J. A. Rice and C. O. Wu. Nonparametric mixed effects models for unequally sampled noisy curves. Biometrics, 57:253–259, 2001.
M. H. Seltzer, W. H. Wong, and A. S. Bryk. Bayesian analysis in applications of hierarchical models: Issues and methods. Journal of Educational and Behavioral Statistics, 21:131–167, 1996.
A. Skrondal and S. Rabe-Hesketh. Generalized Latent Variable Modeling: Multilevel, Longitudinal, and Structural Equation Models. Chapman & Hall/CRC, Boca Raton, FL, 2004.
T. A. B. Snijders. Analysis of longitudinal data using the hierarchical linear model. Quality & Quantity, 30:405–426, 1996.
T. A. B. Snijders and R. J. Bosker. Multilevel Analysis: An Introduction to Basic and Advanced Multilevel Modeling. Sage, London, 1999.
T. P. Speed. Comment on “That BLUP is a good thing: the estimation of random effects” (by G. K. Robinson). Statistical Science, 6:44, 1991.
R. Van der Leeden, E. Meijer, and F. M. T. A. Busing. Resampling multilevel models. In J. de Leeuw and E. Meijer, editors, Handbook of Multilevel Analysis, Chapter. Springer, New York, 2008. (this volume).
G. Verbeke and E. Lesaffre. A linear mixed-effects model with heterogeneity in the random-effects population. Journal of the American Statistical Association, 91:217–221, 1996.
G. Verbeke and G. Molenberghs. Linear Mixed Models for Longitudinal Data. Springer, New York, 2000.
G. Wahba. Bayesian “confidence” intervals for the cross-validated smoothing spline. Journal of the Royal Statistical Society, Series B, 45:133–150, 1983.
G. Wahba. A comparison of GCV and GML for choosing the smoothing parameter in the generalized spline smoothing problem. Annals of Statistics, 4:1378–1402, 1985.
Y. Wang. Mixed effects smoothing spline analysis of variance. Journal of the Royal Statistical Society, Series B, 60:159–174, 1998.
C. Waternaux, N. M. Laird, and J. H. Ware. Methods for analysis of longitudinal data: Blood lead concentrations and cognitive development. Journal of the American Statistical Association, 84:33–41, 1989.
S. Weisberg. Applied Linear Regression, 3rd edition. Wiley, New York, 2005.
S. Wold. Spline functions in data analysis. Technometrics, 16:1–11, 1974.
F. Yao, H.-G. Müller, and J.-L. Wang. Functional data analysis for sparse longitudinal data. Journal of the American Statistical Association, 100:577–590, 2005.
T. Zewotir and J. S. Galpin. Influence diagnostics for linear mixed models. Journal of Data Science, 3:153–177, 2005.
D. Zhang, X. Lin, J. Raz, and M. Sowers. Semiparametric stochastic mixed models for longitudinal data. Journal of the American Statistical Association, 93:710–719, 1998.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Snijders, T.A., Berkhof, J. (2008). Diagnostic Checks for Multilevel Models. In: Leeuw, J.d., Meijer, E. (eds) Handbook of Multilevel Analysis. Springer, New York, NY. https://doi.org/10.1007/978-0-387-73186-5_3
Download citation
DOI: https://doi.org/10.1007/978-0-387-73186-5_3
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-73183-4
Online ISBN: 978-0-387-73186-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)