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References

  • Akaike, H. (1973) Information theory as an extension of the maximum likelihood principle. 2nd International Symposium on Information Theory (eds B.N. Petrov & F. Csaki), pp. 267281. Akademiai Kiado, Budapest.
  • Bates, D., Maechler, M. & Bolker, B. (2011) lme4: linear mixed-effects models. R package, version 0.999375-42. http://CRAN.R-project.org/package=lme4.
  • Bolker, B.M., Brooks, M.E., Clark, C.J., Geange, S.W., Poulsen, J.R., Stevens, M.H.H. & White, J.S.S. (2009) Generalized linear mixed models: a practical guide for ecology and evolution. Trends in Ecology & Evolution, 24, 127135.
  • Bryk, A.S. & Raudenbush, S. (1992) Hierarchical Linear Models. Sage, Newbury Park, CS.
  • Burnham, K.P. & Anderson, D.R. (2002) Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach, 2nd edn. Springer-Verlag, Berlin.
  • Cameron, A.C. & Windmeijer, F.A.G. (1996) R-squared measures for count data regression models with applications to health-care utilization. Journal of Business & Economic Statistics, 14, 209220.
  • Cameron, A.C. & Windmeijer, F.A.G. (1997) An R-squared measure of goodness of fit for some common nonlinear regression models. Journal of Econometrics, 77, 329342.
  • Claeskens, G. & Hjort, N.L. (2009) Model Selection and Model Averaging. Cambridge University Press, Cambridge.
  • Congdon, P.D. (2010) Applied Bayesian Hierarchical Methods. CRC, Boca Raton, FL.
  • Dean, R., Nakagawa, S. & Pizzari, T. (2011) The risk and intensity of sperm ejection in female birds. American Naturalist, 178, 343354.
  • Draper, N.R. & Smith, H. (1998) Applied Regression Analysis, 3rd edn. Wiley, New York.
  • Edwards, L.J., Muller, K.E., Wolfinger, R.D., Qaqish, B.F. & Schabenberger, O. (2008) An R2 statistic for fixed effects in the linear mixed model. Statistics in Medicine, 27, 61376157.
  • Gelman, A. & Hill, J. (2007) Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press, Cambridge.
  • Gelman, A. & Pardoe, L. (2006) Bayesian measures of explained variance and pooling in multilevel (hierarchical) models. Technometrics, 48, 241251.
  • Goldstein, H., Browne, W. & Rasbash, J. (2002) Partitioning variation in multilevel models. Understanding Statistics, 1, 223231.
  • Grueber, C.E., Nakagawa, S., Laws, R.J. & Jamieson, I.G. (2011) Multimodel inference in ecology and evolution: challenges and solutions. Journal of Evolutionary Biology, 24, 699711.
  • Hadfield, J.D. (2010) MCMC methods for multi-response Generalised Linear Mixed Models: the MCMCglmm R package. Journal of Statistical Software, 33, 122.
  • Hamaker, E.L., van Hattum, P., Kuiper, R.M. & Hoijtink, H. (2011) Model selection based on information criteria in multilevel modeling. Handbook of Advanced Multilevel Analysis (eds J. Hox & J.K. Roberts), pp. 231255. Routledge, New York.
  • Hössjer, O. (2008) On the coefficient of determination for mixed regression models. Journal of Statistical Planning and Inference, 138, 30223038.
  • Kvålseth, T.O. (1985) Cautionary note about R2. American Statistician, 39, 279285.
  • Liu, H.H., Zheng, Y. & Shen, J. (2008) Goodness-of-fit measures of R(2) for repeated measures mixed effect models. Journal of Applied Statistics, 35, 10811092.
  • Maddala, G.S. (1983) Limited-Dependent and Qualitative Variables in Econometrics. Cambridge University Press, Cambridge.
  • Menard, S. (2000) Coefficients of determination for multiple logistic regression analysis. American Statistician, 54, 1724.
  • Merlo, J., Chaix, B., Yang, M., Lynch, J. & Rastam, L. (2005a) A brief conceptual tutorial on multilevel analysis in social epidemiology: interpreting neighbourhood differences and the effect of neighbourhood characteristics on individual health. Journal of Epidemiology and Community Health, 59, 10221028.
  • Merlo, J., Yang, M., Chaix, B., Lynch, J. & Rastam, L. (2005b) A brief conceptual tutorial on multilevel analysis in social epidemiology: investigating contextual phenomena in different groups of people. Journal of Epidemiology and Community Health, 59, 729736.
  • Nagelkerke, N.J.D. (1991) A note on a general definition of the coefficient of determination. Biometrika, 78, 691692.
  • Nakagawa, S. & Cuthill, I.C. (2007) Effect size, confidence interval and statistical significance: a practical guide for biologists. Biological Reviews, 82, 591605.
  • Nakagawa, S. & Schielzeth, H. (2010) Repeatability for Gaussian and non-Gaussian data: a practical guide for biologists. Biological Reviews, 85, 935956.
  • Orelien, J.G. & Edwards, L.J. (2008) Fixed-effect variable selection in linear mixed models using R2 statistics. Computational Statistics & Data Analysis, 52, 18961907.
  • Pinheiro, J.C. & Bates, D.M. (2000) Mixed-effects Models in S and S-Plus. Springer, New York.
  • R Development Core Team (2012) R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria.
  • Raudenbush, S. & Bryk, A.S. (1986) A hierarchical model for studying school effects. Sociology of Education, 59, 117.
  • Roberts, J.K., Monaco, J.P., Stovall, H. & Foster, V. (2011) Explained variance in multilevel models. Handbook of Advanced Multilevel Analysis (eds J. Hox & J.K. Roberts), pp. 219230. Routledge, New York.
  • Schielzeth, H. (2010) Simple means to improve the interpretability of regression coefficients. Methods in Ecology and Evolution, 1, 103113.
  • Schielzeth, H. & Forstmeier, W. (2009) Conclusions beyond support: overconfident estimates in mixed models. Behavioral Ecology, 20, 416420.
  • Schielzeth, H. & Nakagawa, S. (2012) Nested by design: model fitting and interpretation in a mixed model era. Methods in Ecology and Evolution, doi: 10.1111/j.2041-210x.2012.00251.x.
  • Schwarz, G.E. (1978) Estimating the dimension of a model. Annals of Statistics, 6, 461464.
  • Snijders, T.A. & Bosker, R.J. (1994) Modeled variance in two-level models. Sociological Methods & Research, 22, 342363.
  • Snijders, T. & Bosker, R. (1999) Multilevel Analysis: An Introduction to Basic and Advanced Multilevel Modeling. Sage, London.
  • Snijders, T. & Bosker, R. (2011) Multilevel Analysis: An Introduction to Basic and Advanced Multilevel Modeling, 2nd edn. Sage, London.
  • Spiegelhalter, D.J., Best, N.G., Carlin, B.R. & van der Linde, A. (2002) Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society Series B-Statistical Methodology, 64, 583616.
  • Tjur, T. (2009) Coefficients of determination in logistic regression models – a new proposal: the coefficient of discrimination. American Statistician, 63, 366372.
  • Vonesh, E.F., Chinchilli, V.P. & Pu, K.W. (1996) Goodness-of-fit in generalized nonlinear mixed-effects models. Biometrics, 52, 572587.
  • Xu, R.H. (2003) Measuring explained variation in linear mixed effects models. Statistics in Medicine, 22, 35273541.