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ESTIMATION AND INFERENCES IN LINEAR MIXED EFFECTS MODELS: A COMPARATIVE STUDY

Year 2013, Volume: 2 Issue: 2, 91 - 102, 06.05.2015

Abstract

Smoothing methods that use basis functions with penalization can be formulated as fits in formlinear mixed effects models. This allows s uch models to be fitted using sta ndard mixed models structures. In this paper we provide an estimation and inference for linear mixed models using restrict- ed maximum likelihood and penalized spline smoothing, and describe the connection between the two. To this end, a real data example is considered and model is fitted in R using diff erent package. We see that penalized spline smoothing expressed in form of linear mixed model gives the better results than standard mixed effects model.

References

  • Coull, B. A., Ruppert, D. and Wand, M.P. (2001). Simple Incorporation of Interactions into Additive Models. Biometrics 57, 539–545.
  • Coull, B.A. , Schwartz, J. and Wand, M.P. (2001). Respiratory Health and Air Pollution: Additive Mixed Model Analysis. Biostatistics 2 , 337–349.
  • Davidian, M and Giltinan, D.M. (1996). Nonlinear Models for Repeated Measurement Data, Chapman and Hall, London.
  • Diggle, P., Heagerty, P., Liang, K.-L., and Zeger, S. (2002). Analysis of Longitudinal Data. 2nd ed, Oxford University Press.
  • Eilers, P.H.C and Marx, B.D. (1996). Flexible Smoothing with B-Splines and Penalties.Statistical Science. 11.
  • Green P. J. and Silverman, B. W. (1994). Nonparametric Regression and Generalized Linear Model, Chapman &Hall, London
  • McCulloch, C.E and Searle, S.R. (2001). Generalized, Linear, and Mixed Models. Willey, New York.
  • O’Sullivan, F. (1986). A Statistical Perspective on Ill-Posed Inverse Problems (C/R: P519-527). Statistical Science 1 , 502–518.
  • Parise, H., Wand, M.P. , Ruppert, D. and Ryan, L. (2001). Incorporation of Historical Controls using Semiparametric Mixed Models. Journal of the Royal Statistical Society: Series C Applied Statistics, 50, 31–42.
  • Pinheiro, J.C. and Bates, D.M. (2000). Mixed Effects Models in S and S-Plus, Springer-Verlag, New York.
  • Ruppert, D., Wand, M. and Carroll, R. (2003). Semiparametric Regression, Cambridge University Press, Cambridge.
  • Shively, T. S., Kohn, R. And Wood, S. (1999). Variable Selection and Function Estimation in Additive Nonparametric Regression using A Data-Based Prior (with discussion). Journal of the American Statistical Association, 94, 777–806.

DOĞRUSAL KARMA ETKİLİ MODELLERDE TAHMİN VE ÇIKARSAMALAR: BİR KARŞILAŞTIRMALI ÇALIŞMA

Year 2013, Volume: 2 Issue: 2, 91 - 102, 06.05.2015

Abstract

References

  • Coull, B. A., Ruppert, D. and Wand, M.P. (2001). Simple Incorporation of Interactions into Additive Models. Biometrics 57, 539–545.
  • Coull, B.A. , Schwartz, J. and Wand, M.P. (2001). Respiratory Health and Air Pollution: Additive Mixed Model Analysis. Biostatistics 2 , 337–349.
  • Davidian, M and Giltinan, D.M. (1996). Nonlinear Models for Repeated Measurement Data, Chapman and Hall, London.
  • Diggle, P., Heagerty, P., Liang, K.-L., and Zeger, S. (2002). Analysis of Longitudinal Data. 2nd ed, Oxford University Press.
  • Eilers, P.H.C and Marx, B.D. (1996). Flexible Smoothing with B-Splines and Penalties.Statistical Science. 11.
  • Green P. J. and Silverman, B. W. (1994). Nonparametric Regression and Generalized Linear Model, Chapman &Hall, London
  • McCulloch, C.E and Searle, S.R. (2001). Generalized, Linear, and Mixed Models. Willey, New York.
  • O’Sullivan, F. (1986). A Statistical Perspective on Ill-Posed Inverse Problems (C/R: P519-527). Statistical Science 1 , 502–518.
  • Parise, H., Wand, M.P. , Ruppert, D. and Ryan, L. (2001). Incorporation of Historical Controls using Semiparametric Mixed Models. Journal of the Royal Statistical Society: Series C Applied Statistics, 50, 31–42.
  • Pinheiro, J.C. and Bates, D.M. (2000). Mixed Effects Models in S and S-Plus, Springer-Verlag, New York.
  • Ruppert, D., Wand, M. and Carroll, R. (2003). Semiparametric Regression, Cambridge University Press, Cambridge.
  • Shively, T. S., Kohn, R. And Wood, S. (1999). Variable Selection and Function Estimation in Additive Nonparametric Regression using A Data-Based Prior (with discussion). Journal of the American Statistical Association, 94, 777–806.
There are 12 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Özlem Aksoy

Dursun Aydın

Publication Date May 6, 2015
Published in Issue Year 2013 Volume: 2 Issue: 2

Cite

APA Aksoy, Ö., & Aydın, D. (2015). ESTIMATION AND INFERENCES IN LINEAR MIXED EFFECTS MODELS: A COMPARATIVE STUDY. Anadolu University Journal of Science and Technology B - Theoretical Sciences, 2(2), 91-102.
AMA Aksoy Ö, Aydın D. ESTIMATION AND INFERENCES IN LINEAR MIXED EFFECTS MODELS: A COMPARATIVE STUDY. AUBTD-B. May 2015;2(2):91-102.
Chicago Aksoy, Özlem, and Dursun Aydın. “ESTIMATION AND INFERENCES IN LINEAR MIXED EFFECTS MODELS: A COMPARATIVE STUDY”. Anadolu University Journal of Science and Technology B - Theoretical Sciences 2, no. 2 (May 2015): 91-102.
EndNote Aksoy Ö, Aydın D (May 1, 2015) ESTIMATION AND INFERENCES IN LINEAR MIXED EFFECTS MODELS: A COMPARATIVE STUDY. Anadolu University Journal of Science and Technology B - Theoretical Sciences 2 2 91–102.
IEEE Ö. Aksoy and D. Aydın, “ESTIMATION AND INFERENCES IN LINEAR MIXED EFFECTS MODELS: A COMPARATIVE STUDY”, AUBTD-B, vol. 2, no. 2, pp. 91–102, 2015.
ISNAD Aksoy, Özlem - Aydın, Dursun. “ESTIMATION AND INFERENCES IN LINEAR MIXED EFFECTS MODELS: A COMPARATIVE STUDY”. Anadolu University Journal of Science and Technology B - Theoretical Sciences 2/2 (May 2015), 91-102.
JAMA Aksoy Ö, Aydın D. ESTIMATION AND INFERENCES IN LINEAR MIXED EFFECTS MODELS: A COMPARATIVE STUDY. AUBTD-B. 2015;2:91–102.
MLA Aksoy, Özlem and Dursun Aydın. “ESTIMATION AND INFERENCES IN LINEAR MIXED EFFECTS MODELS: A COMPARATIVE STUDY”. Anadolu University Journal of Science and Technology B - Theoretical Sciences, vol. 2, no. 2, 2015, pp. 91-102.
Vancouver Aksoy Ö, Aydın D. ESTIMATION AND INFERENCES IN LINEAR MIXED EFFECTS MODELS: A COMPARATIVE STUDY. AUBTD-B. 2015;2(2):91-102.