All Title Author
Keywords Abstract


Marginal Conceptual Predictive Statistic for Mixed Model Selection

DOI: 10.4236/ojs.2016.62021, PP. 239-253

Keywords: Mixed Model Selection, Marginal Cp, Improved Marginal Cp, Marginal Gauss Discrepancy, Linear Mixed Model

Full-Text   Cite this paper   Add to My Lib

Abstract:

We focus on the development of model selection criteria in linear mixed models. In particular, we propose the model selection criteria following the Mallows’ Conceptual Predictive Statistic (Cp) [1] [2] in linear mixed models. When correlation exists between the observations in data, the normal Gauss discrepancy in univariate case is not appropriate to measure the distance between the true model and a candidate model. Instead, we define a marginal Gauss discrepancy which takes the correlation into account in the mixed models. The model selection criterion, marginal Cp, called MCp, serves as an asymptotically unbiased estimator of the expected marginal Gauss discrepancy. An improvement of MCp, called IMCp, is then derived and proved to be a more accurate estimator of the expected marginal Gauss discrepancy than MCp. The performance of the proposed criteria is investigated in a simulation study. The simulation results show that in small samples, the proposed criteria outperform the Akaike Information Criteria (AIC) [3] [4] and Bayesian Information Criterion (BIC) [5] in selecting the correct model; in large samples, their performance is competitive. Further, the proposed criteria perform significantly better for highly correlated response data than for weakly correlated data.

References

[1]  Mallows, C.L. (1973) Some Comments on Cp. Technometrics, 15, 661-675.
[2]  Mallows, C.L. (1995) More Comments on Cp. Technometrics, 37, 362-372.
[3]  Akaike, H. (1973) Information Theory and an Extension of the Maximum Likelihood Principle. In: Petrov, B.N. and Csaki, F., Eds., International Symposium on Information Theory, 267-281.
[4]  Akaike, H. (1974) A New Look at the Model Selection Identification. IEEE Transactions on Automatic Control, 19, 716-723.
http://dx.doi.org/10.1109/TAC.1974.1100705
[5]  Schwarz, G. (1978) Estimating the Dimension of a Model. Annals of Statistics, 6, 461-464.
http://dx.doi.org/10.1214/aos/1176344136
[6]  Sugiura, N. (1978) Further Analysis of the Data by Akaike’s Information Criterion and the Finite Corrections. Communications in Statistics—Theory and Methods A, 7, 13-26.
http://dx.doi.org/10.1080/03610927808827599
[7]  Shang, J. and Cavanaugh, J.E. (2008) Bootstrap Variants of the Akaike Information Criterion for Mixed Model Selection. Computational Statistics & Data Analysis, 52, 2004-2021.
http://dx.doi.org/10.1016/j.csda.2007.06.019
[8]  Azari, R., Li, L. and Tsai, C. (2006) Longitudinal Data Model Selection. Applied Times Series Analysis, Academic Press, New York, 1-23.
http://dx.doi.org/10.1016/j.csda.2005.05.009
[9]  Vaida, F. and Blanchard, S. (2005) Conditional Akaike Information for Mixed-Effects Models. Biometrika, 92, 351-370.
http://dx.doi.org/10.1093/biomet/92.2.351
[10]  Henderson, C.R. (1950) Estimation of Genetic Parameters. Annals of Mathematical Statistics, 21, 309-310.
[11]  Harville, D.A. (1990) BLUP (Best Linear Unbiased Prediction) and beyond. In: Gianola, D. and Hammond, K., Eds., Advances in Staitstical Methods for Genetic Improvement of Livestock, Springer, New York, 239-276.
http://dx.doi.org/10.1007/978-3-642-74487-7_12
[12]  Robinson, G.K. (1991) That BLUP Is a Good Thing: The Estimation of Random Effects. Statistical Science, 6, 15-32.
http://dx.doi.org/10.1214/ss/1177011926
[13]  Dimova, R.B., Mariantihi, M. and Talal, A.H. (2011) Information Methods for Model Selection in Linear Mixed Effects Models with Application to HCV Data. Computational Statistics & Data Analysis, 55, 2677-2697.
http://dx.doi.org/10.1016/j.csda.2010.10.031
[14]  Müller, S., Scealy, J.L. and Welsh, A.H. (2013) Model Selection in Linear Mixed Models. Statistical Science, 28, 135-167.
http://dx.doi.org/10.1214/12-STS410
[15]  Jones, R.H. (2011) Bayesian Information Criterion for Longitudinal and Clustered Data. Statistics in Medicine, 30, 3050-3056.
http://dx.doi.org/10.1002/sim.4323
[16]  Fujikoshi, Y. and Satoh, K. (1997) Modified AIC and Cp in Multivariate Linear Regression. Biometrika, 84, 707-716.
http://dx.doi.org/10.1093/biomet/84.3.707
[17]  Davies, S.L., Neath, A.A. and Cavanaugh, J.E. (2006) Estimation Optimality of Corrected AIC and Modified Cp in Linear Regression. International Statistical Review, 74, 161-168.
http://dx.doi.org/10.1111/j.1751-5823.2006.tb00167.x
[18]  Cavanaugh, J., Neath, A.A. and Davies, S.L. (2010) An Alternate Version of the Conceptual Predictive Statistic Based on a Symmetrized Discrepancy Measure. Journal of Statistical Planning and Inference, 140, 3389-3398.
http://dx.doi.org/10.1016/j.jspi.2010.05.002
[19]  Jiang, J. (2007) Linear and Generalized Linear Mixed Models and Their Applications. Springer, New York.
[20]  Jiang, J. and Rao, J.S. (2003) Consistent Procedures for Mixed Linear Model Selection. Sankhya, 65, 23-42.

Full-Text

comments powered by Disqus

Contact Us

service@oalib.com

QQ:3279437679

微信:OALib Journal