A Comparison of Confidence Interval Methods of Fixed Effect in Nested Error Regression Model

Hatice Tül Kübra Akdur; Deniz Özonur; Hülya Bayrak

doi:10.19113/sdufbed.05095

A Comparison of Confidence Interval Methods of Fixed Effect in Nested Error Regression Model

Abstract

Linear mixed-effects models are very popular and powerful tools in many scientific fields such as zoology, biology, and education. Estimators of fixed effects do not only depend on the variances of error terms but they also depend on random terms in mixed-effect models. When the distributions of random effects are unknown or enough sample size cannot be obtained, standard methods may fail. This study aims to determine a promising confidence interval method among existing methods in terms of coverage probability of true value of parameter. Standard and parametric bootstrap-based confidence interval methods for nested error regression model were compared in the simulation study under small samples. It is observed that parametric bootstrap-based method provides better coverage rates for small intra-correlation and profile likelihood method usually provides better results for moderate and strong correlation.

Keywords

Mixed-effect models; Confidence interval; Parametric bootstrap; Profile likelihood

References

[1] Demidenko, E. 2004. Mixed Models: Theory and Applications. Wiley, 726p.
[2] Eisenhart, C. 1947. The Assumptions Underlying the Analysis of Variance. Biometrics, 3(1), 1-21.
[3] Patterson, H.D., Thompson, R. 1971. Recovery of Inter-block Information When Block Sizes are Unequal. Biometrika, 58(3), 545-554.
[4] Searle, S.R., Casella, G., McCulloch, C.E., 2009. Variance Components (Vol. 391). John Wiley & Sons, 509p.
[5] 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(388), 853-862.
[6] Kenward, M. G. Roger, J. H. 1997. Small Sample Inference for Fixed Effects From Restricted Maximum Likelihood. Biometrics, 1997, 983-997.
[7] Harville, D. A., Fenech, A. P. 1985. Confidence Intervals for a Variance Ratio, or for Heritability, in an Unbalanced Mixed Linear Model. Biometrics, 1985, 137-152.
[8] Savin, A., 2005. Confidence Intervals for Common Mean in One-way Classification Model with Fixed Effects. Measurement, 2005, 15-19.

[9] Hall, P., Maiti, T. 2006. On Parametric Bootstrap Methods for Small Area Prediction. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 68(2), 221-238.
[10] Staggs, V. 2009. Parametric Bootstrap Interval Approach to Inference for Fixed Effects in the Mixed Linear Model, PhD Thesis, University of Kansas, 73 p, Lawrence.
[11] Burch, B. D. 2011. Confidence Intervals for Variance Components in Unbalanced One-way Random Effects Model Using Non-normal Distributions. Journal of Statistical Planning and Inference, 141(12), 3793-3807.
[12] Liu, J. 2013. Statistical Inference for Functions of the Parameters of a Linear Mixed Model, PhD Thesis, Iowa State University, 75p, Ames.
[13] Neyman, J., Pearson, E. S. 1928. On the Use and Interpretation of Certain Test Criteria for Purposes of Statistical Inference: Part I. Biometrika, 1928, 175-240.
[14] Wald, A. 1943. Tests of Statistical Hypotheses Concerning Several Parameters when the Number of Observations is Large. Transactions of the American Mathematical Society, 54(3), 426-482.
[15] Bates, D. M., Pinheiro, J. C. 1994. Model Building for Nonlinear Mixed Effects Models, University of Wisconsin, Department of Biostatistics.
[16] Lehmann, E. L. 1999. Elements of Large-Sample Theory. Springer Science & Business Media, 645p.
[17] Hulting, F. L., Harville, D. A. 1991. Some Bayesian and Non-Bayesian Procedures for the Analysis of Comparative Experiments and for Small-area Estimation: Computational Aspects, Frequentist Properties, and Relationships. Journal of the American Statistical Association, 86(415), 557-568.
[18] Efron, B. 1992. Bootstrap Methods: Another Look at the Jackknife. Breakthroughs in Statistics. 1992, 569-593, New York.
[19] DiCiccio, T. J., Romano, J. P. 1988. A Review of Bootstrap Confidence Intervals. Journal of the Royal Statistical Society. Series B (Methodological), 338-354.
[20] DiCiccio, T. J., Romano, J. P. 1990. Nonparametric Confidence Limits by Resampling Methods and Least Favourable Families. International Statistical Review/Revue Internationale de Statistique, 1990, 59-76.
[21] Goldstein, H. 2011. Multilevel Statistical Models (Vol. 922). John Wiley & Sons, 358p.
[22] Zeger, S. L., Liang, K. Y. 1986. Longitudinal Data Analysis for Discrete and Continuous Outcomes. Biometrics, 1986, 121-130.
[23] Chernick, M. R. 2011. Bootstrap Methods: A Guide for Practitioners and Researchers (Vol. 619). John Wiley & Sons, 369p.
[24] Efron, B., Efron, B. 1982. The Jackknife, the Bootstrap and Other Resampling Plans (Vol. 38). Philadelphia: Society for Industrial and Applied Mathematics, 92p.
[25] Efron, B., Tibshirani, R. J. 1994. An Introduction to the Bootstrap. CRC press, 436p.
[26] Halekoh, U., Højsgaard, S. 2014. A kenward-Roger Approximation and Parametric Bootstrap Methods for Tests in Linear Mixed Models–the R Package pbkrtest. Journal of Statistical Software, 59(9), 1-30.
[27] Bates, D., Maechler, M., Bolker, B., Walker, S. 2014. lme4: Linear Mixed-Effects Models Using Eigen and S4. R Package Version, 1(7).

Details

Primary Language

English

Subjects

-

Journal Section

-

Authors

Hatice Tül Kübra Akdur

Deniz Özonur

Hülya Bayrak

Publication Date

July 26, 2016

Submission Date

February 15, 2016

Acceptance Date

-

Published in Issue

Year 2016 Volume: 20 Number: 2

DOI

https://doi.org/10.19113/sdufbed.05095

IZ

https://izlik.org/JA97GR75MU

Cite

RIS / Bibtex

APA

Akdur, H. T. K., Özonur, D., & Bayrak, H. (2016). A Comparison of Confidence Interval Methods of Fixed Effect in Nested Error Regression Model. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 20(2). https://doi.org/10.19113/sdufbed.05095

AMA

1.Akdur HTK, Özonur D, Bayrak H. A Comparison of Confidence Interval Methods of Fixed Effect in Nested Error Regression Model. J. Nat. Appl. Sci. 2016;20(2). doi:10.19113/sdufbed.05095

Chicago

Akdur, Hatice Tül Kübra, Deniz Özonur, and Hülya Bayrak. 2016. “A Comparison of Confidence Interval Methods of Fixed Effect in Nested Error Regression Model”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 20 (2). https://doi.org/10.19113/sdufbed.05095.

EndNote

Akdur HTK, Özonur D, Bayrak H (August 1, 2016) A Comparison of Confidence Interval Methods of Fixed Effect in Nested Error Regression Model. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 20 2

IEEE

[1]H. T. K. Akdur, D. Özonur, and H. Bayrak, “A Comparison of Confidence Interval Methods of Fixed Effect in Nested Error Regression Model”, J. Nat. Appl. Sci., vol. 20, no. 2, Aug. 2016, doi: 10.19113/sdufbed.05095.

ISNAD

Akdur, Hatice Tül Kübra - Özonur, Deniz - Bayrak, Hülya. “A Comparison of Confidence Interval Methods of Fixed Effect in Nested Error Regression Model”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 20/2 (August 1, 2016). https://doi.org/10.19113/sdufbed.05095.

JAMA

1.Akdur HTK, Özonur D, Bayrak H. A Comparison of Confidence Interval Methods of Fixed Effect in Nested Error Regression Model. J. Nat. Appl. Sci. 2016;20. doi:10.19113/sdufbed.05095.

MLA

Akdur, Hatice Tül Kübra, et al. “A Comparison of Confidence Interval Methods of Fixed Effect in Nested Error Regression Model”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, vol. 20, no. 2, Aug. 2016, doi:10.19113/sdufbed.05095.

Vancouver

1.Hatice Tül Kübra Akdur, Deniz Özonur, Hülya Bayrak. A Comparison of Confidence Interval Methods of Fixed Effect in Nested Error Regression Model. J. Nat. Appl. Sci. 2016 Aug. 1;20(2). doi:10.19113/sdufbed.05095

Cited By

An Adaptation of Pseudo-Score Confidence Interval Method for Linear Mixed Models

Hacettepe Journal of Mathematics and Statistics

https://doi.org/10.15672/hujms.510261