Comparison on Confidence Intervals for Variance of Random Effect in Unbalanced Hierarchical Model
Abstract
The objective of this research is to study and compare three interval estimation methods for variance of random effect in unbalanced hierarchical model; the method by TG (Ting et al., 1990), the method by PB (Park et al., 2003) and the method by LL (Li et al., 2005). The considered criteria are based on the confidence coefficients and the average length of the confidence intervals. The scopes of this research are consisted of the sample sizes: (5,8,10), (5,10,15), (5,2,7,5,7,9) and (5,10,15,5,10,15) the intracluster correlation (p= 0.001, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 0.999) and the confidence level which is 90%. Data is simulated 2,000 times for each situation by Monte Carlo Technique using SAS software. The simulation results show that the method by PB is the best method for almost situations because it provides the smallest average length of confidence interval.References
Burdick, R.K., & Graybill, F.A. (1984). Confidence Intervals on Linear Combinations of Variance Components in
the Unbalanced One-Way Classification. Technometrics, 26(2), 131–136.
Burdick, R.K., & Eickman, J. (1986). Confidence Intervals on the Among Group Variance Component in the
Unbalanced One-Fold Nested Design. Journal of Statistical Computation and Simulation, 26, 205-219.
Burdick, R.K., & Graybill, F.A. (1992). Confidence Intervals on Variance Components. Florida: CRC Press.
Chomtee, B. (2013). Nested Designs. Statistical Experimental Design: Theory and Analysis by Using SAS
Software. (pp. 199). Bangkok: Department of Statistics, Faculty of Science, Kasetsart University. (in Thai)
Khuri, A.I. (1999). Further Insights Concerning the Method of Unweighted Means. (pp. 1-28). Florida:
Department of Statistics, University of Florida.
Li, X., & Li, G. (2005). Confidence Intervals on Sum of Variance Components with Unbalanced Designs.
Communications in Statistics - Theory and Methods, 34, 833–845.
Park, D.J., & Burdick, R.K. (2003). Performance of Confidence Intervals in Regression Models with Unbalanced One-Fold Nested Error Structures. Communications in Statistics - Simulation and Computation, 32(3), 717–732.
Thomas, J.D., & Hultiquist, R.A. (1978). Interval Estimation for the Unbalanced Case of the One-Way Random Effects Model. The Annals of Statistics, 6(3), 582–587.
Ting, N., Burdick, R.K., Graybill, F.A., Jeyaratnam, S., & Lu, T.F.C. (1990). Confidence Intervals on Linear
Combinations of Variance Components. Journal of Statistical Computation and Simulation, 35,135–143.
Van der Rijst, M., Van der Merwe, A.J., & Hugo, J. (2014). Performance of Confidence Intervals on the Among Group Variance in the Unbalanced One-Factor Random Effects Model. Retrieved January 20, 2019, from https://www.ufs.ac.za/docs/librariesprovider22/mathematical-statistics-and-actuarial-science-documents/technical-reports-documents/teg411-1869-eng.pdf?sfvrsn=1833f921_0
the Unbalanced One-Way Classification. Technometrics, 26(2), 131–136.
Burdick, R.K., & Eickman, J. (1986). Confidence Intervals on the Among Group Variance Component in the
Unbalanced One-Fold Nested Design. Journal of Statistical Computation and Simulation, 26, 205-219.
Burdick, R.K., & Graybill, F.A. (1992). Confidence Intervals on Variance Components. Florida: CRC Press.
Chomtee, B. (2013). Nested Designs. Statistical Experimental Design: Theory and Analysis by Using SAS
Software. (pp. 199). Bangkok: Department of Statistics, Faculty of Science, Kasetsart University. (in Thai)
Khuri, A.I. (1999). Further Insights Concerning the Method of Unweighted Means. (pp. 1-28). Florida:
Department of Statistics, University of Florida.
Li, X., & Li, G. (2005). Confidence Intervals on Sum of Variance Components with Unbalanced Designs.
Communications in Statistics - Theory and Methods, 34, 833–845.
Park, D.J., & Burdick, R.K. (2003). Performance of Confidence Intervals in Regression Models with Unbalanced One-Fold Nested Error Structures. Communications in Statistics - Simulation and Computation, 32(3), 717–732.
Thomas, J.D., & Hultiquist, R.A. (1978). Interval Estimation for the Unbalanced Case of the One-Way Random Effects Model. The Annals of Statistics, 6(3), 582–587.
Ting, N., Burdick, R.K., Graybill, F.A., Jeyaratnam, S., & Lu, T.F.C. (1990). Confidence Intervals on Linear
Combinations of Variance Components. Journal of Statistical Computation and Simulation, 35,135–143.
Van der Rijst, M., Van der Merwe, A.J., & Hugo, J. (2014). Performance of Confidence Intervals on the Among Group Variance in the Unbalanced One-Factor Random Effects Model. Retrieved January 20, 2019, from https://www.ufs.ac.za/docs/librariesprovider22/mathematical-statistics-and-actuarial-science-documents/technical-reports-documents/teg411-1869-eng.pdf?sfvrsn=1833f921_0
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Published
2019-06-07
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