Abstract
The theory of optimal test-control block designs provides guidance on treatments allocation in experimental units. However, it is theoretically difficult to find them; therefore, the availability of an efficient and user-friendly algorithm for finding the optimal designs is essential for both researchers and practitioners. This paper describes an algorithm for constructing efficient test-control incomplete block designs with correlated observations. In order to evaluate the algorithm, we compare our results with the optimal designs presented in some published papers. An advantage of our algorithm is its independency to the size of blocks and the structure of correlation. Also, it takes to run between 30 s and 10 min depending on the type of CPU processor and the design.
Similar content being viewed by others
References
Angelis L (2003) An evolutionary algorithm for A-optimal incomplete block designs. J Stat Comput Simul 73(10):753–771
Chatterjee A, Siarry P (2006) Nonlinear inertia weight variation for dynamic adaptation in particle swarm optimization. Comput Oper Res 33(3):859–871
Cutler DR (1993) Efficient block designs for comparing test treatments to a control when the errors are correlated. J Stat Plan Inference 36(1):107–125
Das A, Dey A, Kageyama S, Sinha K (2005) A-efficient balanced treatment incomplete block designs. Aust J Comb 32:243–252
Eberhart RC, Shi Y (2000) Comparing inertia weights and constriction factors in particle swarm optimization. In: Proceedings of the 2000 congress on evolutionary computation. CEC00 (Cat. No. 00TH8512), vol 1. IEEE, pp 84–88
Fan SKS, Chang JM (2007) A modified particle swarm optimizer using an adaptive dynamic weight scheme. In: International conference on digital human modeling. Springer, Berlin, pp 56–65
Hero A, Rajaratnam B (2012) Hub discovery in partial correlation graphs. IEEE Trans Inf Theory 58(9):6064–6078
Iqbal I, Tahir MH (2008) Construction of test-control treatment block designs when \(k> v\). Aligarh J Stat 28:55–73
Jones B (1976) An algorithm for deriving optimal block designs. Technometrics 18(4):451–458
Jones B, Eccleston JA (1980) Exchange and interchange procedures to search for optimal designs. J R Stat Soc Ser B (Methodolo) 42(2):238–243
Kennedy J, Eberhart R (1995). Particle swarm optimization (PSO). In: Proceedings of IEEE international conference on neural networks IV, Perth, Australia, pp 1942–1948
Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220(4598):671–680
Kunert J, Martin RJ, Eccleston J (2010) Optimal block designs comparing treatments with a control when the errors are correlated. J Stat Plan Inference 140(9):2719–2738
Li C, Coster DC (2014) A simulated annealing algorithm for D-optimal design for 2-way and 3-way polynomial regression with correlated observations. J Appl Math 2014:1–7
Li C, Coster DC (2015) Construction of weak universal optimal block designs with various correlation structures and block sizes. J Stat Plan Inference 160:1–10
Majumdar D, Notz WI (1983) Optimal incomplete block designs for comparing treatments with a control. Ann Stat 11(1):258–266
Martin RJ, Eccleston JA (1992) Recursive formulae for constructing block designs with dependent errors. Biometrika 79(2):426–430
Martin RJ, Eccleston JA (2001) Optimal and near-optimal designs for dependent observations. Stat Appl 3(1,2):101–116
Mitchell T.J. (1973) Computer construction of small D-optimal incomplete block designs. In: Proceedings of the 39th session of the ISI, vol 2, pp 199–205
Nguyen NK (1994) Construction of optimal block designs by computer. Technometrics 36(3):300–307
Nguyen NK, Dey A (1990) Computer-aided construction of small (M, S)-optimal incomplete block designs. Aust J Stat 32(3):399–410
Rathore A, Parsad R, Gupta VK (2006) Computer aided search of efficient block designs for making all possible pairwise treatment comparisons. J Stat Appl J Forum Interdis Math 1:15–33
Russell KG, Eccleston JA, Knudsen GJ (1981) Algorithms for the construction of (M, S)-optimal block designs and row-column designs. J Stat Comput Simul 12(2):93–105
Satpati SK, Parsad R, Gupta VK (2007) Efficient block designs for dependent observations—a computer-aided search. Commun Stat Theory Method 36(6):1187–1223
Shi Y, Eberhart R (1998a) A modified particle swarm optimizer. In: 1998 IEEE international conference on evolutionary computation proceedings. IEEE world congress on computational intelligence (Cat. No. 98TH8360). IEEE, pp 69–73
Shi Y, Eberhart R.C (1998b) Parameter selection in particle swarm optimization. In: International conference on evolutionary programming. Springer, Berlin, pp 591–600
Zergaw GA (1989) Sequential method of constructing optimal block designs. Aust J Stat 31(2):333–342
Zhu Z, Coster DC (2004) Weak universal optimal block designs for correlated observations. PhD dissertation, Department of mathematics and statistics, Utah State University
Acknowledgements
This paper is a part of the second author?s Ph.D. thesis. Author’s would like to thank the editor-in-chief and reviewers for their constructive and helpful comments which considerably led to improving the quality of the initial draft of the paper.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Pooladsaz, S., Doosti-Irani, M. An algorithm for finding efficient test-control block designs with correlated observations. Comput Stat 35, 821–836 (2020). https://doi.org/10.1007/s00180-019-00904-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00180-019-00904-z