Skip to main content
SpringerLink
Log in

Optimal designs for a mixed interference model

  • Published:
Metrika Aims and scope Submit manuscript

Abstract

This paper generalizes Kunert and Martin’s (Ann Stat 28:1728–1742, 2000) method for finding optimal designs under a fixed interference model, to find optimal designs under a mixed interference model. The results are based on the properties of information matrices in fixed and mixed models given in Markiewicz (J Stat Plan Inference 59:127–137, 1997). The method is applied to find a design which is optimal for any given variances of random neighbor effects.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Andersson LE, Chang G, Efving T (1995) Criteria for copositive matrices using simplices and barycentric coordinates. Linear Algebra Appl 220:9–30

    Article  MATH  MathSciNet  Google Scholar 

  • Bhatia R (2003) Partial traces and entropy inequalities. Linear Algebra Appl 370:125–132

    Article  MATH  MathSciNet  Google Scholar 

  • David O, Monod H, Lorgeou J, Philippeau G (2001) Control of interplot interference in grain maize: a multi-site comparison. Crop Sci 41:406–414

    Article  Google Scholar 

  • Druilhet P (1999) Optimality of circular neighbor balanced designs. J Stat Plan Inference 81:141–152

    Article  MATH  MathSciNet  Google Scholar 

  • Filipiak K, Markiewicz A (2003) Optimality of neighbor balanced designs under mixed effects model. Stat Probab Lett 61:225–234

    Article  MATH  MathSciNet  Google Scholar 

  • Filipiak K, Markiewicz A (2004) Optimality of type I orthogonal arrays for general interference model with correlated observations. Stat Probab Lett 68:259–265

    Article  MATH  MathSciNet  Google Scholar 

  • Filipiak K, Markiewicz A (2005) Optimality and efficiency of circular neighbor balanced designs for correlated observations. Metrika 61:17–27

    Article  MATH  MathSciNet  Google Scholar 

  • Gill PS (1993) Design and analysis of field experiments incorporating local and remote effects of treatments. Biometrical J 35:343–354

    MATH  MathSciNet  Google Scholar 

  • Jones B, Kunert J, Wynn HP (1992) Information matrices for mixed effects models with applications to the optimality of repeated measurements designs. J Stat Plan Inference 33:261–274

    Article  MATH  MathSciNet  Google Scholar 

  • Kiefer J (1975) Construction and optimality of generalized Youden designs. In: Srivastava JN (ed) A survey of statistical design and linear models. North-Holland, Amsterdam, pp 333–353

    Google Scholar 

  • Kunert J, Martin RJ (2000) On the determination of optimal designs for an interference model. Ann Stat 28:1728–1742

    Article  MATH  MathSciNet  Google Scholar 

  • Kushner HB (1997) Optimal repeated measurements designs: the linear optimality equations. Ann Stat 25:2328–2344

    Article  MATH  MathSciNet  Google Scholar 

  • Li Ch, Mathias R (2000) Extremal characterizations of the Schur complement and resulting inequalities. SIAM Rev 42:233–246

    Article  MathSciNet  Google Scholar 

  • Markiewicz A (1997) Properties of information matrices for linear models and universal optimality of experimental designs. J Stat Plan Inference 59:127–137

    Article  MATH  MathSciNet  Google Scholar 

  • Martin RJ, Eccleston JA (1998) Variance-balanced change-over designs for dependent observations. Biometrika 85:883–892

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematical and Statistical Methods, Agricultural University of Poznań, Wojska Polskiego 28, 60637, Poznań, Poland

    K. Filipiak & A. Markiewicz

Authors
  1. K. Filipiak
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Markiewicz
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. Markiewicz.

Additional information

Research partially supported by the KBN Grant Number 5 P03A 041 21.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Filipiak, K., Markiewicz, A. Optimal designs for a mixed interference model. Metrika 65, 369–386 (2007). https://doi.org/10.1007/s00184-006-0082-7

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00184-006-0082-7

Keywords

Search

Navigation