ENUMERATION OF FIXED EFFECTS AND MIXED MODELS

R.Bayon, N. Lygeros and J.-S. Sereni

For the history of this subject see Mixed Models Site of Ann Marie Hess.

REFERENCES

  • G. Birkhoff : Lattice theory. American Mathematical Society, 3rd edition, 1967.
  • C. Chaunier, N. Lygeros : The number of orders with thirteen elements.
     Order, vol.9 p.203-204, 1992
  • C. Chaunier, N. Lygeros : Le nombre de posets à isomorphie près ayant 12 éléments.
     Theoretical Computer Science, n123 p.89-94, février 1994.
  • R. Fraïssé, N. Lygeros : Petits posets : dénombrement, représentabilité par cercles et compenseurs.
     C.R.Acad.Sci.Paris, t.313, s.I, p.417-420, septembre 1991.
  • A. Hess, H. Iyer : Enumeration of mixed linear models and SAS macro for computation of confidence intervels for variance components.
     Applied Statistics in Agriculture Conference at Kansas State University 2001.
  • N. Lygeros : Calculs exhaustifs sur les posets d'au plus 7 éléments.
     SINGULARITE, vol.2 n4 p.10-24, avril 1991.

    ENUMERATION OF FIXED EFFECTS MODELS

    FactorsFixed Effects ModelsName
    r=01-
    r=11-
    r=22-
    r=35-
    r=416-
    r=563-
    r=6318-
    r=72.045J.Wright 1972
    r=816.999S. K. Das 1977
    r=9183.231R. H. Mohring 1984
    r=102.567.284J. C. Culberson, G. J. E. Rawlins 1990
    r=1146.749.427J. C. Culberson, G. J. E. Rawlins 1990
    r=121.104.891.746C. Chaunier, N. Lygeros 1991
    r=1333.823.827.452C. Chaunier, N. Lygeros 1992
    r=141.338.193.159.771N. Lygeros, P. Zimmermann 2000

    ENUMERATION OF MIXED MODELS

    FactorsMixed Models (Constraint)Name
    r=12A. Hess, H. Iyer 1999
    r=26A. Hess, H. Iyer 1999
    r=322A. Hess, H. Iyer 1999
    r=4101A. Hess, H. Iyer 1999
    r=5576A. Hess, H. Iyer 1999
    r=64.162R.Bayon, N. Lygeros and J.-S. Sereni 2002
    r=738.280R.Bayon, N. Lygeros and J.-S. Sereni 2002
    r=8451.411R.Bayon, N. Lygeros and J.-S. Sereni 2002
    r=96.847.662R.Bayon, N. Lygeros and J.-S. Sereni 2002

    ENUMERATION OF MIXED MODELS

    FactorsMixed Models ( No Constraint)Name
    r=12A. Hess, H. Iyer 1999
    r=27A. Hess, H. Iyer 1999
    r=332A. Hess, H. Iyer 1999
    r=4192A. Hess, H. Iyer 1999
    r=51.490A. Hess, H. Iyer 1999
    r=615.067R.Bayon, N. Lygeros and J.-S. Sereni 2002
    r=7198.296R.Bayon, N. Lygeros and J.-S. Sereni 2002
    r=83.398.105R.Bayon, N. Lygeros and J.-S. Sereni 2002
    r=975.734.592R.Bayon, N. Lygeros and J.-S. Sereni 2002