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

     

    Factors Fixed Effects Models Name
    r=0 1 –
    r=1 1 –
    r=2 2 –
    r=3 5 –
    r=4 16 –
    r=5 63 –
    r=6 318 –
    r=7 2.045 J.Wright 1972
    r=8 16.999 S. K. Das 1977
    r=9 183.231 R. H. Mohring 1984
    r=10 2.567.284 J. C. Culberson, G. J. E. Rawlins 1990
    r=11 46.749.427 J. C. Culberson, G. J. E. Rawlins 1990
    r=12 1.104.891.746 C. Chaunier, N. Lygeros 1991
    r=13 33.823.827.452 C. Chaunier, N. Lygeros 1992
    r=14 1.338.193.159.771 N. Lygeros, P. Zimmermann 2000

    ENUMERATION OF MIXED MODELS

     

    Factors Mixed Models (Constraint) Name
    r=1 2 A. Hess, H. Iyer 1999
    r=2 6 A. Hess, H. Iyer 1999
    r=3 22 A. Hess, H. Iyer 1999
    r=4 101 A. Hess, H. Iyer 1999
    r=5 576 A. Hess, H. Iyer 1999
    r=6 4.162 R.Bayon, N. Lygeros and J.-S. Sereni 2002
    r=7 38.280 R.Bayon, N. Lygeros and J.-S. Sereni 2002
    r=8 451.411 R.Bayon, N. Lygeros and J.-S. Sereni 2002
    r=9 6.847.662 R.Bayon, N. Lygeros and J.-S. Sereni 2002

    ENUMERATION OF MIXED MODELS

     

    Factors Mixed Models ( No Constraint) Name
    r=1 2 A. Hess, H. Iyer 1999
    r=2 7 A. Hess, H. Iyer 1999
    r=3 32 A. Hess, H. Iyer 1999
    r=4 192 A. Hess, H. Iyer 1999
    r=5 1.490 A. Hess, H. Iyer 1999
    r=6 15.067 R.Bayon, N. Lygeros and J.-S. Sereni 2002
    r=7 198.296 R.Bayon, N. Lygeros and J.-S. Sereni 2002
    r=8 3.398.105 R.Bayon, N. Lygeros and J.-S. Sereni 2002
    r=9 75.734.592 R.Bayon, N. Lygeros and J.-S. Sereni 2002