Next: pairwise()
Up: Design Macros Help File
Previous: interblock()
Contents
Usage:
mixed(Model,randomvars[,marg:T] [,restrict:F] [,nonhier:T] [,useneg:T]\
[,keepmixed:T]), CHARACTER scalar model, CHARACTER vector randomvars
mixed(emsResult [,useneg:T] [,keepmixed:T]), emsResult a structure
returned by ems() with keep:T
|
Keywords:
anova, analysis, random effects, factorial
Usage
mixed(Model, randomvars) computes and prints an "ANOVA" table
appropriate for the model and random factors given in CHARACTER scalar
Model and CHARACTER vector randomvars. These arguments are exactly the
same as for ems(). You can also use ems() keywords 'marg', 'restrict'
and 'nonhier'.
mixed(emsResult), where emsResult has been computed by emsResult <-
ems(Model, randomvars [,...],keep:T), does the same.
mixed(Model, randvars [,...], keepmixed:T) returns the table as an
matrix with appropriately labelled rows and columns but does not print
it.
The anova table has one row for each term in the model and the following
seven columns.
Col. 1 Label for term
Col. 2 DF = degrees of freedom for term
Col. 3 MS = mean square for term (numerator of F)
Col. 4 Error DF = degrees of freedom for appropriate error term
Col. 5 Error MS = mean square for appropriate error term
(denominator of F)
Col. 6 F = F-statistic = MS/(Error MS)
Col. 7 P value = tail probability for F test
With keepmixed:T, the matrix returned consists of columns 2 through 7 of
the table, with column 1 used to label rows.
Description of numerator and denominator MS
Numerator and denominator MS's are linear combinations of mean squares
whose expectations differ only by a multiple of the variance component
associated with the line. When the numerator or denominator is not a
simple ANOVA mean square, its degrees of freedom are found using the
Satterthwaite approximation.
By default, only linear combinations of mean squares with positive
coefficients are used. This means that the numerator for a term may be
the sum of the mean square for the term and one or more mean squares
from other terms. If the keyword useneg:T is used, then the numerator
for a term will be the mean square for that term, and denominators may
contain differences as well as sums of mean squares.
Example:
Three populations, all crosses between 4 males and 4 females in each
population with six offspring from each mating randomly assigned to
three environments. Male and female are random. First the simple
ANOVA.
Cmd> anova("y=(pop+m.pop+f.pop+m.f.pop)*env")
Model used is y=(pop+m.pop+f.pop+m.f.pop)*env
DF SS MS
CONSTANT 1 5.4299 5.4299
pop 2 2091.4 1045.7
pop.m 9 112.5 12.5
pop.f 9 370.02 41.113
pop.m.f 27 56.774 2.1027
env 2 206.15 103.08
pop.env 4 0.16527 0.041316
pop.m.env 18 3.4185 0.18992
pop.f.env 18 8.2354 0.45752
pop.m.f.env 54 17.117 0.31698
ERROR1 144 30.448 0.21144
Now compute the expected mean squares, and keep the ems() output.
Cmd> emsstuff<-ems("y=(pop+m.pop+f.pop+m.f.pop)*env",vector("m","f"),
keep:T,print:T)
EMS(CONSTANT) = V(ERROR1) + 6V(pop.m.f) + 24V(pop.f) + 24V(pop.m) +
288Q(CONSTANT)
EMS(pop) = V(ERROR1) + 6V(pop.m.f) + 24V(pop.f) + 24V(pop.m) + 96Q(pop)
EMS(pop.m) = V(ERROR1) + 6V(pop.m.f) + 24V(pop.m)
EMS(pop.f) = V(ERROR1) + 6V(pop.m.f) + 24V(pop.f)
EMS(pop.m.f) = V(ERROR1) + 6V(pop.m.f)
EMS(env) = V(ERROR1) + 2V(pop.m.f.env) + 8V(pop.f.env) +
8V(pop.m.env) + 96Q(env)
EMS(pop.env) = V(ERROR1) + 2V(pop.m.f.env) + 8V(pop.f.env) +
8V(pop.m.env) + 32Q(pop.env)
EMS(pop.m.env) = V(ERROR1) + 2V(pop.m.f.env) + 8V(pop.m.env)
EMS(pop.f.env) = V(ERROR1) + 2V(pop.m.f.env) + 8V(pop.f.env)
EMS(pop.m.f.env) = V(ERROR1) + 2V(pop.m.f.env)
EMS(ERROR1) = V(ERROR1)
Now use mixed().
Cmd> mixed(emsstuff)
DF MS Error DF Error MS F P value
CONSTANT 1.914 7.533 14.01 53.61 0.1405 0.8617
pop 2.008 1048 14.01 53.61 19.54 8.745e-05
pop.m 9 12.5 27 2.103 5.945 0.0001412
pop.f 9 41.11 27 2.103 19.55 1.242e-09
pop.m.f 27 2.103 144 0.2114 9.945 0
env 2.012 103.4 30.75 0.6474 159.7 0
pop.env 56.12 0.3583 30.75 0.6474 0.5534 0.9729
pop.m.env 18 0.1899 54 0.317 0.5991 0.8844
pop.f.env 18 0.4575 54 0.317 1.443 0.1496
pop.m.f.env 54 0.317 144 0.2114 1.499 0.03044
ERROR1 144 0.2114 0 0 MISSING MISSING
The test for environment should be
(MS(env)+MS(m.f.env))/(MS(m.env)+MS(f.env)) = (103.08+.32)/(.190+.458) =
(103.4)/(.6474) = 159.7 as reported in the table.
Cross references
See also ems(), reml().
Gary Oehlert
2006-01-30