Íslenskar landbúnaðarrannsóknir - 01.03.1979, Page 87

TRAITS IN ICEL. TOELTER HORSES I. 85
Statistical Analyses
In the first analyses it was intended to
estimate the magnitude of some of the en-
vironmental effects accounted for in the
records. The data were obviously not ort-
hogonal and the method of fitting con-
stants by least-squares analyses, was ther-
efore assumed to be an efficient way of
estimating the environmental effects and
correction factors. The following model
was used in the first run.
(1)
Yijklmn = /U+Ai+bj+Ck+dl+gm+eijklmn
where:
Y ijklmn = the nth observation within the ith
sire, jth age class, kth sex, lth year of show
and mth district of origin
M = least-squares mean
A; = the effect of the ith sire (i = 1 . . . s)
bi = the effect of the jth sex (j = 1, 2, 3;
stallion, mare, gelding)
ck = the effect of the kth age class (j = 1
... 10; age of (^4) —(>13) years)
di= the effect of the lth year of show (1 = 1
... 15; 1962-1976)
gm = the effect of the mth district of origin
(m = 1 ... 12)
eijkimn = random element; assumed to be
NID (0,<$2e)
The effect of the sires is considered to be
random and all other effects (except e) are
considered to be fixed. Effect of interacti-
ons is assumed to be negligible.
This model fits to the mixed model of
type II as described by Harvey (1972b).
The Least-squares and Maximum Like-
lihood General Purpose Program of Har-
vey (LSMLMM) was used to carry out
the calculations. For detailed description
of the procedure see Harvey (1960, 1972a
and b).
As the number of records exceeded the
number of individuals involved, the model
(1) above is, however, not strictly correct.
Some of the animals were judged more
than once. Therefore the individuals are
to some extent nested within sires, sexes
and districts. But in order to avoid over-
complicating the model this was assumed
acceptable for the purpose of estimating
adjusting factors for the sex, age, district
and year effect, and one may bejustified in
believing that the least squares estimates
are unbiased. On the other hand the res-
idual mean square might be slightly bias-
ed upwards, and therefore not an exact
term for testing.
Before a statistical analyses, which was
aimed at estimating the genetic paramet-
ers, was carried out the data were adjusted
according to the result of the first run for
the effects of sex and age. The following
model was used in the next runs.
(2)
Yijin = /r+Ai+Iíj+di+eijin
where:
Yijin = the nth observation, adjusted for
sex and age, of the jth individual having
the ith sire and judged in the lth year.
Lj = the effect of the jth progeny of the ith
sire
eijin = random element; assumed to be
NID (o, ó2e)
As to the other symbols, see model (1).
Model (2) fits to Mixed Model IV as
described by Harvey (1972b). The eq-
uation u + Ai+Lj was absorbed, and the
analyses of variance and covariance had
the following form.
Analyses of Variance and Covariance
As the analyses using this model were