Ann. Anim. Sci., Vol. 15, No. 1 (2015) 177–183 DOI: 10.2478/aoas-2014-0063
Compa ison o di e en measu emen a iables based
on Hunga ian sHow jumping esul s* *
Ani a Rudiné Mezei, János Pos a♦, Sándo Mihók
Depa men o Animal B eeding, Facul y o Ag icul u al and Food Sciences
and En i onmen al Managemen , Cen e o Ag icul u al and Applied Economic Sciences,
Uni e si y o Deb ecen, H-4032 Deb ecen Böszö ményi, Hunga y
♦Co esponding au ho : pos aj@ag .unideb.hu
abs ac
The aim o he s udy was o ind a possible way o measu e he pe o mance o spo ho ses based
on hei show jumping esul s and o es ima e he he i abili y and epea abili y alues o hese
pe o mances. The pe o mance was measu ed wi h ans o ma ion o anks, aking in o accoun
he numbe o s a e s a compe i ion and he compe i ion le el. The used ans o ma ions we e
loga i hmic, squa e oo and an in e se no mal ans o ma ion known as Blom me hod. Compe i-
ions we e ca ego ized in o i e g oups based on hei le el o di icul y. The le el o di icul y o
he compe i ions was used as weigh ing ac o s, so pe o mance ai s we e dis inguished being
weigh ed and non-weigh ed. Show jumping compe i ion esul s collec ed be ween 1996 and 2011
we e analysed. The da abase con ained 358342 s a s o 10199 ho ses. Iden i y numbe , name and
gende o he ho se, ide , compe i ion yea , he le el and loca ion o he compe i ion and anks
we e eco ded in he da abase. The used epea abili y animal model included ixed e ec s o age,
gende , compe i ion place, yea o compe i ion, and andom e ec s o ide , animal and pe ma-
nen en i onmen e ec . Va iance componen s we e es ima ed wi h VCE-6 so wa e package. The
goodness-o - i o he models was low and mode a e (0.09–0.47). Fi ing models o weigh ed ai s
had be e goodness-o - i alue. The bes goodness-o - i alues we e ound in he case o le el
weigh ed a iables. He i abili y (0.02–0.07) and epea abili y alues (0.09–0.25) we e low o each
measu emen a iable.
Key wo ds: spo ho se, pe o mance measu emen , REML, he i abili y, epea abili y
Show jumping is he mos popula ho se spo discipline in Hunga y ha ing mo e
han 30,000 compe i ion eco ds collec ed om app ox. 150 places annually. Com-
pa ing and measu ing pe o mance objec i ely is impo an i selec ion and p og-
eny es ing a e based on spo ho se pe o mance. The app op ia e measu emen o
pe o mance is complica ed (B uns, 1981; Ta e nie , 1990), as no objec i e me ic
* Sou ce o esea ch inancing: “OTKA-PD83885” esea ch p ojec .
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A.R. Mezei e al.
178
scale exis s o exp ess he ho se’s pe o mance (Hassens ein e al., 1998). Ma hema -
ical ans o ma ions o ea nings and ankings o ho ses a e widely used o measu e
pe o mance. Squa e oo ans o ma ion (Koenen e al., 1995; Huizinga and an
de Meij, 1989; Hassens ein e al., 1998; Lueh s-Behnke e al., 2002), in e se no -
mal ans o ma ion (Janssens e al., 1997; Reilly e al., 1998; Ald idge e al., 2000;
Gómez e al., 2006; Kea sley e al., 2008) and loga i hmic unc ions (B uns, 1981;
Huizinga and an de Meij, 1989; Dubois and Rica d, 2007; Olsson e al., 2008)
we e desc ibed o se e al ho se popula ions. These quan i a i e ai s can be consid-
e ed as epea ing measu emen s du ing he ca ee o he ho se. Many complex ai s
s udied in gene ics ha e ma kedly non-no mal dis ibu ions (Micce i, 1989; Allison
e al., 1999), which o en implies ha he assump ion o no mally dis ibu ed esidu-
als has been iola ed (Beasley, 2009).
The es ic ed maximum likelihood (REML) es ima ion in oduced by Pa e son
and Thompson (1971) has been de eloped o es ima ing a iance componen s in
linea mixed models (O’Neill, 2010). This me hod equi es he no mali y p e equi-
si e men ioned abo e (Oehle , 2012). Gene ic pa ame e s like he i abili y and e-
pea abili y alues a e de i ed om es ima ed a iance componen s.
The aim o he s udy was o ind a possible way o measu e show jumping pe -
o mance h ough he compa ison o di e en models o show jumping esul s o
spo ho ses and o es ima e he i abili y and epea abili y alues.
Ma e ial and me hods
Show jumping compe i ion esul s collec ed be ween 1996 and 2011 we e ana-
lysed. The da a used o analysis we e ob ained om he Hunga ian Eques ian Fed-
e a ion. The inal da ase con ained 358342 compe i ion eco ds o 10199 indi idual
ho ses (2350 si e, 7471 dam) a e da a sc eening; esul s we e ga he ed om Hun-
ga y and o he Eu opean coun ies. Iden i y numbe , name, age (22 classes) and sex
o he ho se (3 classes), ide (4,291 classes), compe i ion yea (16 classes), he le el
(5 classes) and loca ion (506 classes) o he compe i ion and anks we e eco ded in
he da ase . In o ma ion abou pedig ee o he ho ses was ga he ed and se up wi h
help o he Na ional Ho seb eede In o ma ion Sys em. The pedig ee ile con ained
39878 animals going back ou gene a ions.
Compe i ions we e ca ego ized in o i e g oups based on hei le el o di icul-
y ollowing he ca ego iza ion o di icul y le els epo ed by Rudiné Mezei e al.
(2013). Ea ning is no widely used in Hunga ian show jumping compe i ions, so
a ious ans o ma ions o anks we e used o e alua e he pe o mance o spo
ho ses.
The measu emen o compe i ion pe o mance was based on he anking o he
ho se and was ca ied ou using di e en ma hema ical ans o ma ions. These ans-
o ma ions we e: squa e- oo o anks, loga i hmic ans o ma ion o he anks and
Blom ans o ma ion o he anks as epo ed by Janssens e al. (1997). A epea abil-
i y animal model p oposed by M ode (2005) was i ed o hese ai s. The model
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Di e en measu emen s on Hunga ian show jumping esul s 179
included ixed e ec s o age and gende o he ho se, he compe i ion yea , place and
le el as well as andom e ec s o he ide .
As pa o he expe imen , we ied o de elop a weigh ing sys em o he meas-
u emen a iables. The abo e men ioned h ee a iables we e mul iplied wi h he
compe i ion le el and wi h he squa e o he compe i ion le el (Table 1), as sugges ed
by Duc o (2011). The i ed model was he same as men ioned be o e, excep ha he
ixed e ec o compe i ion le el was excluded om his e alua ion model. To ally,
nine di e en a iables we e used wi h wo models in he analysis.
The le el o signi icance o each ixed e ec was de e mined using SAS PROC
GLM (SAS Ins i u e, 1999). Each model was desc ibed wi h he coe icien o de-
e mina ion, oo mean squa e e o (RMSE) and he mean squa ed esidual he i h
obse a ion ha esul s om d opping i and p edic ing i on he basis o all o he
obse a ions (MSEP). These alues we e calcula ed based on he PRESS alues p o-
ided by SAS PROC GLM (SAS Ins i u e, 1999).
Table 1. The ypes o ans o ma ion used o measu emen
Weigh ing o compe i ion
pe o mance
T ans o ma ion
squa e oo
o anks
loga i hmic
ans o ma ion Blom-sco e
No weigh ing 15 – √placing
(1s measu e)
10 log2 (placing)
(4 h measu e)
BlomSco e + 3
(7 h measu e)
Weigh ing is he
compe i ion le el
(15 – √placing)*le el1
(2nd measu e)
10 – log2(placing)*le el1
(5 h measu e)
(BlomSco e + 3)*le el1
(8 h measu e)
Weigh ing is he squa e o
he compe i ion le el
(15 – √placing)*le el2
(3 d measu e)
10 – log2placing)*le el2
(6 h measu e)
(BlomSco e + 3)*le el2
(9 h measu e)
The goodness-o - i o he models was assessed by using coe icien o de e mi-
na ion and he oo mean squa e e o (RMSE) e m. Va iance componen s and hei
s anda d e o s we e es ima ed wi h he epea abili y animal model (men ioned be-
o e) using he REML me hod wi h VCE-6 (Ko ac and G oene eld, 2003) so wa e
package. He i abili y alue (h2) and epea abili y alues ( ) we e p edic ed.
Resul s
Fixed e ec s we e signi ican in all i ed models (P<0.01). The goodness-o - i in
he case o he non-weigh ed (1s , 4 h, and 7 h) measu emen a iable was low and
a ied be ween R2 = 0.09 and 0.18. All he o he models had mode a e goodness-
o - i alues o R2 = 0.43–0.47. In gene al le el ans o ma ion esul ed in be e
models and R2 alues we e highe (Table 2). The weigh ing o he a iables esul ed
in highe RMSE and MSEP alues o each ans o ma ion and weigh ing. The di -
e ence be ween he measu ed and es ima ed pe o mance was he lowes o Blom
ans o ma ion (7 h o 9 h measu emen s) compa ed wi h he di e en weigh ings.
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A.R. Mezei e al.
180
Table 2. Coe icien o de e mina ion (R2), RMSE and MSEP ob ained o di e en models and ai s
T ai R2RMSE MSEP
1s measu e 0.18 1.363 1.911
2nd measu e 0.47 7.010 20.203
3 d measu e 0.46 31.370 358.461
4 h measu e 0.16 1.371 1.887
5 h measu e 0.43 4.495 49.134
6 h measu e 0.45 18.948 982.705
7 h measu e 0.09 0.867 0.770
8 h measu e 0.45 2.231 4.982
9 h measu e 0.46 9.087 82.471
The Kolmogo o -Smi no no mali y es showed ha he dis ibu ion o he e-
siduals did no ollow no mal dis ibu ion in he in es iga ed ai s (P<0.01). Es i-
ma ed a iance componen s a e shown in Table 3. The weigh ing o he a iables
esul ed in highe a iance p opo ions o ide and pe manen en i onmen e ec s
and lowe p opo ion o he esidual compa ed o hose o he o iginal measu e-
men s.
Table 3. P opo ions o a iance componen s ela i e o pheno ypic a iance
T ai Ride Pe manen en i onmen Residual
1s measu e 0.06 0.06 0.85
2nd measu e 0.15 0.18 0.60
3 d measu e 0.12 0.17 0.65
4 h measu e 0.07 0.06 0.85
5 h measu e 0.12 0.17 0.64
6 h measu e 0.11 0.17 0.66
7 h measu e 0.05 0.07 0.83
8 h measu e 0.11 0.16 0.66
9 h measu e 0.11 0.17 0.67
Table 4. He i abili y (h2) and epea abili y ( ) es ima es o di e en ai s
T ai h2
1s measu e 0.02 0.09
2nd measu e 0.07 0.25
3 d measu e 0.06 0.23
4 h measu e 0.02 0.08
5 h measu e 0.07 0.23
6 h measu e 0.06 0.22
7 h measu e 0.05 0.13
8 h measu e 0.07 0.23
9 h measu e* 0.05 0.22
*= No op imal (op imiza ion s a us 3).
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Di e en measu emen s on Hunga ian show jumping esul s 181
Es ima ed he i abili y and epea abili y alues a e p esen ed in Table 4. He i-
abili ies a e signi ican ly di e en om ze o and low, a ying be ween h2=0.02 and
0.07. The weigh ing o he a iables inc eased bo h he i abili y and epea abili y al-
ues, and he highes he i abili y and epea abili y alues we e es ima ed o he 2nd,
5 h and 8 h weigh ed measu emen a iables.
Discussion
Ranking does no e lec he le el a which he esul has been ob ained, which is
he eason o using weigh ing ac o s. Weigh ing is an al e na i e o ans o ma ion
o pe o mance measu emen ai s. When compa ing wo ho ses ha ob ained he
same placing, he ho se compe ing a highe le els ge s highe sco es. Ano he op-
ion is ha pe o mance a di e en le els could be conside ed as di e en ai s and
analysed in a mul i a ia e analysis (Huizinga and an de Meij, 1989; Hassens ein e
al., 1998; Ald idge e al., 2000). The changes o he a iance p opo ions (Table 3)
we e simila o each ans o ma ion, so he eason is mainly he inc eased a iance
and no he di e en ma hema ical ans o ma ion.
Pos a e al. (2009) es ima ed simila he i abili y alues using some non-weigh ed
ma hema ical unc ions, whe eas he epea abili y alues we e highe compa ed o
he non-weigh ed and in line wi h he weigh ed measu emen a iables. This indi-
ca es ha he he i abili y and epea abili y could change depending on he da ase
size and ime in e al co e ed. The low he i abili y alues oge he wi h highe ide
and pe manen en i onmen a iance p opo ions show impo an in luence ac o s
o compe i ion pe o mance. He i abili ies based on squa e oo o anks we e low-
e o hose o Lueh s-Behnke e al. (2002), h2=0.11; Jai ne and Reinha d (2003),
h2=0.10; and Viklund e al. (2011), h2=0.11. Meina dus (1988) and Sp enge (1992)
epo ed simila ly low alues (h2=0.02–0.06) based on absolu e ankings. The es-
ima ed he i abili y alues could sugges he possible use o BLUP gene ic e alu-
a ion sys em o he Hunga ian jumping ho ses. Ou esul s could s eng hen he
use ulness o he used ma hema ical ans o ma ions. The main aim o his wo k was
o show al e na i es o he b eeding alue e alua ion sys em h ough hese di e -
en ans o ma ions. The RMSE and MSEP alues calcula ed o a iables weigh ed
wi h he squa e o he compe i ion le el we e qui e high and migh indica e he isk
o such weigh ing.
Di e en compe i ion le els we e ea ed as di e en ai s, and low he i abili y
alues we e es ima ed by Huizinga and an de Meij (1989), h2=0.10–0.20; Koenen
e al. (1995), h2=0.17; and Hassens ein e al. (1998), h2=0.07–0.11, whe e he pe -
o mance ai was he squa e oo o ank.
When measu ing show jumping pe o mance as no malized sco es, Janssens
e al. (1997) epo ed h2=0.02–0.10, and Ald idge e al. (2000) h2=0.07–0.10 alues.
When ea ing pe o mance a di e en compe i ion le el as di e en ai s, Kea sley e
al. (2008) epo ed highe he i abili y alues (h2=0.08–0.23) o no malized sco es.
Loga i hmic ans o ma ion was used in se e al s udies o ea nings o he ho s-
es. B uns (1981) es ima ed h2=0.04–0.15 alue o Ge man iding ho ses. Rica d and
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A.R. Mezei e al.
182
Chanu (2001) es ima ed h2=0.14 o F ench e en ing ho ses, and es ima ed epea -
abili y alue was =0.45.
The epea abili y alues we e highe o weigh ed a iables. This migh indica e
some ela ionship among he di e en pe o mances o he ho ses, hough ou es i-
ma ed alues a e s ill qui e low. Repea abili ies based on squa e oo o anking we e
simila o hose o Jai ne and Reinha d (2003), =0.31. Repea abili ies based on
no malized sco es we e simila ly low o Janssens e al. (1997), =0.09–0.27.
Conside ing pe o mance a di e en compe i ion le el as di e en ai s, es i-
ma ed epea abili y based on squa e oo o anking was =0.14–0.21 in Hassens ein
e al. (1998), and es ima ed epea abili y based on absolu e anking was =0.09 in
Meina dus (1988).
The op imiza ion esul o he Blom sco e based weigh ed measu e (9 h measu e)
migh indica e ha he used model does no eally i he da a, so he ans o med
anks migh be weigh ed wi h oo la ge mul iplica ion ac o s.
Conclusions
Inclusion o compe i ion le el as weigh ing ac o is easonable du ing measu ing
o show jumping pe o mance wi h di e en ans o ma ions. The weigh ed Blom
sco e migh be he bes i ed ans o ma ion (h2=0.07, and =0.23). The signi ican
he i abili y alues o he p esen wo k sugges ha selec ion o jumping compe i ion
pe o mance could be success ul in he Hunga ian jumping ho se popula ion.
Acknowledgemen s
This wo k was made possible by he inancial suppo o he “OTKA-PD83885”
esea ch p ojec . The Associa ion o Hunga ian Ho se B eede s and Ho se O ganiza-
ion, and Discipline o Show jumping o The Hunga ian Eques ian Fede a ion a e
g a e ully acknowledged o p o iding he da a se o he s udy.
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Accep ed: 16 VII 2014
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