Faculty of Sport, University of Ljubljana, ISSN 1318-2269  13
  ANALYSIS OF CORRELATION BETWEEN 
SCORES OF PERFORMANCE FACTORS IN 
CROSS-COUNTRY SKIERS OBTAINED BY 
V ARIOUS METHODS OF DETERMINATION 
OF WEIGHTS IN EXPERT MODELLING
 ANALIZA POVEZANOSTI OCEN 
DEJAVNIKOV USPEŠNOSTI SMUČARJEV 
TEKAČEV DOBLJENIH NA PODLAGI 
RAZLIČNIH METOD DOLOČANJA UTEŽI 
PRI EKSPERTNEM MODELIRANJU
Abstract
In the research, two universal reduced models of 
potential competition performance in cross-country 
skiing were constructed. The MMPS model covers the 
motor, morphological, psychological, and sociological 
subspace of the psychosomatic status of competitors, 
while in the MFMPS model, a functional subspace has 
also been added. Within both models, we wanted to 
establish a degree of correlation between the scores of 
some important levels of psychosomatic status obtained 
by the SMMS procedure of expert modelling by the 
method of dependent and independent determination 
of weights. On a sample of 14 competitors (older juniors) 
the agreement between the scores of variables obtained 
by the two different methods of weight determination 
was established. We found that the final score of both 
models (URMPU) is highly correlated with their 
subspaces, except with the sociological one. The degree 
of interrelations between individual subspaces varies; 
however, the highest correlation exists between the 
motor and psychological subspaces in the method of 
dependent determination of weights. Both methods of 
determination of weights are in a statistically highly 
significant agreement. Somewhat better and more pre-
dictive results are yielded by the method of dependent 
determination of weights, while the utility of the method 
of independent determination of weights is larger.
Key words: cross-country skiing, potential competition 
performance, expert modelling, methods of 
determination of weights
1
 Primary school Domžale, Domžale, Slovenia
2
 Faculty of Sport, University of Ljubljana, Slovenia
Izvleček
V raziskavi smo izgradili dva univerzalna reducirana 
modela potencialne tekmovalne uspešnosti v smučar-
skem teku. Model MMPS zajema motorični, morfološki, 
psihološki in sociološki podprostor psihosomatičnega 
statusa tekmovalcev, v modelu MFMPS pa je dodan 
še funkcionalni podprostor. Znotraj obeh modelov 
smo želeli ugotoviti stopnjo povezanosti med ocenami 
nekaterih pomembnih ravni psihosomatičnega statusa, 
dobljenih po postopku ekspertnega modeliranja SMMS 
z metodo odvisnega in neodvisnega določanja uteži. 
Na vzorcu 14 tekmovalcev (starejših mladincev) smo 
v obeh modelih ugotavljali tudi skladnost ocen spre-
menljivk, dobljenih po različnih metodah določanja 
uteži. Ugotovili smo, da je končna ocena obeh modelov 
(URMPU) v visoki povezanosti s svojimi podprostori, 
razen s sociološkim. Stopnja medsebojnih povezav 
posameznih podprostorov je različna, najmočneje pa 
se povezujeta motorični in psihološki podprostor pri 
metodi odvisnega določanja uteži. Obe metodi do-
ločanja uteži sta v veliki statistično značilni skladnosti. 
Nekoliko boljše, prediktivnejše rezultate daje metoda 
odvisnega določanja uteži, medtem ko je uporabna 
vrednost metode neodvisnega določanja uteži večja.
Ključne besede: smučarski tek, potencialna tekmovalna 
uspešnost, ekspertno modeliranje, metode določanja 
uteži 
* Corresponding author:
Osnovna šola Domžale
Bistriška cesta 19, SI-1230 Domžale, Slovenia
Tel.: + 386 1 7219580, Fax: +386 1 7211842
E-mail: branimir.cernohorski@guest.arnes.si
Branimir Černohorski
1
*
Janez Pustovrh
2
 Kinesiologia Slovenica, 11, 1, 13–30 (2005)

14 Expert modelling in cross-county skiing Kinesiologia Slovenica, 11, 1, 13–30 (2005) 
INTRODUCTION
The theory of sport as a complex, interdisciplinary theory tries to encompass all important 
and essential issues in the field of sport. To better learn the laws that govern live systems, we 
use models by which the structure of the system and/or processes are analysed. The purpose 
of modelling is advance information on how the system would in all probability behave, if the 
initially selected, limiting conditions of the model happened (Mulej, 1996).
Based on the concept of psychosomatic status, a general potential model of competition per-
formance in Nordic skiing was set up (Jošt, Dežman, & Pustovrh, 1992). This also includes 
cross-country skiing. The intent was to discover the essential laws of successful guidance of the 
transformation process, which should lead to high-level competition performance. It could be 
argued that performance of an athlete depends on the state of all model dimensions which repre-
sent a linear combination of performance (equation of performance-specific action). According 
to up-to-date scientific knowledge, the quality process of preparation of athletes can be guided 
only by a model. The model should thus start out from the actual athlete's (competition) result, 
as well as from the impacts of all individual and interrelated dimensions of the psychosomatic 
st at u s . W hen we spea k about a n at h lete, we have i n m i nd a n i nteg r a l persona l it y defi ned by t he 
essential abilities, characteristics and traits on which the athlete's performance in the chosen 
sport depends. These most predictive factors affecting the structure of a competition result 
are studied in the so-called reduced model of potential performance. Limitations occur also 
in terms of methodology. This is precisely why in 1985, experts working at the Institute of 
Kinesiology and the Laboratory of Artificial Intelligence at the Jožef Stefan Institute in Ljubljana 
came together to develop an information system of initial selection and advising of children 
in choosing sports (Šturm et al., 1992). A weakness of the multivariate methods (which are, 
however, still indispensable) is, in fact, their limitedness as regards the nature of variables 
(linear correlation, normality of distribution, etc.), and especially number of subjects subjected 
to measurements. In some sports, a small base of athletes makes it difficult to elaborate a study 
by apply i ng mu lt iva r iate met hod s ; cros s-cou nt r y sk i i ng a lso belongs to such spor t s . The u se of 
a large number of variables and dimensions of the psychosomatic status is often questionable 
as well. Decisions on the management of transformation processes, however, cannot be based 
on partial findings. Application of expert knowledge and methods solves these shortcomings 
in a satisfactory manner.
In expert systems, application of methods of artificial intelligence is the essential feature. One 
of the most important characteristics of expert systems is their capacity to explain the solution 
whereby the system becomes transparent or comprehensible to the user (Urbančič, Lavrač, & 
Filipič, 1988). Despite the fact that in dealing with expert systems we do not underestimate an 
active use of knowledge, and hence the solving of the problem (inference mechanism), and that we 
cannot ignore the user interface facilitating a dialogue between an expert and the expert system, 
the essential work of experts is only associated with the modulation of the knowledge base. The 
quality of an expert system is basically the function of the scope and quality of its knowledge base. 
This contains the knowledge related to a given, specific problem field; in our case, performance of 
cross-country skiers. In setting up the knowledge base, it is first necessary to acquire knowledge in 
the field of performance in sport and to present it appropriately in a formalism. This encompasses 
three inseparably connected components (Ulaga, 2001): the referenceability of the knowledge 
base (criteria tree), the dimensional configuration of the knowledge base (decision rules or 

Expert modelling in cross-county skiing 15 Kinesiologia Slovenica, 11, 1, 13–30 (2005)
weights), and the positional configuration of the knowledge base (normalisers). Once it has been 
constructed the knowledge base must be embedded into the shell of the expert system consisting 
of the said mechanism for making inferences and of the user interface. A SMMS program (Sport 
Measurement Management System, Version 1.0), developed at the Faculty of Sport in Ljubljana, 
is a computer application intended to longitudinally monitor the results of the measurements 
carried out in athletes. In this program, two different methods of dimensional configuration (the 
method of dependent and the method of independent determination of weights) will be tested 
in assessing the competition potential of the subjects measured. The obtained different scores on 
the factors of competition performance will be analysed in terms of interrelations.
METHOD
Participants
The s a mple of s u bje c t s e nc omp a s s e d 14 c omp e t itor s , i .e . c ro s s - c ou nt r y s k ie r s i n t he c omp e t it ion 
c a t e g o r y o f o l d e r j u n i o r s ( b o r n i n 19 8 4 a n d 19 8 5) . A l l r a n k e d i nt o t h e fi n a l l i s t o f S L O – F I S p o i nt s 
in the 2001/2002 season.
Instruments 
The MFMPS model of potential competition performance and the MMPS model included 70 and 
64 variables, respectively. A detailed description of the variables and the measurement protocol 
are available from the authors at the Faculty of Sport in Ljubljana.
Variables of the motor subspace: MMENSDM – long jump from standing, MTRSK – triple jump 
from standing, MSRKF – balance frontally, MSRKS – balance sagitally, MTAPRO – tapping with 
hand, MSCT – Cooper's test (2,400 m), MEMTEK – 20-m sprint (high start), MMENS60 – 60-m 
run, MPON – polygon backwards, MKAOSP – eight with bending, MKVS – side steps, MSMIZT 
– hang with elbows bent, MSDTSK – trunk lifting on Swedish gymnastic bench, MSPSK – jumps 
over Swedish gymnastic bench, MSSNB – bent hangs on parallel bars, MTPK – bending forward 
on bench, MEMMED - heavy ball throw. 
Variables of the functional subspace: VO
2
max_LP – oxygen consumption at lactate threshold, 
VO
2
max_ANP (4 mmol l
-1
) – oxygen consumption at anaerobic threshold, VO
2
max_ABS 
– maximal oxygen consumption, WATT_LP – load at lactate threshold, WATT_ANP (4 mmol 
l
-1
) – load at lactate threshold, W ATT_ABS – maximal load. VO
2
max was measured relatively in 
ml min
-1 
kg
-1
 of body weight. Relative loading W ATT (W ATT kg
-1 
of body weight) was calculated 
according to the instructions (Mijnhardt, 1991). A standardised test for cross-country skiers on 
a Woodway treadmill was carried out. The subject walked on the treadmill with skiing poles at 
a speed of 7 km h
-1
 in the first 9 minutes, and then carried on at a speed of 7.5 km h
-1 
until the 
end of the test,. The inclination of the treadmill was increased every 3 minutes.
Variables of the morphological subspace: ATV – body height, ATT – body weight, ADZGO 
– length of upper limbs, ADSPO – length of lower limbs, AON – circumference of relaxed upper 
arm, AOPR – chest circumference, AOS – thigh circumference, APKOM – elbow diameter, ASR 
– shoulder width, ASM – pelvis width, APKOL – knee diameter, AKGT – abdominal skin fold.
Variables of the psychological subspace: Special psychological abilities were measured with a 
10-minute series test (TN–10-A; Pogačnik, 1994) and a Test of concentration and achievement 

16 Expert modelling in cross-county skiing Kinesiologia Slovenica, 11, 1, 13–30 (2005) 
(TKD; Bele-Potočnik, 1976): FLUIDINT – fluid intelligence, FUNVZPOD – function of 
encouragement, FUNKONTR – function of control. Motivation or dynamic component of 
personality was measured by Costello's performance motivation questionnaire (Costello, 
1967), Willis' competitive motivation questionnaire (Willis, 1982), and by the self-motivation 
questionnaire (Dishman, Ickes, & Morgan, 1980): USPEZDEL – performance (success) 
based on work, USPNGDEL – performance (success) irrespective of work, MOC – motive of 
power, POZITIVN – positive competition motivation, NEGATIVN – negative competition 
motivation, SAMOMOT – self-motivation. Personality traits were measured by the Freiburg 
personality questionnaire (FPI questionnaire – 76; Bele-Potočnik, Hruševar, & Tušak, 1990), 
by a perseverance questionnaire (Černohorski & Železnik) and by Spielberg's anxiety scale 
(Spielberg, 1970): NEVROTIC – neuroticism, SPONTAGR – spontaneous aggressiveness, 
DEPRESIV – depressiveness, RAZDRAZL – irritability, DRUZABN – sociability, OBVLADAN 
– self-control, REAKTAGR – reactive aggressiveness, ZAVRTOST – inhibition, ODKRITO – 
sincerity, EKSTRA V – extroversion, EMOCLAB – emotional lability, MASKULIN – masculinity, 
VZTRAJNO – endurance, TEKMANKS – competition anxiety, ANKOSLAS – anxiety as 
personality trait.
Variables of the sociological subspace: SIZOBR_M – education of mother, SIZOBR_O – educa-
tion of father, PDOBPOG – conditions for training, PDOBSTDE – good expert work, PDOBORG 
– good organisation of club, PSP AKT_M – involvement of mother in sport, PSP AKT_O – involve-
ment of father in sport, IKLFUN_M – function of mother in club, IKLFUN_O – function of 
father in club, IDELMS_M – position of mother at work, IDELMS_O – position of father at 
work. 
Procedure
Measurements were carried out at the Faculty of Sport in Ljubljana in March 2002. The subjects 
underwent the tests of motor abilities in a sports hall and on an athletic running track; the func-
tional test protocol was performed in the laboratory for sport physiology. Data were processed 
with the SPPS software package and SMMS program. In line with the objectives and hypotheses, 
the research consisted of the following phases. 
Two models of potential competition performance of cross-country skiers were set up in the 
form of a decision tree. The MMPS model covered the motor, morphological, psychological, 
a nd sociolog ic a l subspaces of t he ps ychosomat ic st at u s of compet itors . I n add it ion to t he above 
subspaces, a functional subspace had also been included in the MFMPS model.
Normalisers for all elementary variables (tests) in the MFMPS model were set up, representing 
the points that determine the utility function v, which for a given measured (raw) result x on 
the base criterion determines its value or utility (Chankong & Haimes, 1983). The function is 
determined in such a way that in the variable for raw results, an arbitrary number of points is 
defined. The expert thus gives only the explicit, numerical and attribute values of the utility 
function for some points, while for other points, the values are determined by computing the 
straight line between two points by means of interpolation.
An example of normalisers for the MSPSK variable – jumps over Swedish gymnastic bench (see 
Table 1: e.g. 31 : 8 means that 31 repetitions in the test received the numerical score 8 – very 
good).

Expert modelling in cross-county skiing 17 Kinesiologia Slovenica, 11, 1, 13–30 (2005)
Table 1: An example of setting up the normalisers for the MSPSK variable
Value of variable 8 24 26 27 29 31 33 42
S c o r e o f v a r i a b l e0 2457891 0
Numerical and descriptive values of scores: 0-1.99 = unsatisfactory, 2-3.99 = satisfactory, 4-6.99 = good, 7-8.99 = very 
good, 8.99-10.00 = excellent.
What experts have before their eyes when evaluating individual variables is a vision of top-
level creativity in this sport (champion model) and at the same time the features of long-term 
developmental characteristics of an athlete. Thus, expert's evaluation becomes far-reachingly 
useful. In this way, longitudinal treatment of an athlete and the associated universal model of 
potential performance are attained. Namely, athletes go through various developmental, age and 
competition periods in their transformation process. 
Decision rules for all nodes in the MFMPS and MMPS models were set up. They represent the value 
of a hypothetical contribution (in %) of each variable to competition performance at the respec-
tive node of individual model. The decision rules (weights) were determined by two methods: 
the method of dependent and the method of independent determination. In the method using 
dependent determination of weights (Šturm et al., 1992), total contribution of the weights of all 
variables of lower order that constitute a variable of higher order is, in relative terms, 100 at any 
individual node. In absolute terms, the sum total of the weights of all variables of lower order (tests) 
in the MFMPS model is 100. By the method of independent determination of weights (Ulaga, 2001), 
however, the absolute contribution of each variable to the score of competition performance is 
determined in such a way that for each basic and each derived variable a weight from 0 to 100 is 
determined. Hence, the weights are determined independently of other variables at the node. 
With the SMMS program, scores for all variables at all levels in the MFMPS and MMPS models 
were calculated for each subject. First, for elementary variables (tests) and then gradually for all 
composite variables at higher nodes, up to the highest node (URMPU), the so-called prognostic 
score of competition performance of the subject. The calculation was made according to the 
following formula (Jošt, Dežman, & Pustovrh, 1992):
Svr = (Snr
1
 x P) + (Snr
2
 x P) +…+ (Snr
n
 x P) 
Svr – normalised value of a higher-order variable 
Snr – normalised value of a lower-order variable 
P – weight of a lower-order variable (decision rule, weight).
The data were processed at the Institute of Kinesiology at the Faculty of Sport in Ljubljana. The SPSS 
program package and SMMS program were used. T o establish the correlation between the scores 
of variables in the MFMPS and MMPS models, the Pearson’s correlation coefficient was used.
RESULTS
An example of the construction of the MFMPS model
Table 2 shows the structure of the MFMPS model at the highest levels and also part of the 
structure of the motor subspace (energy component of movement). There is also an example of 
the score of potential competition performance of the subject at the shown levels of the MFMPS 
model according to the method of dependent and independent determination of weights.

18 Expert modelling in cross-county skiing Kinesiologia Slovenica, 11, 1, 13–30 (2005) 
Table 2: Part of the structure of the MFMPS model, weights, normalisers and an example of 
evaluation of potential competition performance by both methods of determination of weights 
Variables and test's codes
WEIGHTS
NORMALISERS
Competitor "A"
Dependent Independent
D I R E Sf ( x )R E Sf ( x )
URMPU 10 0 10 0 7. 55 7. 41
 Morphology 12.5 80 6.34 6.65
 Functional dimensions 30 100 8.70 8.87
 Sociological characteristics 10 70 7. 6 7 7. 3 8
 Psychology 17. 5 8 5 7. 8 0 7. 2 7
 Motor abilities 30 100 6.70 6.72
 Energy comp. of movement 20.4 100 6.99 7.08
 Excitation duration 12.8 100 8.38 8.56
 Endurance power 5.6 75 7.48 7.88
 Repetitive power 4.2 70 6.95 6.86
 MSPSK 1.6 80
8:0, 24:2, 26:4, 27:5, 29:7, 31:8, 
33:9, 42:10
33 9.00 33 9.00
 MSSNB 1.2 65
1:0, 10:2, 14:4, 16:5, 18:7, 20:8, 
22:9, 25:10
12 3.00 12 3.00
 MSDTSK 1.4 70 0:0, 12:2, 15:4, 17:7, 19:9, 21:10 18 8.00 18 8.00
 Static power 1.4 60 9.06 9.06
 MSMIZT 1.4 60
0:0, 56:2, 65:4, 85:7, 102:9, 
120:10
103 9.06 103 9.06
 Running endurance 7.2 100 9.08 9.08
 MSCT 7.2 100
480:10, 492:9, 504:8, 515:7, 
530:5, 537:4, 554:2, 820:0
4 9 19 . 0 84 9 19 . 0 8
 Excitation intensity 7.6 70
Legend:
URMPU – universal reduced model of potential performance, D – dependent, I – independent, 
RES – raw test results, f (x) – numerical score, SCORE – attribute score
Numerical and descriptive values of scores: 0-1.99 = unsatisfactory, 2-3.99 = satisfactory, 4-6.99 = good, 7-8.99 = very 
good, 8.99-10.00 = excellent 
Correlation between scores of variables 
Correlation between the final score of the universal reduced model of potential performance 
(URMPU) and the scores of individual subspaces in the MMPS model (motor, morphological, 
p s y c h o l o g i c a l , a n d s o c i o l o g i c a l s u b s p a c e s ) i s s h o w n i n Ta b l e s 3 i n 4 . I n t h e m e t h o d o f i n d e p e n d e n t 
determination of weights, the final score of the model (URMPU) is slightly less correlated with 
the motor and psychological subspaces than in the method of dependent determination of 
weights. Correlation between the final score and the morphological and sociological subspaces 
is, however, higher than in the method of dependent determination of weights. In the method 

Expert modelling in cross-county skiing 19 Kinesiologia Slovenica, 11, 1, 13–30 (2005)
of dependent determination of weights, the relation between the final score and the sociological 
subspace is statistically insignificant.
Ta ble 3 : Correlation between the scores of subspaces and individual subspaces with the final score 
(URMPU) in the MMPS model built by the method of dependent determination of weights
URMPU
Motor abilities
Morphology
Psychology
Sociology
URMPU 1.00
Motor abilities 0.91** 1.00
Morphology 0.64* 0.36 1.00
Psychology 0.65* 0.56* 0.07 1.00
Sociology 0.31 0.10 0.45 -0.04 1.00
Legend: 
** p ≤0.01, * p ≤ 0.05
In the method of dependent determination of weights, the degree of interrelation between 
individual subspaces of the psychosomatic status of cross-country skiers is in the range from 
low to medium high (see Table 3). The highest, statistically significant correlation is between the 
motor and psychological subspace. 
Ta ble 4 : Correlation between the scores of subspaces and individual subspaces with the final score 
(URMPU) in the MMPS model built by the method of independent determination of weights
URMPU
Motor abilities
Morphology
Psychology
Sociology
URMPU 1.00
Motor abilities 0.83** 1.00
Morphology 0.67** 0.26 1.00
Psychology 0.55* 0.43 0.01 1.00
Sociology 0.57* 0.25 0.54* 0.09 1.00
Legend: 
** p ≤0.01, * p ≤ 0.05

20 Expert modelling in cross-county skiing Kinesiologia Slovenica, 11, 1, 13–30 (2005) 
In the method of independent determination of weights (see Table 4), the trend and direction 
of correlations remained more or less unchanged, if compared with the method of dependent 
determination of weights. In general, only the power of correlations between individual subspaces 
changes and is slightly smaller in this method. Only the correlation between the morphological 
and the sociological subspaces is statistically significant, however, it only slightly exceeds the 
level of statistical significance. 
In the MFMPS model (motor, functional, morphological, psychological, and sociological 
subspaces), we focused slightly more on the motor and functional subspaces, which are the 
most important in terms of potential performance of cross-country skiers. An examination 
of correlations between the scores of variables obtained by both methods of determination of 
weights revealed only minimal differences (see Tables 5 in 6). 
Table 5: Correlation between the scores of variables at different levels in the MFMPS model, 
obtained on the basis of dependent determination of weights
 
Dimensions and variable's codes
Motor. Funct. Morph. Psych. Socio.
URMPU (MFMPS model) 0.84** 0.86** 0.50 0.51 0.29
Motor. Funct. Morph. Psych. Socio.
–  Motorabilities
1.00 0.54* 0.36 0.62* 0.20
ENKOGI INKOGI
– ENKOGI
1.00 0.57* 0.96**
TRAEKS INTEKS
– TRAEKS 1.00 0.07 0.87** 0.29 0.77**
– INTEKS 0.07 1.00 0.56* 0.64* 0.65*
– INKOGI
0.57* 1.00 0.77**
REGSIN KOORD
– REGSIN 1.00 0.72** 0.50 0.91** 0.69**
– KOORD 0.72** 1.00 0.55* 0.94** 0.74**
– Functional
0.54* 1.00 0.24 0.17 0.15
VO2max WATT
– VO2max 1.00 0.49 0.38 0.92**
– WATT 0.49 1.00 0.60* 0.80**
– Morphology
0.36 0.24 1.00 0.06 0.54*
– Psychology
0.62* 0.17 0.06 1.00 -0.00
– Sociology 0.20 0.15 0.54* -0.01 1.00
Legend:
** p ≤0.01, * p ≤ 0.05
ENKOGI – energy component of movement, TRAEKS – excitation duration, INTEKS – excitation intensity, INKOGI 
– information component of movement, REGSIN – regulation of synergists, KOORD – coordination, VO2max – relative 
oxygen consumption, WATT – loadings at thresholds 

Expert modelling in cross-county skiing 21 Kinesiologia Slovenica, 11, 1, 13–30 (2005)
Table 6: Correlation between the scores of variables at different levels in the MFMPS model, 
obtained on the basis of independent determination of weights
 
Dimensions and variable's codes
Motor. Funct. Morph. Psych. Socio.
URMPU (MFMPS model) 0.78** 0.84** 0.67** 0.32 0.38
Motor. Funct. Morph. Psych. Socio.
–  Motorabilities
1.00 0.51 0.29 0.43 0.25
ENKOGI INKOGI
– ENKOGI
1.00 0.51 0.92**
TRAEKS INTEKS
– TRAEKS 1.00 0.09 0.83** 0.20 0.67**
– INTEKS 0.09 1.00 0.62** 0.63* 0.71**
– INKOGI
0.51 1.00 0.81**
REGSIN KOORD
– REGSIN 1.00 0.67** 0.31 0.84** 0.60*
– KOORD 0.67** 1.00 0.54* 0.97** 0.82**
– Functional
0.51 1.00 0.47 -0.03 0.26
VO2max WATT
– VO2max 1.00 0.51 0.33 0.89**
– WATT 0.51 1.00 0.57* 0.85**
– Morphology
0.29 0.47 1.00 0.01 0.54*
– Psychology
0.43 -0.03 0.01 1.00 0.09
– Sociology 0.25 0.06 0.54* 0.09 1.00
Legend: 
** p ≤0.01, * p ≤ 0.05
The largest differences between both methods are exactly at the highest level of the model, i.e. 
between the URMPU score and the scores of individual subspaces. In the method of dependent 
determination of weights, the final score of the model is highly statistically significantly cor-
related with the motor and functional subspaces. In the method of independent determination 
of weights, the degree of correlation of the URMPU increased in the case of morphological and 
sociological subspaces, and decreased in the case of psychological and motor subspaces.
If we look at the final score of motor abilities, we can see that it statistically significantly correlates 
w i t h b o t h d i r e c t l y s u b o r d i n a t e d c o m p o n e n t s ( E N KO G I , I N KO G I ) . Th e s c o r e o f m o t o r a b i l i t i e s i s 
the most strongly correlated with the energy component, and slightly less with the information 
component of movement. In the method of independent determination of weights, a slightly 
lower correlation between the score of motor abilities and the score of the energy component 
of movement should be mentioned as well as a higher correlation with the score of information 
component, compared to the method of dependent determination of weights.

22 Expert modelling in cross-county skiing Kinesiologia Slovenica, 11, 1, 13–30 (2005) 
In the motor subspace, we also wanted to establish a correlation between all four hypothetical la-
tent dimensions that emerge in numerous researches. Correlation between the energy component 
o f m o v e m e n t ( E N KO G I ) a n d b o t h d i r e c t l y s u b o r d i n a t e d m e c h a n i s m s i s h i g h i n b o t h m e t h o d s o f 
dimensional configuration, especially with the duration of excitation (TRAEKS). The duration of 
excitation and the intensity of excitation (INTEKS), which belong to the superordinate node of 
t h e e n e r g y c o m p o n e n t o f m o v e m e n t , t u r n e d o u t t o b e p o o r l y c o r r e l a t e d d i m e n s i o n s i n o u r s a m p l e 
of subjects. The information component of movement (INKOGI) is also statistically significantly 
correlated with its hypothetically subordinated components (KOORD and REGSIG), which are 
again mutually statistically significantly correlated (0.72 in the method of dependent and 0.67 
in the method of independent determination of weights), which could not be noticed in the 
case of TRAEKS and INTEKS. The information component of movement is also statistically 
significantly correlated with the energy component of movement; however, only in the method 
of dependent determination of weights. The correlations between both components of movement 
(ENKOGI, INKOGI) and the remaining two opposite mechanisms are important and two of 
them are even statistically significant (ENKOGI with KOORD and INKOGI with INTEKS) in 
both methods of determination of weights.
The correlation between the final score of the functional subspace and the score of oxygen 
consumption (VO
2
ma x) is sl ig ht ly h ig her t ha n w it h t he score of t he abi l it y of overcom i ng load s 
(WATT) in both methods of dimensional configuration, although in both cases correlation is 
high and statistically significant (p ≤ 0.01). Both nodes are to a rather low extent interrelated in 
both methods of weight determination (0.49 and 0.51). 
From the aspect of a predominant impact of motor abilities on performance in sport, we are 
mainly interested in correlations between this subspace and other subspaces. In the method 
of dependent determination of weights, the score of motor abilities has the highest and also 
statistically significant correlation with the score of the psychological subspace, while in the 
method of independent determination of weights this correlation is slightly smaller and statisti-
cally insignificant. Correlations between the score of motor abilities and the score of functional 
subspace are just above the limit of statistical significance in the method of dependent determina-
tion of weights and statistically insignificant in the method of independent determination of 
weights. It has also been found that there are no statistically significant correlations between 
the score of motor abilities and the score of morphology. The correlation between these two 
subspaces is slightly smaller in the method of independent determination of weights. There 
are no statistically significant correlations between the score of motor abilities and the score of 
sociological subspace.
Among all other correlations between the studied subspaces we should mention a statistically 
significant correlation (just above the limit of statistical significance) between the scores of the 
morphological and sociological subspaces in both methods of dimensional configuration. 
The agreement, i.e. the correlation between the scores of variables obtained by various methods 
of determination of weights was established by the Pearson’s correlation coefficient.

Expert modelling in cross-county skiing 23 Kinesiologia Slovenica, 11, 1, 13–30 (2005)
Table 7: Agreement between the scores of variables obtained by different methods of weight determination 
in the MFMPS and MMPS models.
Dimensions and variables MFMPS MMPS
URMPU 0.988** 0.981**
– Motor abilities 0.985** 0.979**
– Energy component of movement 0.989** 0.982**
– Excitation duration 0.990** 0.987**
– Endurance power 0.910** 0.879**
– Repetitive power 1.00 1.00
– Excitation intensity 0.980** 0.989**
– Fast power 1.00 1.00
– Information component of movement 0.961** 0.965**
– Regulation of synergists 0.788** 0.787**
– Balance 0.972** 0.987**
– Speed 0.947** 0.977**
– Coordination 0.999** 0.993**
– Functional dimensions 0.997**
– Relative oxygen consumption 0.999**
–  Loadings at thresholds 0.999**
– Morphology 0.954** 0.976**
– Psychology 0.929** 0.968**
– Sociological characteristics 0.961** 0.926**
Legend: 
** p ≤ 0.01
Table 7 shows that the agreement between the scores of both dimensional configuration methods 
is statistically significant, at a probability level of p ≤ 0.01 in both models (MMPS and MFMPS). 
Only the correlations at the nodes of both universal reduced models of potential performance 
are given.
The values of correlations at the level of elementary variables are complete (1.00) since in both 
methods of determination of weights, identical normalisers were used for raw results (tests).
Where the relationship between weights of both methods of determination of weights is the 
same or very similar, the agreement between the scores of the variables in the model is also 
complete, hence 1.00 (repetitive power, fast power). The lowest agreement (although highly 
statistically significant) between the variables obtained by both methods of determination of 
weights was recorded in the aggregated criterion of the mechanism of regulation of synergists. 
To explain this smaller agreement, the trend of scores of the mechanism for the regulation of 
synergists in relation to the URMPU score is given in Figure 1 and Figure 2 for all subjects. A 
detailed examination of the scores in the coordinate system (correlation of the URMPU with 
the mechanism for regulation of synergists) in both methods shows that the scores of subjects 
3, 6, 8 and 14 vary the most.

24 Expert modelling in cross-county skiing Kinesiologia Slovenica, 11, 1, 13–30 (2005) 
  
REGSIN
8 7 6 5 4 3 2
U
R
M
P
U
8
7
6
5
4
3
14
13
12
11
10
9
8
7
6
5
4
3
2
1
Figure 1: Correlation of the scores of the regulation of synergists with the final score (URMPU) 
in the method of dependent determination of weights (MFMPS model)
REGSIN
8 7 6 5 4 3 2
U
R
M
P
U
8,0
7,0
6,0
5,0
4,0
3,0
14
13
12
11
9
8
7
6
5
4
3
2
1
Figure 2: Correlation of the scores of the regulation of synergists with the final score (URMPU) 
in the method of independent determination of weights (MFMPS model)

Expert modelling in cross-county skiing 25 Kinesiologia Slovenica, 11, 1, 13–30 (2005)
In Table 8, the scores of the mechanism of regulation of synergists and its respective variables 
are shown for the mentioned subjects. The largest disagreements between both methods occur 
in the score of the speed node. In the score of the balance node, this disagreement is smaller, 
while in the score of the flexibility node, it is the same, due to the fact that the said node contains 
only one elementary variable. 
Table 8: Comparison between the scores of the mechanism for regulation of synergists and its 
variables, obtained by both methods of determination of weights for subjects 3, 6, 8 and 14.
Variable's and test's codes
WEIGHTS
SCORES OF 
DEPENDENT METHOD
SCORES OF 
INDEPENDENT METHOD
DI3681 43681 4
URMPU 100 100 3.07 6.83 6.62 6.79 3.93 7.01 6.76 6.85
– Information component of movement  12 85 2.30 6.54 5.17 4.62 2.98 5.65 4.41 5.11
– Regulation of synergists 4.8 65 3.21 7.74 6.28 4.30 4.74 5.75 4.63 5.43
– Balance 0.8 55 3.88 7.05 4.67 4.08 3.70 6.26 4.57 3.84
– MSRKS 0.3 50 2.88 2.75 4.13 2.75 2.88 2.75 4.13 2.75
– MSRKF 0.5 60 4.38 9.19 4.94 4.75 4.38 9.19 4.94 4.75
– Speed 3.4 75 2.32 9.00 7.57 3.74 3.69 8.41 6.82 4.69
– MTAPRO 0.8 55 7.00 7.00 5.00 7.00 7.00 7.00 5.00 7.00
– MMENS60 2.6 85 1.54 9.33 8.00 3.20 1.54 9.33 8.00 3.20
– Flexibility 0.6 60 7.00 1.95 1.95 7.80 7.00 1.95 1.95 7.80
– MTPK 0.6 60 7.00 1.95 1.95 7.80 7.00 1.95 1.95 7.80
DISCUSSION
When searching for interrelations between the scores of individual subspaces in the MMPS 
model, it is necessary to mention the correlation between the score of motor abilities and psychol-
ogy despite the fact that in the method of independent determination of weights, the degree of 
correlation is no longer statistically significant. The correlation is quite understandable; however, 
it is difficult to tell what the cause is and what the effect. To trust in his own abilities (including 
the motor ones), it is necessary that a cross-country skier forms a stable self-image. Marentič 
Požarnik (1988) says: "It is a whole of opinions and attitudes that a young person holds of himself 
– his mental and physical capacities." However, in the developmental period of adolescence, rapid 
changes occur and the competitor's self-image tends to vary considerably. On the other hand, 
Marsh and O’Neill (1984) found that self-image is significantly affected by the environment 
(external factors). Actively involved are those who deal with the adolescent every day. In addition 
to the family and friends, sport also plays an important role here. Sport should contribute to the 
development of personality by transforming socially less acceptable reactions. In this way, the 
foundations for a grown-up personality are being constantly upgraded. 

26 Expert modelling in cross-county skiing Kinesiologia Slovenica, 11, 1, 13–30 (2005) 
In the MFMPS model, an extremely low correlation between the dimensions of the duration 
and the intensity of excitation, belonging to the energy component of movement, is particularly 
evident. The TRAEKS variable involves the ability of persisting in the elevated state of excitation 
despite the inhibitory tendencies in the peripheral and central structures; the INTEKS variable, 
however, involves the ability of activating a large number of motor units in short time intervals. 
I n accord a nce w it h some resea rches we wou ld ex pec t a h ig her (posit ive) cor relat ion ; especia l ly 
owing to the fact that in these age categories, the effects of specific training can be rather general 
(Dykstra, Demetriou, Copay, & Boileau, 1996); the progress in one structure is followed by the 
progress in another one. On the other hand, the reason for statistically insignificant correlation 
between the TRAEKS and the INTEKS variables can also be sought in the theoretical bases of 
the motor subspace structure. Theories speak about specific adjustments produced by training of 
the explosive power and endurance, as otherwise the hypothetical hierarchically arranged motor 
subspace would not point to two different latent dimensions (Kurelić, Momirović, Stojanović, 
Šturm, Radojević, & Viskić-Štalec, 1975). It is necessary to add here that these scores are derived 
from the raw results (they are transformed) and do not permit any overall generalisation to the 
theories derived from standardised values of variables.
In the functional subspace we should mention a rather low correlation between both directly 
subordinated nodes of this subspace, which points to the fact that two relatively independent 
dimensions of the functional subspace are involved, despite the fact that loading (WATT) 
indirectly results from energy processes at different intensity levels (VO
2
max). 
For a more thorough analysis of the correlations between individual subspaces, additional multi-
variate data processing and, above all, a larger sample of measured subjects would be necessary. 
Despite that and the fact that derived (transformed) scores are concerned, we can give a basic 
evaluation of directions of the said correlations, primarily for motor abilities. This evaluation has 
the highest correlation with the score of the psychological subspace (in the method of dependent 
determination of weights). This subspace consists of special psychological abilities (intelligence, 
concentration) and motivational and personality dimensions. If greater motor efficiency is taken 
as an indicator of greater competition performance and this is connected with the dimensions 
of the psychological subspace, then the obtained correlation can be compared with the results of 
some researches. More successful athletes are, as a rule, more dominant (Thakur & Thakur, 1980) 
and emotionally more stable (Butt, 1987); more successful athletes have a lower degree of pre-
competition anxiety (Martens & Gill, 1976), and a smaller degree of neuroticism has a positive 
i mp a c t on c o ord i n at ion a nd b a l a nc e (I s m a i l , 19 76) . R e s e a rc he s (e . g . , K i r k e nd a l l & G r u b e r, 19 70 ; 
Mejovšek, 1976) also showed no correlations between intelligence and simple motor movements. 
However, we can agree with the opinion of Adams (1981) that in carrying out the motor tasks, 
cognitive factors are more important until the movement becomes automated. The questions that 
arise here are: how long does the elimination of faults in the movement technique take and how 
fast is the adaptation to new disciplines, if the level of cognitive factors is lower? Responses to 
training are triggered, determined and dictated by the brain. If for certain reasons we dedicate 
insufficient attention to the encoding of exact movement patterns, the cross-country skier has 
difficulty in focusing on more important factors during the race itself.
The correlations between the score of motor abilities and the score of functional subspace only 
indicate (as generally known) that through the activities which have the character of long-lasting 
cyclic movements it is possible to exert substantial influence on the oxygen transport system 
(ventilation, cardiac output and pulmonary diffusion capacity), which is one of the indicators of 

Expert modelling in cross-county skiing 27 Kinesiologia Slovenica, 11, 1, 13–30 (2005)
the energy capacity of the organism. Hence, the correlation between the score of motor abilities 
and the two scores of the dimensions of functional abilities is understandable and expected, 
despite the fact that in the method of independent determination of weights the association 
between these two subspaces is no longer statistically significant.
The interrelation between the motor and morphological subspaces has been the subject of many 
researches (Ambrožič, 1996). In our case, statistically significant correlations between the two 
subspaces were not established. The correlation is slightly smaller in the method of independent 
determination of weights. Despite that, in both methods of determination of weights and in both 
model s (M M PS , M FM PS) t he score of mor pholog y i s relat ively h ig h ly cor related w it h t he score 
of the entire model (URMPU).
The latent structures of the sociological and motor subspaces are fairly well investigated; however, 
the results of researches carried out on different samples are difficult to compare. In our group 
of subjects, stat ist ica l ly sig ni fica nt correlat ions do not occur. Perhaps we ex pected a somewhat 
larger correlation between both subspaces since the sociological subspace also consisted of the 
socialisation subsystem dimensions (education of parents), which could indirectly point to the 
i n fluence of t hat subs ystem on t he development of motor abi l it ies . The rea son i n a l l probabi l it y 
lies in the nature of the sport itself since execution of simple movements does not involve high 
cognitive demands (Planinšec, 1999), if they can be hypothetically considered as a transmittable 
hereditary factor of highly educated parents. Despite all, however, correlations between these 
two subspaces are not without importance, especially because this is the first attempt of this 
kind to set up a sociological model of performance in sport. Between the motor and sociologi-
cal subspaces, the most consistent correlation can be seen with respect to the applied various 
methods of weight determination.
The correlation between the morphological and sociological subspaces is somewhat unexpected 
in both methods of dimensional configuration. Perhaps this points to the fact that athletes with 
well-ordered factors of the socialisation, institutional, and consequential subsystems have all of 
the primary conditions for a harmonious physical development.
We have found that the scores of variables obtained by different methods of determination 
of weights agree highly statistically significantly. A slightly lower (yet still highly statistically 
significant at the probability level of p ≤ 0.01) agreement at the node of regulation of synergists 
(REGSIN) occurs because the relationships between the weights representing the degree of the 
variance in the significance of individual nodes are disproportionate. If we decreased (increased) 
the criterion of significance in the method of independent determination of weights and thus 
artificially attained a more appropriate relationship between both methods, a question would 
arise about suitability of placing the individual variables into the model and hence, about the 
informative value of the universal reduced model of potential performance. We would also 
undermine the applicability of the whole expert modelling by this method of weight determina-
tion, since according to both methods the dimensional configuration (determination of weights) 
should be independent.
The speed node (HITR) has the largest influence on smaller agreement of the superordinate node 
(REGSIN). Here the disproportion in the weights between both methods is the largest at the level 
of elementary variable of tapping with hand (MTAPRO) and 60-m run (MMENS60) (0.8 : 2.6 and 
55 : 85), therefore the final scores at the speed node also differ the most in all four subjects (Table 

28 Expert modelling in cross-county skiing Kinesiologia Slovenica, 11, 1, 13–30 (2005) 
8). A disproportion in weights between both methods can also be seen at the remaining two nodes 
of balance and flexibility, which is consequently carried over into the superordinate node.
By applying expert knowledge of individual scientific disciplines, we have constructed two 
universal reduced models of potential performance in cross-country skiing with the intent to 
discover the relationships and interactions between individual psychosomatic status dimensions. 
Information yielded by both models should veer towards treating each cross-country skier as 
a bio-psycho-social whole. However, models are not theories or laws; they are only a reduced 
form of the system-athlete (man) relationship. Success in sport depends on the concomitance 
of numerous factors, which must be perfectly intertwined. The model thus does not include the 
variables of the cross-country skiing technique and movement economics, representing essential 
variable factors of excellence in cross-country skiing. Despite the fact that in scoring individual 
dimensions and subspaces we proceeded from the transformed values and that it was difficult 
to generalise, connect and also compare them with the standardised ones, these values can, 
nevertheless, serve as an important aid from the aspect of practical and theoretical starting points 
in planning of transformation processes. Above all, the correlations between motor abilities and 
the functional and psychological dimensions established by us can be of great help in planning 
and monitoring of successful/unsuccessful competition performance and they often lead away 
from blind alleys in which those athletes practising sports with a strongly emphasised endurance 
component often end.
In both models, two methods of dimensional configuration were tested. The question that arises 
here is the question about the qualitative value and the utility of both methods of determination 
of weights. By the method of dependent determination of weights, slightly higher correlations 
between the elementary and derived variables of cross-country skiers’ psychosomatic status were 
obtained in general. As regards the accuracy of determination of contributions to individual 
elementary variables, the method of dependent determination of weights seems to be more 
appropriate. However, this is not the only reason for the evaluation of appropriateness. In the 
method of dependent determination, expert modelling is much more focused on the urgent need 
for an interdisciplinary treatment of the cross-country skier’s psychosomatic status. However, in 
t he c a se of i ndependent deter m i nat ion of weig ht s , t h is is not pos sible to such a n ex tent , a s t here 
is no division of weights on a given criterion. In the latter method, overvaluation or undervalu-
ation of individua l dimensions is a lso possible. The positive side of the method of independent 
determination of weights is its fast, simple, and unproblematic application when one wants to 
measure only a specific scope of the psychosomatic status dimensions. In such cases it is not 
necessary to rebalance the model and to set up anew the decision rules. 
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