Optimal Scaling For Categorical Canonical Crrelation And Regression Analysis Of Bilateral Dominance Trends In Athletes

Introduction
Extensive research has focused on the phenomenon of asymmetries in healthy individuals and athletes [1, 2]. Part of
this phenomenon, the lateral dominance, has received a great scientific attention as well [3, 4, 5]. Laterality trends for
hands, foots, eyes and ears in the general population have been examined via questionnaires and classical nonparametric
statistical methods. The multivariable structure of lateral dominance in athletes of highly asymmetric sports,
such as volleyball, is unclear. Yet, the conventional univariate techniques for categorical data induce serious limitations
to the validity of the results. The present study examined this phenomenon through optimal scaling transformation of
the laterality profiles of elite volleyball players. The central idea was to overcome the distributional asymmetry of
questionnaire data by non-linear canonical correlation and regression fits.

Methods
A total of 154 volleyball athletes (69 men & 85 women) were tested for their anthropometric and athletic profiles. They
were classified via two valid questionnaires for 10 upper (p1) and 10 lower limp (q1) literalities on a 5-point scale
(1=highly left sided, 5=highly right sided). Due to substantial asymmetry the raw data were subjected to optimal scaling
transformation and analysis to produce: (a) selected 2-dimensional canonical correlation analyses and (b) a series of
multiple regression analyses appropriate for common scale multi-categorical ordered data.

Results
The results of the two canonical correlations for multi-categorical data are shown in Table 1. The eigenvalues for both
sets of variables showed high degrees of explained variance for both dimensions (i.e. λ1=0.890), as indicated by the
relatively consistent component loadings (fig. 1). This strongly indicated the multivariate type of non-linear relationship
between the two sets of correlates. Separate highly significant multiple categorical regressions confirmed the validity of
this general trend and depicted the distinct facets of the phenomenon of body segment- & function-specific lateralities.

Discussion/Conclusions
Strong multivariate associations were identified which are indicative of the multifaceted structural interdependencebetween upper and lower extremities in terms of laterality trends. The method of optimal scaling proved to be highlyconsistent and explanatory for these types of multiple nominal categorical data and permitted a much better statistical
searching of the functional correlates of the existing laterality trends in highly asymmetric sports, such as competitive
volleyball. Conclusive remarks are made with regards to the use of non-linear statistical techniques in cases of
categorical data, such as the so-called bilateral dominance traits, which are assessed on invented quantitative Likert
scales. These scales are frequently subject to violations of the parametric assumption of being normally distributed and,
therefore, need to be transformed and processed by optimal scaling techniques, which provide tools for multivariate
approximations of categorical data.

References:
[1] Kannus P. et al. (1995). Ann. Int. Med., 123, 27-31.
[2] Kramer J. F. & Balsor B. E. (1990). Can. J. Sports Sc., 15, 180-184.
[3] Mandal et al (1992). J. Psych., 126 (2), 155-162.
[4] Strauss E. (1986). Cortex, 22 (3), 475-482.
[5] Vagenas G. & Hoshizaki B. (1991). I.J.S.B., 7, 311-329.

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