Models of structural theories of motor abilities and performance Petr Blahuš Charles University Faculty of Physical Education and Sport Department of Kinanthropology Division of Methodology Prague, The Czech Republic

There are several “secret - latent - hidden” precious stones, formal methods items in the methodological treasure of behavioral sciences incl. kinanthropology, viz. latent variables models: - CFA - confirmatory common factor analysis - IRT models -Item Response Theory models - SEM - structural equations and path analysis models

Theories of motor performance - incl. athletic performance, are structural theories i.e. combination theories of a composition of motor abilities for example cf. the following naively intuitive model: performance = 30% endurance + 40% power + 20% speed

One-level ?

Coordination Hierarchical ?

Structural Equation Models (SEM) with latent variables and theories of athletic performance 1. Static simultaneous combination of manifest indicators of training: multiple regression model 2. Static simultaneous combination of motor abilities and concepts: common latent factor model 3. Static but sequential combination ordering of motor abilities and concepts: path analysis with latent variables 4. Dynamic sequence and combination: VARMA for longitudinal analysis of longitudinal training documentation

Training indicator 1 Practice / training indicator 2 Practice / training indicator 3 Practice / training indicator 1 Control test 1 Control test 2 Performance This composition of training should produce That performance Composite manifest prediction multiple regression

Endurance F1 Power F2 Speed ability F3 Test 1 Test 2 Test 3 Test 4 Test 5 Test 6 Performance Y Combination of theoretical concepts / abilities latent common factors model w1 F1 + w2 F2 + w3 F3 = Y Weighted combination Performance of abilities / concepts produces

Sequential ordering and combination Level of ability F4 Practice method 4 Test 4,1 Test 4,2 Starting level of ability F1 Level of ability F3 Level of ability F2 Level of ability F5 Practice method 3 Test 3,1 Test 3,2 Test 5,1 Test 5,2 Test 2,1 Test 2,2 Performance Practice method 2 Practice method 5 Test 1, 1 Test 1,2 path analysis

F1F1 T est 1 Practice method 1 T est 2 Practice method 2 Final performance Practice method 3 F2F2 F1F1 F2F2 F2F2 F1F1 F1F1 F2F2 T est 4 T est 3 T est 1 T est 2 T est 3 T est 4 Performance T I M E Vector Autoregressive Moving Averages VARMA model