Assessment of the Functional Form of the Relationship between Balance Control and Physical Activity Regarding Demographic, Anthropometrical, and Eye Impairment Explanatory Covariates in 9- to 11-Year-Old Children: Results of Polynomial and Cluster Analyses

Explaining the causal and functional relationship between balance control and physical activity (PA) when comparing demographic, anthropometric, and eyesight impairment is uncharted. This study aimed to assess the shape of the relationships between balance control and PA and to verify the usefulness of explanatory variables (sex, chronological age, biological age, myopia, and BMI) in explaining the formation of functional forms between both abovementioned variables. The current contribution evaluated data from 9–11-year-old children (47 boys, 58 girls) and attempts to explain the shape of the relationship between the overall stability index and PA synthetic index, sorting children into clusters depending on their balance features and PA and comparing the separated groups in terms of explanatory variables. The analysis demonstrates four larger clusters that displayed distinct functional relationships. Only BMI and myopia turned out to be useful in explaining cluster memberships. Children in clusters with a linear-constant decline functional form were mostly non-myopic girls, thin, and less mature. Meanwhile, it becomes clear that children with an L-shape were myopic, early-maturated boys with a BMI in the middle of the range for normal weight. The pattern of an inverted U-shaped functional form was distinctive for myopes with rather high BMIs compared to their peers but normally matured