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

SIMPLE SUMMARY: The shape of an association between balance control and physical activity (PA) concerning sex, body mass index (BMI), calendar age, biological age, and myopia is not a well-described issue. Therefore, this study aimed to establish the relationship between balance control and PA in the presence of the above-mentioned demographic, anthropometric, and eyesight impairment factors. In our study, 47 boys and 58 girls aged 9–11 years participated. The results showed that only BMI and myopia affected the relationship between balance and PA, demonstrating three kinds of shapes of the relationships. Non-myopic girls with a low BMI and less maturity constantly improved their balance control with increased PA volume. Early-matured boys with a BMI slightly over average or in a normal range achieved a plateau in PA level for balance-control development. Myopic boys and girls with higher BMIs than their peers but maturing at an average pace had a peak value of PA, which is the threshold for the volume of PA when the stimulating effect starts. Future studies should be focused on evaluating the causal relationship between balance control and PA using other explanatory variables. ABSTRACT: 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.