## 3 Results
### Identification of Poor Balance Indicators Derived from Data Measured at Lower Back  
In the independent variable selection process for the logistic regression model, several IMU-derived characteristics were excluded to mitigate multicollinearity issues. The ellipse fitting area and bounding box area were omitted due to their high correlation (r \(>\) 0.99) with the area under the acceleration magnitude curve. RMS acceleration was eliminated due to its strong correlation (r \(>\) 0.98) with both area measures and mean acceleration X. Mean acceleration X was also excluded, owing to its high correlation with multiple variables. These exclusions aimed to reduce redundancy while retaining a diverse set of 1D, 2D, and 3D measures that capture distinct aspects of movement. As shown in Table 3, after adjusting for confounding factors (age, sex, weight, and height), key findings from the logistic regression include the following:* The area under the acceleration magnitude curve was positively correlated with poor balance (coef = 0.78, \(p\) = 0.002), indicating that increased movement activity and more pronounced accelerations were associated with a higher risk of fall.
* RMS angular velocity showed a positive effect on poor balance (coef = 0.32, \(p\) = 0.004), suggesting that faster and more varied rotations may indicate balance instability.
* Total path length was negatively correlated with poor balance (coef = \(-\)1.82, \(p\) = 0.0006), implying that more extensive movement paths were associated with better stability.
* Movement volume was negatively correlated with poor balance (coef = \(-\)0.52, \(p\) = 0.02), suggesting that larger movement volumes indicate better balance control within our experimental context.  
\begin{table}
\begin{tabular}{l c c c} \hline \hline
**Variable** & **Lower Back** & **Torso** & **Head** \\ \hline \multicolumn{4}{l}{_1D-based variables_} \\ Mean acceleration X (m/s\({}^{2}\)) & & \\ Mean (SD) & 1.94 (2.24) & 1.98 (2.34) & 0.53 (0.86) \\
[Q1, Q3] & [0.  
The final model included these variables along with jerk measures and selected mean accelerations, ensuring a comprehensive, yet non-redundant, representation of postural control characteristics. Finally, the model's AUC of 0.73 indicated an acceptable discriminative ability of this logistic regression model.  
\begin{table}
\begin{tabular}{l c c c} \hline \hline
**Variable** & **Coefficient** & **Std. Error** & \(p\)**-Value** \\ \hline \multicolumn{4}{c}{_Confounding Variables_} \\ Age (years) & 0.783 & 0.162 & \(<\)0.0001 \\ Sex (0 = female, 1 = male) & 0.576 & 0.177 & 0.001 \\ Weight (kg) & \(-\)0.542 & 0.197 & 0.006 \\ Height (cm) & \(-\)0.038 & 0.196 & 0.84 \\ \hline \multicolumn{4}{c}{_IMU-Derived Predictors_} \\ Area under the curve (m/s) & 0.780 & 0.254 & 0.002 \\ Jerk X (m/s\({}^{3}\)) & \(-\)0.250 & 0.146 & 0.08 \\ Jerk Y (m/s\({}^{3}\)) & 0.054 & 0.139 & 0.69 \\ Jerk Z (m/s\({}^{3}\)) & \(-\)0.031 & 0.133 & 0.81 \\ Mean acceleration Y (m/s\({}^{2}\)) & 0.145 & 0.141 & 0.31 \\ Mean acceleration Z (m/s\({}^{2}\)) & \(-\)0.110 & 0.123 & 0.38 \\ RMS angular velocity (rad/s) & 0.320 & 0.110 & 0.004 \\ Total path length (m) & \(-\)1.820 & 0.528 & 0.0006 \\ Volume (m\({}^{3}\)) & \(-\)0.521 & 0.226 & 0.02 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Mean (SD) of the coefficients of the predictors of poor balance among various movement characteristics calculated from IMU data measured at the lower back.  
Figure 4: Correlation matrix of IMU-derived movement characteristics.