# Walking-Age Estimator Based on Gait Parameters Using Kernel Regression
## 4 Discussion  
As shown in Section 3, the kernel regression analysis with selected variables exhibited an average correlation coefficient between the estimated and actual ages of 0.78, with an absolute mean error of 9.99 years. These values were better than those of the multiple-regression model. This suggests that nonlinear relationships between the age and gait parameters [41] were captured by the kernel regression model. The selected variables differed between multiple-regression analysis and kernel regression analysis, as listed in Table 5. In the multiple regression analysis, the mediolateral velocity of the CoM was included in the explanatory variables, whereas in the kernel regression, anterior velocity of the CoM was included in the explanatory variables. As many earlier studies indicated [1, 3, 7, 8, 9, 41, 51], the anterior velocity or walking speed exhibits a negative correlation with age. In contrast, the mediolateral velocity appears to not be correlated with age [13]. Hence, the variables selected for multiple-regression analysis are partly not in agreement with the literature. In the multiple-regression analysis, both height and weight are explanatory variables, but in the kernel regression, only weight is selected as an explanatory variable. In our dataset, the correlation coefficient between age and height was \(-0.38\) (\(p<0.001\)) and that between age and weight was \(0.17\) (\(p=0.15\)). Height exhibited a stronger linear relationship with age than that of weight. However, in the kernel regression analysis, weight remained in the explanatory variables instead of height. This suggests that weight allows us to estimate the age in combination with other explanatory variables in a nonlinear manner. Step width and stride length are explanatory variables in both the kernel regression and multiple-regression models. The stride length decreased and the step width increased with age [1, 2, 3, 41, 51, 13, 12, 13, 4, 51]; hence, both the step width and stride length can be good predictors of age. The minimum foot clearance is used only in the kernel regression model. The age-dependence of the minimum foot clearance appears minimal in terms of the mean value; however, its variability depends on age [52]. Hence, the use of the minimum foot clearance as a general parameter to estimate the age of walkers is uncertain. In summary, the variables selected for the kernel regression model are mostly reasonable, whereas the validity of the weight and minimum foot clearance should be studied in the future. Cadence was not included in the explanatory variables selected for the multiple-regression and kernel regression analyses. The relationship between cadence and age has not been agreed upon in earlier studies [3], with some studies claiming an increase with age [2,4] and others claiming no correlation between age and cadence [7]. [PERSON] et al. [40] reported that the cadence is predicted by a nonlinear function of the age, and its model function differs between men and women. Hence, the contribution of cadence to the estimation of the age of walkers is still debated. When the kernel regression analysis was used to estimate the age using only the seven gait parameters, excluding height and weight, the mean correlation coefficient between the estimated and actual ages was 0.67. However, when weight was added to the model, the mean correlation coefficient increased to 0.78, as listed in Table 2. This indicates that even a minimal amount of self-declared information, such as weight, helps improve the model accuracy. In practice, the use of such information is recommended. As described in Section 3.3, the results indicate that age estimation errors tend to increase with age. Interestingly, similar age-related trends in estimation accuracy have been reported in studies employing different estimation methods [32]. We speculate that this is largely due to greater inter-individual variability in physical abilities among older adults. For example, [PERSON] et al.