## 3 Results

Table 5: Results of partial correlation analysis between handwriting features and clinical data. the maximum of horizontal velocity, horizontal jerk, and velocity for the repetitive letter \(l\); the mean of the vertical velocity for the Archimedean spiral; and the mean of horizontal acceleration for repetitive loops. For PD duration (in-air movement), the following FD-based features achieved a statistical significance of correlation: the median of jerk (\(\alpha~{}=~{}0.4\)) for sentence, the maximum of jerk (\(\alpha~{}=~{}0.1\), \(\alpha~{}=~{}0.2\), \(\alpha~{}=~{}0.3\)) and velocity (\(\alpha~{}=~{}0.1\)) for repetitive word _les_. The following conventional features achieved a statistical significance of correlation (\(p\)-value of only one of the coefficients was below the threshold): the median and mean of horizontal jerk for the word _lektorka_, the maximum of the velocity for the word _neppodnout_, and the mean of horizontal velocity for the repetitive word _lektorka_ and the word _neppodnout_. The results of the multivariate binary classification analysis are summarized in Table 6. In total, we built and evaluated nine different classification models. These models were selected according to the following criteria: movement type (on-surface, in-air, all), feature type (FD features, conventional features, all). We built models based on the combinations of these criteria as well. For more information, see Table 4.  
With respect to the classification performance, the highest MCC achieved was 0.95 was for eight out of the total nine feature sets (with the exception being the feature set composed of conventional handwriting features computed for the on-surface movements). An interesting fact to note is that for all models based on conventional handwriting features, only a single feature was capable of providing the classification models with such a high discrimination power. In terms of the specific features important for the trained models, the following feature importances were returned by the models (feature importance quantifies the relative importance of the features in the ensemble of the trained XGBoost model [49]; therefore, the higher the value of the feature importance, the more important the feature for the prediction of the dependent variable): conventional on-surface (horizontal jerk (median) of repetitive loops), conventional in-air (horizontal velocity (median) of the sentence), conventional together (horizontal velocity (median) of the sentence), FD on-surface (jerk (max) \(\alpha~{}=~{}0.3\) of the letters _le_), FD in-air (vertical acceleration (mean) \(\alpha~{}=~{}0.6\) of the word _neppodnout_ (FI \(=~{}0.33\)), horizontal jerk (mean) \(\alpha~{}=~{}0.9\) of the word _neppodnout_ (FI \(=~{}0.33\)), horizontal jerk (mean) \(\alpha~{}=~{}0.2\) of the repetitive word _lektorka_ (FI \(=~{}0.33\))), FD together (jerk (max) \(\alpha~{}=~{}0.3\) of the letters _le_ (on-surface; FI \(=~{}0.67\)), horizontal jerk (mean) \(\alpha~{}=~{}0.9\) of the word _neppodnout_ (in-air; FI \(=~{}0.33\))), all on-surface (horizontal jerk (median) of repetitive loops (FI \(=~{}0.50\)), jerk (max) \(\alpha~{}=~{}0.3\) of the letters _le_ (FI \(=~{}0.50\))), all in-air (horizontal velocity (median) of the sentence), and all together (horizontal velocity (median) of the sentence (in-air)). The results of multivariate regression analysis are summarized in Table 7. For this purpose, we used UPDRS V and PD duration as our target variables. As in the case of binary classification, we built and evaluated nine different regression models according to the same criteria. For each of the