## 4 Results  
### Interpretive Modeling  
To begin exploring the relationships between the physiological features and self-reported mental effort, we first inspected the parameter estimates from our interpretable machine-learning models: logistic regression (ordinal logit link) (Table 2) and the two-state Markov-switching dynamic regression (Table 3). The logistic-regression model suggested that although all of the features were highly significant due to the large number of time samples, EDA and skin temperature had the biggest effect sizes. Specifically, the model indicated that a higher EDA was indicative of a higher level of mental effort (odds ratio (OR) = 2.48, \(p<0.001\)), while a drop in skin temperature may be indicative of higher levels of mental effort (OR = 0.82, \(p<0.001\)). Of the three acceleration axes, acceleration in the Y and Z directions may be indicative of mental effort, with negative (OR = 0.99, \(p<0.001\)) and positive (OR = 1.01, \(p<0.001\)) relationships, respectively. The two-state Markov switching model expanded on this story by providing a glimpse of the relative effects of these features in low and high mental effort states. When the participant was in a low mental effort state (State 1), it appeared that skin temperature was the most important physiological response indicator, with lower values indicative of higher levels of mental effort (estimate = \(-0.057\), standard error (SE) = 0.0018, \(Z=-32.4\), \(p<0.001\)). In this state of lower mental effort, EDA (estimate = \(-0.274\), SE = 0.028, \(Z=-9.8\), \(p<0.001\)) tended to go down with increasing mental effort. This relationship switched, however, when the participant entered the high mental effort state (State 2), with higher EDA values indicating higher levels of mental effort (estimate = 0.96, SE = 0.0175, \(Z=55.0\), \(p<0.001\)). In this state, we also observed that the effect of skin temperature retained its negative relationship, but the strength of the association became stronger (estimate = \(-0.27\), SE = 0.0014, \(Z=-194.0\), \(p<0.001\)). As far as movement was concerned, in the low mental effort state, movement tended to have a positive relationship with mental effort. While this positive relationship was retained for acceleration in the X direction when the participant entered the higher mental workload state, acceleration in the Y and Z directions switched to being indicators of lower mental workload. From these relationships, it appeared that motion of the arms tended to increase with mental workload until the point when the participant entered a state of more intense concentration (higher mental effort), at which time movement slowed down as concentration further increased. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Feature a** & **Estimate** & **SE** & \(\mathbf{\chi^{2}}\) **(df = 1)** & **OR** \\ \hline EDA & 0.91 & 0.026 & 1200.9 & 2.48 \\ TEMP & \(-0.19\) & 0.0019 & 10,369.3 & 0.82 \\ HR & \(-0.0012\) & 0.0002 & 29.7 & 1.00 \\ ACC X & 0.0011 & 0.00014 & 62.2 & 1.00 \\ ACC Y & \(-0.0087\) & 0.00010 & 7164.4 & 0.99 \\ ACC Z & 0.0063 & 0.00011 & 3263.0 & 1.01 \\ \hline \hline \end{tabular} a  
\end{table} 
Table 2: Parameter estimates from the ordinal logistic regression model (threshold values omitted).