## 2 Materials and Methods
### Statistics and Machine Learning
These models were trained and tested using the following variant of leave-one-out cross-validation. For each cross-validation fold, the model was trained on data from all but one participant and then tested on the held-out participant's data. The leave-one-participant-out approach maximizes the amount of training data available in each fold, but also prevents the model from training and testing on the same participant's data. Leave-one-participant-out cross-validation sees each participant in the test set exactly once, so a single prediction is made for each data point. The cross-validated model's performance was evaluated by calculating the proportion of recordings correctly classified as at admission (first day) or discharge (last day), the area under the receiver operating characteristic curve, sensitivity, and specificity. Confusion matrices were also generated to visually inspect model performance. The logistic regression model was also used to identify the features that best discriminated between voices at admission and discharge. The odds ratios for each feature coefficient \(\beta_{\text{i}}\) was calculated as \(e^{\beta_{\text{i}}}\). An odds ratio farther from 1 (either above or below) indicates greater predictive power for that variable. This data set had many features relative to the number of data points, so there was a high risk of overfitting causing poor test accuracy. To reduce overfitting, the model fitting process used L1 (or lasso) regularization [42]. Without regularization, the learner finds feature coefficients that minimize classification loss. In L1 regularization, a term given by the sum of the absolute values of the coefficients is added to the loss function:  
\[\underset{\beta}{min}\ \frac{1}{n}\!\!\sum_{i}\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\! \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\! sion or discharge. Grey-shaded (upper-right and lower-left) squares indicate incorrectly classified points. These results represent the average performance of the models created during cross-validation. However, it is also desirable to identify a single set of feature weights, since these weights can provide information about each feature's predictive power. To identify a single set of feature weights, we trained new MPT- and MPT+ models without cross-validation, using all the training data. The resulting odds ratios (given by \(e^{\beta}\), where \(\beta\) is the feature weight) are listed in Tables 2 and 3. These normalized odds ratios for each feature indicate the change in the probability of discharge when values for that feature increase by one standard deviation. An odds ratio farther from 1 indicates that a feature makes a greater contribution to the classification decision. \begin{table}
\begin{tabular}{l l r r} \hline \hline
**Feature** & **Task** & **Effect Size (MIC)** & **Effect Size (ACC)** \\ \hline Total phrase duration & Rainbow Passage & \(-0.50\) & \(-0.33\) \\ Total phrase duration & 2 nd passage & \(-0.50\) & \(-0.22\) \\ Phonation time & Max phonation & 0.49 & 0.45 \\ F0 mean & Vowel & 0.35 & 0.35 \\ CPP SD & Sentences & \(-0.27\) & \(-0.30\) \\ CPP mean & Sentences & \(-0.25\) & \(-0.31\) \\ CPP median & Sentences & \(-0.22\) & \(-0.28\) \\ CPP median & Vowel & 0.21 & \(-0.018\) \\ CPP SD & Vowel & \(-0.17\) & \(-0.29\) \\ CPP mean & Vowel & 0.17 & \(-0.036\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Effect size (paired Cohen’s d) for selected features computed from the acoustic microphone (MIC) and neck-surface accelerometer (ACC) from the given speech tasks, sorted in decreasing order of MIC-based effect size magnitude. Figure 2: Confusion matrices and optimized lambda values (\(\lambda\)) for the microphone-based and accelerometer-based models without (MPT\(-\)) and with (MPT+) the maximum phonation task.