## 2 Materials and Methods
### Laboratory Data Analysis
#### 2.3.4 Ps Estimation Method 3: Multiple Linear Regression Model  
The third method of Ps estimation expands the simple linear regression model in Method 2 to incorporate multiple voice production measures. The multiple linear regression model was designed to take into account non-modal phonatory effects, which prior work demonstrated increases the accuracy for estimating Ps in individuals with a typical voice [44]. The current study extends on that work by investigating whether the multiple linear regression model increases Ps estimation accuracy in patients with voice disorders as well. The ACC-based glottal airflow waveforms were obtained using subglottal impedance-based inverse filtering (IBIF), which was applied to each vowel segment [50]. The average level of the oral airflow signal was subtracted since the ACC signal was a zero-mean (AC) signal. Five IBIF model parameters were estimated for each subject: skin inertance, skin resistance, skin stiffness, tracheal length, and accelerometer position. IBIF model properties were obtained using particle swarm optimization [50; 96]. For laboratory data analysis, IBIF model estimation was optimized for each vowel segment. Vowel segments with IBIF measures that were outside the physiologically relevant ranges were not included in the multiple regression (ACFL < 1 mL/s, MFDR < 1 L/s\({}^{2}\), and QQ outside of 0-100% range); in addition, vowels with \(f_{\rm o}\) > 500 Hz due to the known limitation of glottal inverse filtering at high values of \(f_{\rm o}\). Table 2 lists the ten ACC-based vocal function measures input into the multiple linear regression model. This set of measures was computed from each vowel segment (including all vowel types and pitch conditions) to minimize the error in predicting Ps from the ACC signal given the presence and degree of different vocal modes and pathological glottal conditions. Figure 3 illustrates the parameterization of the original ACC and inverse-filtered signal to yield the set of ten vocal function measures. The first three measures (RMS, \(f_{\rm o}\), and CPP [56]) are computed directly from the raw ACC signal (Figure 3A). The rest of the seven measures are computed from the glottal airflow waveform (Figure 3B): AC flow amplitude (ACFL), maximum flow declination rate (MFDR), open quotient (OQ),  
speed quotient (SQ), spectral tilt (H1-H2), harmonic richness factor (HRF), and normalized amplitude quotient (NAQ). The ten measures were input as dependent variables into a stepwise linear regression model with the reference Ps value per vowel segment as the independent variable. The stepwise regression model was described in detail in prior work [44]. Briefly, a screening step was included to determine whether each measure was sufficiently useful for inclusion into the regression model; the \(p\)-value of an F-statistic was computed to screen whether the additional measure contributed significantly to model prediction. The regression model was evaluated per study participant using five-fold cross-validation; i.e., training sets comprised 80% of the vowel segments and test sets comprised 20% of the remaining vowel segments (no overlap). The fold exhibiting the lowest root-mean-square error (RMSE) for the test set was selected for comparison with the other Ps estimation methods.