## 3 Experiment 2: F0 Range Estimation from a Bilingual Parallel Corpus
### Results and Discussion  
The results of estimates from the bilingual parallel speech corpus using the refined spectrum-based model and direct F0 analysis are compared in Table 2. Both the means and the standard deviations of the estimates over all speakers are shown. A comparison between DFA-J and DFA-C indicates that these speakers used different surface F0 ranges in their Japanese and Chinese speech. Linear mixed effect regression (LMER) models were used to compare the estimations from DFA-J and DFA-C (LMER syntax (taking ceiling as an example): predicted_ceiling \(\sim\) Language + (1! speaker). Significant level: 95% (for all LMER models in this study)). Results showed that both ceiling and mean F0 were significantly higher in the L1 Japanese utterances than in the L2 Mandarin utterances (ceiling: _estimate_ = 0.028, \(SE\) = 0.012, \(p\) = 0.036; mean: _estimate_ = 0.027, \(SE\) = 0.008, \(p\) = 0.003), while the difference in the floor F0 was marginally significant (_estimate_ = 0.012, \(SE\) = 0.006, \(p\) = 0.06). This finding coincides with the reports in previous studies on that bilinguals often show narrower SF0 ranges in their L2 [46, 47]. In contrast, LMER models on SBM-J and SBM-C showed that there was no significant difference in any of the three F0 parameters: mean (_estimate_ = 0.007, \(SE\) = 0.004, \(p\) = 0.147), ceiling (_estimate_ = 0.006, \(SE\) = 0.004, \(p\) = 0.18), and floor (_estimate_ = 0.008, \(SE\) = 0.005, \(p\) = 0.111). These results suggest that the estimation from the spectrum-based model is independent of the language being spoken, whether it is L1 Japanese or L2 Chinese. We further examined whether the two methods statistically differ in terms of the independence of the speech content, using another LMER model. For both methods and for each speaker, we calculated the estimation differences from their L1 and L2 speech. The estimation difference was the response in the MLER model and _Method_ was used as the predictor (LMER syntax (taking ceiling as an example): ceiling_difference\(\sim\)Method + (1! speaker)). Results revealed that the SBM showed significantly smaller estimation differences from L1 and L2 speech inputs on ceiling (_estimate_ = -0.435, \(SE\) = 0.137, \(p\) = 0.006) and mean (_estimate_ = -0.446, \(SE\) = 0.124, \(p\) = 0.002) parameters, than the DFA method. The estimation difference on parameter floor was non-significant (_estimate_ = -0.049, \(SE\) = 0.123, \(p\) = 0.696). Overall these results indicated that SBM is less affected by the speech content than DFA in estimating a speaker's F0 range. Moreover, the results of the refined model for each of the 18 speakers are shown in Figure 3, where for most individuals the estimates from the L1 Japanese utterances (in dots) and from the L2 Chinese utterances (in triangles) are both close to the actual values (in black bars). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **DFA-JC (Taken as the Actual Value)** & **SBM-J** & **SBM-C** & **DFA-J** & **DFA-C** \\ \hline Ceiling & 2.410 (0.12) & 2.387 (0.09) & 2.380 (0.09) & 2.402 (0.12) & 2.374 (0.13) \\ Mean & 2.243 (0.12) & 2.206 (0.08) & 2.199 (0.09) & 2.256 (0.12) & 2.229 (0.12) \\ Floor & 2.084 (0.13) & 2.056 (0.08) & 2.048 (0.08) & 2.100 (0.13) & 2.088 (0.13) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Means and standard deviations (in parentheses) of F0 range parameters (in the logarithmic scale) estimated from the Japanese-Chinese parallel speech corpus. SBM-J and SBM-C represent the results of the refined spectrum-based model estimated from the 20 Japanese utterances and from the 20 Chinese utterances, respectively. DFA-J and DFA-C indicate the results of direct F0 analysis from the Japanese and Chinese utterances, respectively, while DFA-J indicates the result of direct F0 analysis from all 40 utterances, which is here regarded as the actual value of the underlying F0 range. Figure 3 also shows that the estimates are more accurate in male than in female speakers.