9.3 Modeling perceived phonemic variation
9.3.3 Models for normalized data
The remaining 11 normalization procedures (12 minus HZ, the baseline procedure) were carried out on the raw acoustic data. This process was identical to the process described in Chapter 7, the only difference is that this time the procedures were applied to a subset of the database used in Chapter 7.
Because the procedures were applied to different sets of vowel data than was the case in Chapter 7, some of the scale factors that were used by the procedures were re-calculated. The scale factors used in the two vowel-extrinsic/formant-extrinsic procedures,NORDSTROM¨ & LINDBLOM and MILLER were set as follows. The scale factor k in equation (2.13) was calculated as described in section (2.4.4) and set to 0.91 based on the values for the 20 speakers. MILLER scale factor k in equation (2.14) was set to 185.66 Hz, the geometric mean ofµF0 for the 10 female speakers (230.30 Hz) and for the 10 male speakers (149.68 Hz).
For each of the 11 procedures, three LRAs were carried out. In each of these LRAs, the four transformed acoustic variables (D0,D1,D2, andD3) were stepwise entered as predictor variables, with either the mean Height values, Advancement values, or the Rounding values as criterion. Again, only the significant (p <0.01) predictor variables are used in the final models.
Vowel-intrinsic/formant-intrinsic procedures
Table 9.6 showsR2×100from the LRAs on the scale transformations. It can be observed that the portions of explained variance (R2×100) do not differ considerably from the baseline. The highest portion explained variance for all three criterion variables is observed forERB. Compared with the baseline, the values are 4% higher for Height, 3% higher for Advance- ment, while for Rounding a deterioration can be observed: 2% lower than the baseline. In addition, no great differences can be observed between the four vowel-intrinsic/formant- intrinsic procedures.
The regression models for Height, Advancement, and Rounding for the LOG-transformed data are displayed in the equations in (9.2).
Height = −0.88DL 1 +0.26D2L −0.14DL3 Advancement = 0.29DL 1 −0.91D2L +0.11DL3 Rounding = 0.21DL 0 −0.33D1L −0.64D2L −0.16DL3 (9.2)
The regression models for acoustic data transformed toBARKare displayed in the equations in (9.3).
Table 9.6: R2×100 for the linear regression analyses for the three perceptual criterion variables Height, Advancement, and Rounding with the acoustic variablesD0,D1,D2, and
D3as predictor variables, normalized toLOG,BARK,ERB, andMEL, respectively.
R2×100 Height Advancement Rounding
HZ 82 88 61 LOG 86 90 58 BARK 85 91 59 ERB 86 91 59 MEL 85 90 59 Height = 0.17DB 0 −0.84D1B +0.25DB2 −0.065DB3 Advancement = 0.27DB 1 −0.91DB2 +0.12DB3 Rounding = 0.22DB 0 −0.34D1B −0.65DB2 −0.16DB3 (9.3)
The regression models for acoustic data transformed toERBare displayed in the equations in (9.4).
Height = 0.14DE0 −0.88D1E +0.25D2E
Advancement = 0.27D1E −0.91D2E +0.12DE3
Rounding = 0.21DE0 −0.34D1E −0.65D2E −0.15DE3
(9.4)
The regression models for acoustic data transformed toMELare displayed in the equations in (9.5). Height = 0.15DM 0 −0.86D1M +0.25D2M Advancement = 0.25DM 1 −0.91D2M +0.14DM3 Rounding = 0.22DM 0 −0.35D1M −0.66D2M −0.15DM3 (9.5)
The following general observations can be made about these sets of regression models. First, the models show patterns similar to those found for the baseline data: Height’s primary predictor isD1, Advancement can be modeled primarily byD2, andD2served as the most relevant predictor for Rounding. However, these models differ from the baseline models in thatD3plays a (small) role in the explained variance for Rounding; for all four procedures
Vowel-intrinsic/formant-extrinsic procedures
The resulting values ofR2×100 from the LRAs on the data transformed followingSYRDAL &GOPALare displayed in Table 9.7. Here, it can be observed that the value ofR2×100 for SYRDAL & GOPALis higher than the baseline values for Height (2% higher than the raw data). However, the values show a deterioration compared to the baseline: 1% lower for Advancement and 15% lower for Rounding. The corresponding regression models for acoustic data transformed withSYRDAL&GOPALare displayed in the equations in (9.6).
Table 9.7: R2×100 for the linear regression analyses for the three perceptual criterion variables Height, Advancement, and Rounding with the acoustic variablesD0,D1,D2, and
D3as predictor variables, normalized followingSYRDAL&GOPAL.
R2×100 Height Advancement Rounding
HZ 82 88 61
SYRDAL&GOPAL 84 87 46
Height =−0.85D1s&g−0.25D s&g 2 Advancement =−0.22D1s&g+ 0.88D s&g 2 Rounding =−0.44D1s&g+ 0.58D s&g 2 (9.6)
In the equations in (9.6), it can be observed that both dimensions are included in the models for Height, Advancement, and Rounding.Ds&g
1 was found to correspond primarily to Height, whileDs&g2 could be used to model Advancement. For Rounding, the difference between the
βcoefficients is smaller than for Height and Advancement,Ds&g
1 shows a larger coefficient thanDs&g2 .
Vowel-extrinsic/formant-intrinsic procedures
A total of nine LRAs was carried out to obtain the results for the three vowel-extrinsic/for- mant-intrinsic procedures. Table 9.8 shows the results forGERSTMAN,LOBANOV, andCLIH-
i4. In this table, it can be seen that the explained variance is considerably higher for the vowel- extrinsic/formant-intrinsic procedures than for the baseline. The highest portion explained variance for all three criterion variables can be observed for LOBANOV. Compared with Table 9.5, the values are 7% higher for Height, 3% higher for Advancement, and the largest improvement, 11% was obtained for Rounding.
The regression models for acoustic data transformed usingLOBANOV are displayed in the equations in (9.7).
Table 9.8: R2for the linear regression analyses for the three perceptual criterion variables Height, Advancement, and Rounding with the acoustic variablesD0,D1, D2, andD3 as predictor variables, normalized followingGERSTMAN,LOBANOV, andCLIHs4.
R2×100 Height Advancement Rounding
HZ 82 88 61 GERSTMAN 88 90 70 LOBANOV 89 91 72 CLIHi4 88 91 65 Height = −0.82Dlobanov 1 +0.24D2lobanov −0.14Dlobanov3 Advancement = 0.17Dlobanov 1 −0.91D2lobanov +0.12Dlobanov3
Rounding = −0.45Dlobanov1 −0.70D2lobanov −0.28Dlobanov3
(9.7)
The regression models for acoustic data transformed followingGERSTMANare displayed in the equations in (9.8). Height = −0.84Dgerstman1 +0.24D gerstman 2 −0.16D gerstman 3 Advancement = 0.17Dgerstman1 −0.90D gerstman 2 +0.11D gerstman 3 Rounding = −0.44Dgerstman1 −0.69D gerstman 2 −0.28D gerstman 3 (9.8)
The regression models for acoustic data transformed followingCLIHi4are displayed in the equations in (9.9). Height = −0.88Dclihi4 1 +0.24Dclihi42 −0.09Dclihi43 Advancement = −0.90Dclihi4 2 +0.28Dclihi43 Rounding = −0.36Dclihi4 1 −0.66Dclihi42 −0.29Dclihi43 (9.9)
In these nine regression models, the same pattern can be observed in results for the baseline data and for the vowel-intrinsic/formant-intrinsic models: Height’s primary predictor isD1, whileD2is the most important predictor for Advancement and for Rounding. A difference between the baseline model for Rounding and the models for the vowel-extrinsic/formant- intrinsic procedures for Rounding, is thatD3contributes significantly for the vowel-extrin- sic/formant-intrinsic models, however it was never the dominant cue. Finally, the role ofD0 appears to be nonexistent in the vowel-extrinsic/formant-intrinsic models.
Vowel-extrinsic/formant-extrinsic procedures
A total of nine LRAs was carried out to obtain the results for the three vowel-extrinsic/for- mant-intrinsic procedures. The results forMILLER,NORDSTROM¨ &LINDBLOM, andCLIHs4 are displayed in Table 9.9.
Table 9.9: R2×100 for the linear regression analyses for the three perceptual criterion variables Height, Advancement, and Rounding with the acoustic variablesD0,D1,D2, and
D3as predictor variables, normalized followingMILLER,NORDSTROM¨ &LINDBLOM, and CLIHs4.
R2×100 Height Advancement Rounding
HZ 82 88 61
MILLER 85 91 46
NORDSTROM¨ &LINDBLOM 84 89 62
CLIHs4 87 91 60
Table 9.9 shows that the explained variance for Height and Rounding for the vowel-ex- trinsic/formant-extrinsic procedures is lower than for the vowel-extrinsic/ formant-intrinsic procedures, for Advancement, the performance is about equal. MILLERshows a very low value for Rounding (46%). Of the three procedures,CLIHs4has the highest scores for Height and Advancement, whereas for Rounding the value is slightly below the value for Rounding for NORDSTROM¨ & LINDBLOM and HZ. Nevertheless, the performance for CLIHs4 was considerably poorer than the performance ofCLIHi4.
The regression models for acoustic data transformed to MILLER are displayed in the equations in (9.10). Height = −0.58Dmiller 1 +0.41Dmiller2 Advancement = −0.35Dmiller 0 −0.88Dmiller2 +0.31D3miller Rounding = −0.43Dmiller 1 +0.56Dmiller2 (9.10)
In equation (9.10), it can be observed thatD1milleris the most relevant contributor for Height (−0.58), followed byDmiller
2 (0.41). For Rounding, onlyDmiller1 andDmiller2 contributes signifi- cantly (−0.43and−0.88, respectively). For Advancement, all three ofMILLER’s dimensions contribute significantly (−0.35,−0.88, and 0.31, respectively). For Rounding, again only
Dmiller
1 ,D2millercontributes significantly (−0.43 and 0.56 respectively).
The regression models for acoustic data transformed toNORDSTROM¨ &LINDBLOMare displayed in formula (9.11).
Height = 0.11D0n&l −0.80D1n&l +0.25D2n&l −0.10Dn&l3
Advancement = 0.18D1n&l −0.90D2n&l +0.14Dn&l3
Rounding = −0.43Dn&l
1 −0.68D2n&l −0.14Dn&l3
(9.11)
ForNORDSTROM¨ &LINDBLOM’s results, the pattern is as follows. For HeightDn&l1 is the dominant predictor (−0.80), followed byDn&l
2 (0.25),D0n&l(0.11), and finallyDn&l3 (0.10). For Advancement, three out of four predictors were significant, whereDn&l
2 is dominant (−0.90), followed by Dn&l
1 (0.18), and Dn&l3 (0.14). For Rounding, three predictors were contributed significantly,Dn&l
2 is dominant (−0.68), followed byDn&l1 (−0.43),Dn&l3 (0.14). The regression models for acoustic data transformed with CLIHs4 are displayed in the equations in (9.12). Height = −0.88Dclihs4 1 +0.25Dclihs42 −0.07D3clihs4 Advancement = 0.08Dclihs4 0 0.27Dclihs41 −0.90Dclihs42 Rounding = −0.18Dclihs4
0 −0.41Dclihs41 −0.64Dclihs42 −0.25D3clihs4
(9.12)
ForCLIHs4, Height’s dominant predictor isDclihs41 (−0.88), followed byD2clihs4(0.25). Ad- vancement and Rounding’s dominant predictor isDclihs4
2 (0.27 and 0.64, respectively). Com- pared with the models forCLIHi4(9.9), the models show the following differences.Dclihi40 is not significant for Advancement or Rounding forCLIHi4, andDclihs40 contributes significantly to the model forCLIHs4for Advancement and Rounding. In addition, for Height,Dclihi41 does not contribute significantly to the model forCLIHi4, whileD1clihs4contributes significantly to the model forCLIHs4. Finally, for Advancement,Dclihi43 contributes significantly to the model forCLIHi4, whileDclihs43 does not contribute significantly to the model forCLIHs4.
9.3.4
Summary
Table 9.10 shows an overview of the values ofR2×100for all 12 procedures, for the three criterion variables Height, Advancement, and Rounding. These results were presented earlier throughout section 9.3.3. Overall, these results show that the perceived phonemic variation in the three criterion variables could be modeled satisfactorily; the percentages explained variance are between 82% and 89% for Height, between 87% and 91% for Advancement, and between 46% and 72% for Rounding. It can further be observed that applying the normalization procedures to the raw acoustic data generally improved the fit between the acoustic data and the articulatory perceptual data; nine out of 11 procedures performed better than the baseline (HZ).LOBANOV’s procedure shows the highest scores.SYRDAL&GOPAL’s procedure performed poorer than the baseline, although only for Rounding and Advancement. MILLERperformed poorer than the baseline as well, but only for Rounding.
Table 9.10:R2×100%for all 12 procedures for the linear regression analyses for the three perceptual criterion variables Height, Advancement, and Rounding with the transformed acoustic variables F0, F1, F2, and F3 as predictor variables. S & Grefers to SYRDAL &GOPALandN&Lrefers toNORDSTROM¨ &LINDBLOM.
R2×100 Height Advancement Rounding Mean Ranking
HZ 82 88 61 77 10 LOG 86 90 58 78 7.5 BARK 85 91 59 78 7.5 MEL 85 90 59 78 7.5 ERB 86 91 59 79 4.5 S&G 84 87 46 72 12 GERSTMAN 88 90 70 83 2 LOBANOV 89 91 72 84 1 CLIHi4 88 91 65 81 3 CLIHs4 88 91 60 79 4.5 MILLER 85 91 46 74 11 N&L 84 89 62 78 7.5
When the scores for the different classes of normalization procedures are compared, it is clear that the vowel-extrinsic/formant-intrinsic procedures performed best: LOBANOVranks first in Table 9.10, GERSTMANranks second, and CLIHi4 ranks third. Furthermore, the vowel- intrinsic/formant-intrinsic procedures performed second best:LOG,BARK,MEL, andERBall rank 6.5th, followed by the vowel-extrinsic/formant-extrinsic procedures:CLIH
s4ranks 4.5th, NORDSTROM¨ &LINDBLOMranks 7.5th, andMILLERranks 11th. The vowel-intrinsic/formant-
extrinsic procedure performed poorest:SYRDAL&GOPALranks 12th.67