This section describes the modeling of the perceived sociolinguistic variation. The 12 nor- malization procedures were evaluated on how well they model the Height, Advancement, and Rounding judgments within each vowel category. The analyses were carried out on the mean
67All analyses described in this section were repeated for the seven individual phonetically-trained listeners. The
results for these analyses showed the same pattern, i.e., the highest scores forLOBANOV’s procedure, followed by GERSTMANandCLIHi4.
values for the seven phonetically-trained listeners, as was done in the previous section. The sociolinguistic variation was modeled to be able to describe differences between realizations of vowel tokens belonging to the same vowel category (for instance the differences in the perceived tongue height of /I/ between a male and a female speaker from the N-R region in the Netherlands).
9.4.1
Models for baseline data
The first step was to calculate the models for the raw data per vowel category. A series of linear regression analyses was carried out withF0,F1,F2, andF3 in Hz as the predictor variables, using Height, Advancement, and Rounding, respectively, as the criterion variables. Table 9.11 lists the values ofR2×100per vowel. It can be observed that overall the values forR2×100are considerably lower than the percentages that were found when the analyses were carried out across vowels (see Table 9.5). In addition, some vowel categories show no significant predictors (/E/, /O/, and /y/), or only significant predictors for one of the three variables. Furthermore, the significant predictors do not show the same pattern as was found for the models of phonemic variation, which showed thatF1was generally the most relevant predictor for Height and that F2 was the dominant predictor for both Advancement and Rounding. Here, no such pattern can be observed; for instance,F0is the dominant predictor for Rounding and Advancement for /i/,F1is the most relevant predictor for Rounding for /u/. No such patterns were observed for the comparisons across vowels (i.e., for the phonemic variation).
Table 9.11: R2×100%for the baseline data for Height, Advancement, and Rounding with the acoustic variablesF0,F1,F2, andF3as predictor variables per vowel category. Only values significantly different from zero at the p<0.01 level are given.
R2×100 Height Advancement Rounding
/
A
/ - 49 (F2,F3) 21 (F2) /a
/ - 60 (F2,F0) - /E
/ - - - /I
/ 64 (F0) - - /i
/ - 23 (F0) 65 (F0,F1) /O
/ - - - /u
/ - 62 (F2,F1) 35 (F1) /Y
/ 60 (F1,F0,F2) - - /y
// - - -9.4.2
Models for normalized data
This section discusses the results for the sociolinguistic models (within vowel categories) for all normalization procedures. For each procedure, linear regression analyses were carried out for each vowel separately, using Height, Advancement, and Rounding as criterion variables and the transformed acoustic variables as predictor variables.
However, not all results are presented here. When the results of the normalization pro- cedures were investigated, a pattern similar to the baseline data (Table 9.11) was observed: relatively low scores forR2, and for some vowels no models could be created. Furthermore, the most important predictors for each vowel category were not the same as the ones found for the phonemic comparisons (across vowels); no systematic pattern could be observed in the relevant acoustic predictors per vowel. Instead, for each vowel, a different pattern was found (e.g., /A/ showed different predictors than /Y/) as well as across normalization proce- dures (e.g., Height’s dominant (and only) predictor variable for /I/ isF0forNORDSTROM¨ & LINDBLOMandF1forCLIHs4).
An example is provided by showing the results for two normalization procedures that show patterns that were exemplary for those found across the results for all procedures. Tables 9.12 and 9.13 show the results forLOG, one of the vowel-intrinsic/formant-intrinsic procedures, and forCLIHs4, one of the vowel-extrinsic/formant-extrinsic procedure, respec- tively68.
Table 9.12: R2×100% for the LRAs for Height, Advancement, and Rounding with the acoustic variables transformed toLOGas predictor variables per vowel category.
R2×100 Height Advancement Rounding
/
A
/ - 50 (DL 3,DL2) - /a
/ - 64 (DL 2,DL0) - /E
/ - - - /I
/ 60 (DL 0) 57 (DL0) - /i
/ - 59 (DL 0,DL1) /O
/ - 43 (DL 2,DL1) - /u
/ - 0.61 (DL 2,DL1) 36 (DL1) /Y
/ 45 (DL 1,DL0) - - /y
/ - - -68The results forCLIHs4are in fact the most interpretable of all normalization procedures; for the majority of the
Table 9.13: R2×100% for the LRAs for Height, Advancement, and Rounding with the acoustic variables transformed toCLIHs4as predictor variables per vowel category.
R2×100
Height Advancement Rounding
/
A
/ - 50 (Dclihs4 2 ),D3clihs4) - /a
/ - 38 (F2) - /E
/ 33 (Dclihs4 1 ) 38 (D1clihs4) - /I
/ 40 (Dclihs4 10 ) 54 (D0clihs4) - /i
/ - - 51 (Dclihs4 1 ) /O
/ 46 (Dclihs42 ) 56 (Dclihs42 ,Dclihs41 ) 41 (Dclihs42 )
/
u
/ - - -/
Y
/ 41 (F1) - -/
y
/ - - -No systematic significant differences were found between the 12 normalization procedures, grouped into the four classes of procedures. Still, some general observations across classes could be made. First, it appeared that none of the procedures produced data that allowed more vowel categories to be modeled through linear regression analysis than the raw baseline data. Second, there appeared to be an inverse relationship between the success of the procedure in modeling phonemic variation and the number of vowels that could be modeled; if the procedure modeled phonemic variation very well (e.g.,LOBANOV) then the number of vowel categories that could be modeled was low (forLOBANOV, only two vowel categories could be modeled). If the procedure performed poorly on modeling phonemic category variation, then the number of categories that could be modeled was high (forSYRDAL&GOPALsignificant predictors could be found for seven out of nine vowel categories), although the number of categories that could be modeled was never higher than those for the baseline.
To establish whether the data contained variation that could be modeled systematically, the perceptual data was pooled across the (intended) vowel categories and the LRAs were run again. This time, the data for the 180 vowel tokens for Height, Advancement, and Rounding were corrected for their respective vowel. This was done as follows, first the mean Height, Advancement, and Rounding per vowel category was calculated. Second, this mean value was subtracted from every vowel token in that vowel category. This process was repeated for all nine vowel categories. This way only the within-vowel (sociolinguistic) variation remained in the data. This was done to be able to use all data and to remove as much between-vowel (phonemic) variation as possible, so that only the sociolinguistic variance would remain. If listeners use the dimensions Height, Advancement, and Rounding systematically, they should have do so in the same way within and between vowels. The results for these LRAs are shown in Table 9.14.
Table 9.14:R2×100%for Height, Advancement, and Rounding, corrected for each vowel category’s mean value, with the transformed acoustic variables D0, D1, D2, and D3 as predictor variables. Only values significantly different from zero at p<0.001 were included. For each percent, the corresponding significant predictor variable(s) is/are listed between brackets.S&Grefers toSYRDAL&GOPALandN&Lrefers toNORDSTROM¨ &LINDBLOM.
R2×100 Height Advancement Rounding HZ 6 (F0) 17 (F2,F1) 3 (F0) LOG 6 (D0) 18 (D2,D1) 3 (D3) BARK 6 (D0) 15 (D2) 3 (D3) MEL 6 (D0) 18 (D2,D1) 3 (D0) ERB 6 (D0) 18 (D2,D1) 3 (D3) S&G - 16 (D2,D1) - GERSTMAN - 14 (D2,D1) - LOBANOV - 13 (D2,D1) - CLIHi4 7 (D0) 15 (D2,D1) - CLIHs4 - 13 (D2,D1) - MILLER - 18 (D3,D1) - N&L 7 (D0) 17 (D2,D1) -
In Table 9.14, it is easier to observe a pattern in the results than for the individual vowels. The results for Advancement are almost identical across normalization procedures. Overall, between 13% and 18% in the variation in the data for Advancement could be explained using D2 and D1. However, for Height and Rounding the results are less univocal, for Height only 6% can be predicted using D0. D0 andD3 appear to be the only variables that can account for (very little of) the variance in Rounding. Furthermore, none of the procedures performed better than the baseline. The vowel-extrinsic/formant-intrinsic and the vowel-intrinsic-formant-extrinsic procedures do not appear to model Height or Rounding at all. Although Table 9.14 shows a more systematic pattern than was found in Table 9.11, the results are still lower than, and not as systematic as, the results for the models for the phonemic variation. However, overall, F2 or D2 andF1 or D1 were the most relevant predictor variables, a pattern consistent with that found for most of the phonemic models in section 9.3. Nevertheless, in Table 9.14 for Height (and in some cases for Rounding as well), it was generally found thatF0 orD0was the most relevant predictor. Generally,D0
showed the smallest coefficients of all significant predictors (or it was not significant at all, as was found for the phonemic model for CLIHi4). In sum, given the results presented in this section, it must be concluded that the perceived sociolinguistic variation could not be modeled satisfactorily69.