Cognitive control and the degree to which bilingual speakers participate in ongoing sound changes

  • Berry (2018) studied the bilingual Puerto Rican community of Philadelphia, PA. The goal was to gain insight into the degree to which Spanish-English bilingual speakers participate in ongoing sound changes in English and how cognitive control contributes to this
  • Cognitive control is a concept proposed by Braver (2012) in his dual-mechanisms framework:
    • Cognitive control is defined as: “the ability to regulate thoughts and actions in accordance with internally represented behavioral goals” (Braver, 2012)
    • It is composed of two mechanisms:
      • Proactive control is defined as: “the sustained and anticipatory maintenance of goal-relevant information […] to enable optimal cognitive performance.” (Braver, 2012)
      • Reactive control is defined as: “Transient, stimulus-driven goal reactivation […] based on interference demands or episodic associations.” (Braver, 2012)
  • Here we will only consider Berry’s (2018) dataset on a phonological phenomenon called Canadian Raising(e.g., about is pronounced somewhat like aboot)
  • The dataset contains a selection of the following columns:
    • norm_F1: The frequency value of the F1 vowel formant, the frequency created by resonance in the laryngeal cavity. Lower values indicate a higher level of vowel raising (Woolums, 2012)
    • Proactive: Did the situation require weaker or stronger Proactive control?
    • Reactive: Did the situation require weaker or stronger reactive control?
    • Style: Read (reading experiment) or Conversational (Sociolinguistic interview)
    • BirthYear: Year of birth of the participant
    • Sex: Sex of the participant
    • PartnerEthnicity: Ethnicity of the participant’s partner
    • PhillyLiveTime: Amount of time the participant has lived in Philadelphia
    • HighSchoolType: The type of high school the participant attended
    • Occupation_Group: The particpant’s occupational category
    • wordLength: The length of the word, in characters

1. Loading and exploring the data

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2. Getting to know the data: the dependent variable norm_F1

2.1 Central tendency

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2.2 Dispersion

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3. Getting to know the data: Proactive

3.1 Counts

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4. Getting to know the data: Reactive

4.1 Counts

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5. Getting to know the data: Style

5.1 Counts

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6. Getting to know the data: BirthYear

6.1 Central tendency

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6.2 Dispersion

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7. Getting to know the data: Sex

7.1 Counts

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8. Getting to know the data: PartnerEthnicity

8.1 Counts

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9. Getting to know the data: PhillyLiveTime

9.1 Counts

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10. Getting to know the data: HighSchoolType

10.1 Counts

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11. Getting to know the data: Occupation_Group

11.1 Counts

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12. Getting to know the data: wordLength

12.1 Central tendency

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12.2 Dispersion

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13. Removing outliers

  • Our previous exercises have shown that there are outliers in our dependent norm_F1 variable. Let’s remove them!
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14. Exploring the relationships between the dependent variable and the independent variables

  • We should perform pairwise plotting and correlation tests to see if the numeric independent variables are linearly related to the dependent variable and how strong their correlations are.

14.1 BirthYear vs norm_F1

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14.2 wordLength vs norm_F1

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15. Exploring the relationships between the independent variables

  • At this point we should perform pairwise cor.test, chisq.test and assocstats tests to search for correlations and associations between our independent variables.
  • In previous classes, we have done this all by hand, but this takes a horrible lot of time!
  • With some programming, we can automate the tests so we only have to interpret them
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16. Scouting for interactions: BirthYear vs norm_F1, by the other variables

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17. Scouting for interactions: wordLength vs norm_F1, by the other variables

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18. Scouting for interactions: Proactive vs norm_F1, by the other variables

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19. Scouting for interactions: Reactive vs norm_F1, by the other variables

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20. Scouting for interactions: Style vs norm_F1, by the other variables

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21. Scouting for interactions: Sex vs norm_F1, by the other variables

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22. Scouting for interactions: PartnerEthnicity vs norm_F1, by the other variables

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23. Scouting for interactions: PhillyLiveTime vs norm_F1, by the other variables

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24. Scouting for interactions: HighSchoolType vs norm_F1, by the other variables

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25. Deciding on our contrasts

  • Our work here is corpus-based, so sum constrasts make more sense than treatment contrast. Let’s go ahead and specify sum contrasts.
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26. Fitting an initial model to validate the assumptions

  • Recall that these are our assumptions:
  • There are no outliers/overly influential observations
  • The relationships are linear
  • There is no multicollinearity
  • The observations are independent from one another (there is no autocorrelation)
  • The residuals are not autocorrelated
  • The variability of the residuals does not increase or decrease with the explanatory variables or the response (i.e., there is no heteroskedasticity)
  • The residuals follow the normal distribution. This is less important if the sample size is large

26.1 There is no multicollinearity

  • With so many interactions in our model and given that there were quite a few strongly correlated variables, the first thing we should check for is multicollinearity
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26.2 There are no overly influential observations

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26.3 There is no heteroskedasticity

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26.5 The relationships are linear

  • To find out if the relationships are linear, we have to simplify our model a little bit as the crPlot in the car package does not work when there’s interactions.
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26.6 The residuals and the observations are not autocorrelated

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26.7 The residuals are normally distributed

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27. Towards a parsimonious model

  • At this point, we have checked all of our model assumptions. This has shown that our model meets all of these, except the one that refers to the autocorrelation of the residuals
  • Now it is time to apply Occam’s razor to the model to see if there are any superfluous predictors in there
  • Recall that we should look for predictors that have tiny effect sizes and are not significant
  • We should start with interactions and then move on to the main effects if necessary
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27.1 Towards a parsimonious model: Dropping Proactive * Reactive

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

27.2 Towards a parsimonious model: Dropping Proactive * Sex

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

27.3 Towards a parsimonious model: Dropping Proactive * HighSchoolType

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27.4 Towards a parsimonious model: Dropping Occupation_Group

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27.5 Towards a parsimonious model: Dropping BirthYear

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28. Bootstrap validation

  • We have validated our assumptions and we have checked to see if we could exclude some predictors that may be superfluous
  • Now it is time to check if our coefficients are numerically stable and generalize to the population beyond the sample
  • If we find coefficients with large confidence intervals, it may be a good idea to delete the predictors associated with those coefficients
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29. Interpreting the model

  • Now it is time to remove the coefficients that did not turn out to be stable under bootstrap validation
  • Afterwards, we can interpret our model
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Acknowledgements

A Big Thank You! goes to Grant M. Berry (Penn State), who generously provided the data for this exercise

References

  • Berry, G. M. (2018). Liminal voices, central constraints: Minority adoption of majority sound change. State College: Penn State University PhD Dissertation.
  • Braver, T. S. (2012). The variable nature of cognitive control: A dual-mechanisms framework. Trends in Cognitive Science, 16(2). 106–113.
  • Woolums, N. (2012). Phonetic manifestations of /ai/ raising. Linguistic Portfolios. Article 19.

© 2018 Jeroen Claes