1. Intra-individual variability in early child language Representing and testing variability and variability change Paul van Geert University of Groningen Representing and testing variability and variability change Paul van Geert University of Groningen

2. intra-individual variability in early child language 2 Why variability … and how? Variability may provide information about underlying developmental processes Emergence of new forms How to specify variability How to specify eventual changes in variability? Variability may provide information about underlying developmental processes Emergence of new forms How to specify variability How to specify eventual changes in variability?

3. intra-individual variability in early child language 3 Spatial Prepositions (1 of 6) 4 sets of data Prepositions used productively in a spatial- referential context Why language? Categorical nature: preposition or not Relatively easy to observe and interpret High sampling frequency possible Prepositions used productively in a spatial- referential context Why language? Categorical nature: preposition or not Relatively easy to observe and interpret High sampling frequency possible

4. intra-individual variability in early child language 4 Spatial Prepositions (2 of 6)

5. intra-individual variability in early child language 5 Spatial Prepositions (3 of 6)

6. intra-individual variability in early child language 6 Spatial Prepositions (4 of 6)

7. intra-individual variability in early child language 7 Spatial Prepositions (5 of 6)

8. intra-individual variability in early child language 8 Representing variability (1 of 6) Plotting distances between consecutive values Plotting extremes: Max-Min methods Smoothing (denoising) and calculating residuals Plotting distances between consecutive values Plotting extremes: Max-Min methods Smoothing (denoising) and calculating residuals

9. intra-individual variability in early child language 9 Distance method Take absolute differences between any two consecutive observations See Excel file Suppose we would want to know whether the decrease in variability is statistically significant… Permutation method See Excel file Take absolute differences between any two consecutive observations See Excel file Suppose we would want to know whether the decrease in variability is statistically significant… Permutation method See Excel file

10. intra-individual variability in early child language 10 Plotting extremes In developmental data, extremes are informative After removal of mechanical or unproductive utterances Plot moving window of maximum and minimum Plot progressive maximum and regressive minimum Expectation: low values first, high values later Thus: early high values and late low values are informative See excel file In developmental data, extremes are informative After removal of mechanical or unproductive utterances Plot moving window of maximum and minimum Plot progressive maximum and regressive minimum Expectation: low values first, high values later Thus: early high values and late low values are informative See excel file

11. intra-individual variability in early child language 11 Smoothing methods Apply a flexible smoothing method to the data Loess smoothing: Locally weighted least squares regression Determine optimal window size Calculate differences between data and smoothed curve Application: increase in the average number of words Apply a flexible smoothing method to the data Loess smoothing: Locally weighted least squares regression Determine optimal window size Calculate differences between data and smoothed curve Application: increase in the average number of words

12. intra-individual variability in early child language 12 Pauline Number of Words (1 of 8) Pauline French-speaking girl From 14 to 36 months Recordings made once in two weeks, later once a month 60 utterances per observation; monthly observations were split (2 x 60) Number of words from one-word to multi- word sentences

13. intra-individual variability in early child language 13 Pauline Number of Words (2 of 8) And so forth... Hypothesis: three types of sentences One-word utterances 2 and 3 word utterances (combinatorial principle) 4 and more word utterances (“real” syntax) Hypothesis: three types of sentences One-word utterances 2 and 3 word utterances (combinatorial principle) 4 and more word utterances (“real” syntax)

14. intra-individual variability in early child language 14 Pauline Number of Words (3 of 8) Apply a Loess-smoothing procedure Follows the data and results in (relatively) symmetrically distributed residuals) Apply a Loess-smoothing procedure Follows the data and results in (relatively) symmetrically distributed residuals)

15. intra-individual variability in early child language 15 Pauline Number of Words (4 of 8)

16. intra-individual variability in early child language 16 Pauline Number of Words (5 of 8) Calculate residuals as the distance between observed frequencies and smooth model

17. intra-individual variability in early child language 17 Pauline Number of Words (6 of 8)

18. intra-individual variability in early child language 18 Pauline Number of Words (7 of 8)

19. intra-individual variability in early child language 19 Pauline Number of Words (8 of 8) Method Use the smoothed curves as an estimation of the probability that an M1, M23 or M4-22 sentence will be produced and simulate sets of 60 sentences over 46 simulated observations. Calculate difference between simulated sentences and model; calculate total variability and retain highest peak Repeat 1000 times Results Simulation reconstructs average variability, but not the observed variability peak Discussion Increased variability at the transition from “combinat- orial” to “syntactic” sentences Method Use the smoothed curves as an estimation of the probability that an M1, M23 or M4-22 sentence will be produced and simulate sets of 60 sentences over 46 simulated observations. Calculate difference between simulated sentences and model; calculate total variability and retain highest peak Repeat 1000 times Results Simulation reconstructs average variability, but not the observed variability peak Discussion Increased variability at the transition from “combinat- orial” to “syntactic” sentences

20. intra-individual variability in early child language 20 Summary and conclusion Lack of attention for variability comes not only from our suspicion that it is “wrong”, that it amounts to error… But also from our lack of methods for representing and statistically testing variability questions Methods that focus on extremes (Min and Max) may help represent developmentally meaningful variability Statistical methods based on permutation, resampling and \Monte Carlo techniques may help us test hypotheses about variability Lack of attention for variability comes not only from our suspicion that it is “wrong”, that it amounts to error… But also from our lack of methods for representing and statistically testing variability questions Methods that focus on extremes (Min and Max) may help represent developmentally meaningful variability Statistical methods based on permutation, resampling and \Monte Carlo techniques may help us test hypotheses about variability