Intra-individual variability in early child languageIntra-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

intra-individual variability in early child language 2

Why variability … and how?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?

intra-individual variability in early child language 3

Spatial Prepositions (1 of 6)Spatial Prepositions (1 of 6)

• 4 sets of data• 4 sets of dataname ages

number of observations

gender

Heleen 1;6,4 – 2;5,20 55 Female

Jessica 1;7,12 – 2;6,18 52 Female

Berend 1;7,14 – 2;7,13 50 Male

Lisa 1;4,12 - 2;4.12 48 Female

• 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

intra-individual variability in early child language 4

Spatial Prepositions (2 of 6)Spatial Prepositions (2 of 6)

0

5

10

15

20

25

30

35

40

-180 -130 -80 -30 20 70 120 170 220

age

freq

uen

cy

lisa

intra-individual variability in early child language 5

Spatial Prepositions (3 of 6)Spatial Prepositions (3 of 6)

0

5

10

15

20

25

30

-270 -220 -170 -120 -70 -20 30 80

age

freq

uen

cy

heleen

intra-individual variability in early child language 6

Spatial Prepositions (4 of 6)Spatial Prepositions (4 of 6)

0

5

10

15

20

25

30

35

40

-40 10 60 110 160 210 260 310

age

freq

uen

cy

berend

intra-individual variability in early child language 7

Spatial Prepositions (5 of 6)Spatial Prepositions (5 of 6)

0

5

10

15

20

25

30

35

40

-100 -50 0 50 100 150 200

age

freq

uen

cy

jessica

intra-individual variability in early child language 8

Representing variability (1 of 6)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

intra-individual variability in early child language 9

Distance methodDistance 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

intra-individual variability in early child language 10

Plotting extremesPlotting 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

intra-individual variability in early child language 11

Smoothing methodsSmoothing 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

intra-individual variability in early child language 12

Pauline Number of Words (1 of 8)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

• 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

intra-individual variability in early child language 13

Pauline Number of Words (2 of 8)Pauline Number of Words (2 of 8)

0

10

20

30

40

50

60

14 19 24 29 34

age

freq

uenc

y

M1 M2 M3 M4 M5 M6

And so forth ...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)

intra-individual variability in early child language 14

Pauline Number of Words (3 of 8)Pauline Number of Words (3 of 8)

0

10

20

30

40

50

60

14 19 24 29 34

age

freq

uenc

y

M1 M23 M422

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)

intra-individual variability in early child language 15

Pauline Number of Words (4 of 8)Pauline Number of Words (4 of 8)

-10

0

10

20

30

40

50

60

14 19 24 29 34

age

freq

uenc

y

M1 M23 M422

intra-individual variability in early child language 16

Pauline Number of Words (5 of 8)Pauline Number of Words (5 of 8)

-10

0

10

20

30

40

50

60

14 19 24 29 34

age

freq

uenc

y

M1 M1 smooth M23 M23 smooth M422 M422 smooth

Calculate residuals as the distance between observed frequencies and smooth model

Calculate residuals as the distance between observed frequencies and smooth model

intra-individual variability in early child language 17

Pauline Number of Words (6 of 8)Pauline Number of Words (6 of 8)

15

20

25

30

35

40

24 25 26 27 28 29 30 31

age

freq

uenc

y

M23 m23 smooth

intra-individual variability in early child language 18

Pauline Number of Words (7 of 8)Pauline Number of Words (7 of 8)

0

2

4

6

8

10

12

14

14 19 24 29 34

age

freq

uenc

y

M1 var M23 var 422 var

intra-individual variability in early child language 19

Pauline Number of Words (8 of 8)Pauline Number of Words (8 of 8)

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

14 19 24 29 34

age

freq

uenc

y

M1 M23 M422 total var smoothed rescaled

MethodUse 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 peakRepeat 1000 timesResultsSimulation reconstructs average variability, but not the observed variability peak DiscussionIncreased variability at the transition from “combinat-orial” to “syntactic” sentences

MethodUse 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 peakRepeat 1000 timesResultsSimulation reconstructs average variability, but not the observed variability peak DiscussionIncreased variability at the transition from “combinat-orial” to “syntactic” sentences

intra-individual variability in early child language 20

Summary and conclusionSummary 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