Comparing Word Diversity Versus Amount of Speech in Parents’ Responses to Infants’ Prelinguistic Vocalizations

Abstract

Our prior research posits that the prelinguistic vocalizations of infants may elicit caregiver speech which is simplified in its linguistic structure. Caregivers’ speech clearly contributes to infants’ development; infants’ communicative and cognitive development are predicted by their ambient language environment. There are at least two sources of variation in infants’ language environment: the number and the diversity of words infants hear. We compare the change in total number of words (tokens) to the diversity of words against one another. Distributions of words of differing sizes are difficult to compare to one another because the size of the distribution largely determines the word diversity of the distribution. A novel approach to minimizing the challenges of comparing distributions of words is applied to data which were previously reported. We also conducted a new simulation study to estimate the probability that these results are expected by chance. We found that the linguistic structure of caregivers’ responses to infants’ prelinguistic vocalizations has fewer word types as compared to infant-directed but non-contingent speech. Our new method shows that contingent word distributions remain simplified as the number of total words sampled increases. By vocalizing, infants elicit caregiver speech which is simpler in structure and may be easier to learn.

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Transactions on Cognitive and Developmental Systems
Comparing word diversity versus amount of speech in
parents’ responses to infants’ prelinguistic vocalizations
Steven L. Elmlinger
Psychology Department
Cornell University
Ithaca, New York - USA
sle64@cornell.edu
Deokgun Park
Computer Science & Engineering
University of Texas
Arlington, Texas – USA
deokgun.park@uta.edu
Jennifer A. Schwade
Psychology Department
Cornell University
Ithaca, New York - USA
jas335@cornell.edu
Michael H. Goldstein
Psychology Department
Cornell University
Ithaca, New York – USA
mhg26@cornell.edu
Abstract—Our prior research posits that the prelinguistic
vocalizations of infants may elicit caregiver speech which is
simplified in its linguistic structure. Caregivers’ speech clearly
contributes to infants’ development; infants’ communicative
and cognitive development are predicted by their ambient
language environment. There are at least two sources of
variation in infants’ language environment: the number and
the diversity of words infants hear. We compare the change in
total number of words (tokens) to the diversity of words against
one another. Distributions of words of differing sizes are
difficult to compare to one another because the size of the
distribution largely determines the word diversity of the
distribution. A novel approach to minimizing the challenges of
comparing distributions of words is applied to data which were
previously reported. We also conducted a new simulation study
to estimate the probability that these results are expected by
chance. We found that the linguistic structure of caregivers’
responses to infants’ prelinguistic vocalizations has fewer word
types as compared to infant-directed but non-contingent
speech. Our new method shows that contingent word
distributions remain simplified as the number of total words
sampled increases. By vocalizing, infants elicit caregiver speech
which is simpler in structure and may be easier to learn.
Keywords—Parent-infant interaction, prelinguistic vocal
production, conversational turn-taking, speech environment,
simulation
I. INTRODUCTION
Caregivers’ behavior, which is organized around the
nascent vocalizations of their offspring, is crucial for
communicative development. Vocal learning in songbirds
[1], marmosets [2], and humans [3] is facilitated by social
feedback from adults that is contingent on the immature
vocalizations of offspring. An initial step in human infants’
gradually developing vocal communication is the formation
of expectations that their immature vocalizing reliably elicits
social input [4,5]. No two caregivers talk to their children in
exactly the same way and differences in infants’ social
environment influence the nature of their communicative
development. Variability in the linguistic structure of parents’
speech to prelinguistic infants predicts vocabulary growth [6].
Early communicative and language development is guided by
the form and timing of caregivers’ responsiveness [7] and
infant-directed speech [8]. However, the role infants play in
eliciting these behaviors from their parents is only just
beginning to be investigated [9]. In particular, little attention
has been paid to the linguistic patterning of caregivers’ speech
in response to infants’ vocalizations.
New studies have found that infant vocalizations facilitate
the production of more simplified talk from adult caregivers
[10]. This response moves the complexity of caregivers’
speech into a range that may facilitate infant learning. The
lexical and syntactic structure of caregiver speech is
simplified in response to infants’ vocalizations. Caregivers
uttered fewer unique word types, fewer words per utterance
and higher proportions of utterances which contained only a
sinlge word when talk was contingent on vocalizations. At
present, it is unclear if this effect of simplification is stable
when larger corpora (i.e., larger samples of talk) are analyzed.
Ongoing efforts employ sophisticated techniques to
distinguish genuine word diversity effects from effects due to
the sample size of words among different corpora (i.e.,
samples of talk) [11]. The goals of the current work are to
better understand how the simplification of talk (specifically
lexical diversity) may scale with the size of the sample of talk,
and to more precisely quantify the simplification of
caregivers’ contingent speech.
Figure 1. A word-rank by word-frequency graph of contingent and non-
contingent words.
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Transactions on Cognitive and Developmental Systems
New challenges associated with interpretation and
analysis of increasingly large-scale data collection efforts are
being uncovered [12]. These challenges are being met with
new techniques to address them. A central problem in
understanding word diversity at scale is the fact that word
frequency rank distributions are non-Gaussian (i.e., do not
form a normal distribution). For example in Elmlinger et al.,
2019, word ranks show that few words are very frequent and
many words are infrequent (Figure 1, also see Piantadosi,
2014 for a detailed review of near-Zipfian distributions in
natural language [13]). Heavy-tailed distributions such as
these are characteristic of the objects encountered throughout
infants’ early visual experience, the labels of those objects
infants hear, and the object-referent mappings children begin
to understand first [14]. These distributions are not amenable
to the summary statistics traditionally used in psychology
because data-clustering around the center does not occur [15].
Derivations of caregiver type-token ratios (TTR), a ratio
comparing the count of unique words (types) to the count of
words (tokens), have recently been shown to be predictive of
children’s language outcomes [6, 16]. There are at least two
issues surrounding TTR measures which remain
understudied. First, because TTR nonlinearly scales with
sample size, comparisons of TTR measures which were
calculated from two different subsets (corpora) of words with
unequivalent sample sizes are difficult to interpret [17].
Second, TTR measures are highly sensitive to the sample time
period. Counting up the number of unique words from one
corpus, for example, does little to illuminate the number of
word types in another corpus which differs in total number of
words. Initial attempts at addressing these issues are starting
to yield new techniques [11]. Sampling techniques can give
researchers insight into the sample size at which diversity of
talk may be expected to generalize. Here we contribute an
additional sampling technique alongside the central question
posed in the present work: how does the word count relate to
the number of unique words that infants’ vocalizations elicit
from their caregivers?
Recordings of naturalistic parent-infant interactions at
large scales afford new opportunities for connecting the real-
time structure of interaction to phenomena such as language
learning which emerges over longer developmental time
scales. The everyday learning context of infants’ linguistic
environment operates at multiple timescales. Learning
happens in the moment when caregivers organize responses
contingently around infants’ babbling [18]. Learning also
occurs incrementally over longer timescales through
sequences of vocal turn-taking bouts [19]. The extent to
which shorter and longer timescales can be analytically
compared to one another has received little attention. The
present study connects the multiple time scales through the
analysis of caregiver speech during unstructured play
sessions and simulates the change in word diversity as a
function of talk which was either coordinated around infants’
vocalizations or not.
II. METHODS
A. Participants
In this study, thirty caregiver-infant pairs participated.
The mean infant age was 9 months 20 days with a range of 9
months 12 days to 10 months 4 days. We recruited these
subjects from birth announcements in advertisements and
announcements in local newspapers. As a gift for their
participation, families received a t-shirt or a bib. The
participants reported in the present research were also
reported on in previous studies [3,10, 20].
B. Apparatus
All recording sessions took place in a naturalistic
environment which consisted of a twelve foot by eighteen
foot playroom comprised of a toy box, toys and animal
posters. This environment afforded infants free range to play
and explore around the room as they wished. In the room were
three digital cameras which were remote-controlled by
experimenters capturing the video recordings. Infants wore
overalls which concealed a wireless microphone (Telex
Figure 2. (a) Caregivers and infants were recorded wirelessly with microphones while they played with toys in the lab. Graphical representation of turn-
taking data collated into categories of contingent caregiver speech (b) and non-contingent speech (c). Speech within turn-taking was categorized as
contingent if it occurred within 2 seconds of infants’ non-cry vocalization.
Child
Speech
Time (s)
Parent Wireless
Microphone
Non-contingent
Speech
Contingent
Speech
...
Child Wireless
Microphone
Naturalistic Lab Environment
(a) (b) (c)
Parent
Speech
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Transactions on Cognitive and Developmental Systems
FLM-22; Telex Communications, Inc., Burnsville, MN)
along with a transmitter (Telex USR-100). Before each
session, wireless lapel microphones (Telex FLM-22) were
affixed to caregivers’ shirts. Caregiver microphones were
connected to transmitters which were hidden in a pouch
around their waist (Telex USR-100) (Figure 2a). Distinct
audio channels were utilized in the recording of infants’
vocalization and caregiver speech, respectively.
C. Procedure
Each participant engaged in 30-minute play sessions in
the lab. During these sessions, parents were asked to play like
they would at home, which resulted in unstructured free-play.
D. Speech Transcription
The speech that parents produced was completely
transcribed (see [10] for reliability measures). If parents’
utterances were separated by silence for longer than two
seconds and/or if the pitch contours exhibited were terminal,
they were segmented into separate utterances [21]. Following
prior corpus transcription conventions, inflections were
disregarded (dog, dogs, and doggy = dog) [22]. If parents’
utterances occurred before two seconds after the offset of
infants’ vocalizations, then they were considered contingent
utterances (Figure 2b). Responses which occurred after a two
second time frame were considered non-contingent [23] (see
Figure 2c). The mean and range F0 of caregivers’ contingent
and non-contingent speech are consistent with previous
descriptions of naturally produced infant-directed speech [8]
(see Elmlinger et al., 2019 for more details). All caregiver
utterances were directed at their infant. We excluded
caregivers’ production of sound effects and their responses to
infant vegetative vocalizations such as coughs, cries, and
fusses from the analyses.
E. Sampling procedure
The values derived by TTR track closely with the size of
the sample and therefore cannot be interpreted through an
isolated sample run [11]. To circumvent this constraint, we
capture several measures of word diversity along a continuum
of total word sizes. To understand the changes in the counts
of unique word types as number of total words increases, we
pool all of the speakers in our corpora together and randomly
sample from contingent and non-contingent corpora in
increasing increments of size from the respective corpora
separately. Because we are mainly interested in changes in
type-token relationships over a range of token sizes, we
allow individual caregivers to vary naturally in the number
of words they contribute to the pooled corpora.
Test Sample. We built samples through computing
iteratively larger random samples starting at 100 words up to
3000 words, incrementing in steps of 100 words (Table 1).
We sampled with replacement to ensure that every sample
was drawn from the entirety of the word distributions in both
corpora. We conducted the sampling 100 times for each
sample size. We then counted the number of unique word
types for each sample.
Control Sample Techniques. The contingent word
corpus contains far fewer total words (n = 6,199) than the
non-contingent word corpus (n = 19,548) (Table 1). In
previous work we utilized size-matched random control
samples to better understand how this difference in sample
size may contribute to the TTR curves generated from the two
Figure 3. Control sample techniques. (a) Graphical depiction of size-matched random control samples where a single distribution is created from mixing
contingent and non-contingent corpora into one unlabeled distribution of words [20]. To test whether we sample from the same underlying distribution when
we generate TTR curves from original contingent and non-contingent corpora, we create new contingent-sized and non-contingent-sized corpora from a single
distribution and derive control TTR curves to compare to the original TTR curves. If the curves differ from original to control samples, then this is evidence
for the original samples not being drawn from the same distribution of words. (b) The extent of word diversity in the non-contingent corpora is investigated
by plotting TTR curves of the word distribution after deeming a proportion of the corpora ineligible for sampling.
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Transactions on Cognitive and Developmental Systems
corpora [20]. In this approach, a single distribution is created
from mixing contingent and non-contingent corpora into one
unlabeled distribution of words (Figure 3a). The goal of this
technique was to test whether we sampled from the same
underlying distribution when we generated TTR curves from
original (test) contingent and non-contingent corpora. We
created new contingent-sized and non-contingent-sized
corpora drawn from the unlabeled distribution and derived
control TTR curves to compare to the test TTR curves. The
new control corpora produced from this technique test the
effects of sample size because the effects of contingent or
non-contingent words themselves would be inherent in both
samples as a result of randomization. This approach was
tailored to provide evidence for or against our test samples
having been drawn from the same distribution of words. If the
control TTR curves differ from the test curves, then this is
evidence for the test samples not being drawn from the same
distribution of words. In previous work we found that the
curves generated from the size-matched random control
samples indeed yielded curves which differed from the curves
generated from the test samples [20].
The extent of word diversity in the non-contingent
corpora is investigated by plotting TTR curves of the word
distribution after deeming a proportion of the corpora
ineligible for sampling (Figure 3b). The goal of size-reduced
random control sampling is to observe how the TTR curves
of non-contingent words changes as we reduce the number of
eligible words which generate the curve. We observed the
curve generated when deeming 90, 60 and 30 percent of the
word corpora eligible for sampling. Crucially, reducing the
non-contingent word corpus to 30 percent of its original size
matches approximately to the size of the contingent word
corpus. Curve comparisons between the non-contingent 30
percent eligibility corpora and contingent corpora establishes
whether reducing non-contingent corpora’s eligible size to
match that of the contingent corpora’s size produces similar
TTR curves.
TABLE I. STUDY SAMPLE SIZES
Original corpora
All sampling techniques
Contingent
6,199
100 - 3,000
Non-contingent
19,548
100 - 3,000
III. RESULTS
We report on two pieces of evidence which demonstrate
that caregivers simplify their speech which is coordinated
around their infants’ vocalizations. The comparison of
primary importance is whether caregiver contingent and non-
contingent speech diverge in their TTR curves (counts of the
number of unique word types as a function of increasing word
token sizes). The approach we follow creates data which
approximates the speech an infant would hear if they
randomly selected samples of speech across all of our
subjects. In addition, the simulations allow observations of
hypothetical data at a larger scale of time than could be
implemented within our laboratory (assuming that more time
leads to more caregiver speech). If we see divergences
between TTR curves of contingent and non-contingent
speech as we increase sample size, this provides evidence for
caregivers differentiating the complexity of their talk as they
organize it around their infants’ vocalizing.
Figure 4. (A) Average counts of word types (number of unique words) as related to the total count of words (tokens) taken from random samples of words
which were contingent and non-contingent on infants’ vocalizations and the individual type-token values for individual subjects. (B) Maximum and
minimum counts of word types as related to the total count of words (tokens) taken from random samples of words which were contingent and non-
contingent on infants’ vocalizations.
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Transactions on Cognitive and Developmental Systems
Finally, we conducted null hypothesis testing with Monte
Carlo simulations to verify whether the difference in the
number of tokens in contingent and non-contingent
conversation is due to chance.
Test Sample Results. Figure 4a is a plot of the average
count of the number of word types as a function of counts of
total word tokens from the test samples of contingent and
non-contingent words. In comparing the number of word
types from contingent and non-contingent samples we found
that 53 of the 100 pairs of random samples had more
contingent unique word types than non-contingent speech at
token size 100. With tokens at size 400 we found that 38 of
the 100 pairs of samples had more unique word types in
contingent than in non-contingent speech. Tokens at size 400
and above, all exhibited comparisons which showed greater
unique word types in non-contingent speech; furthermore,
tokens at size 1600 and above all showed that all 100 paired
random samples included a greater number of non-
contingent word types. The ranges of unique word types
were completely nonoverlapping at all tokens at size 2400
and above (Figure 4b). Our estimates suggest that contingent
and non-contingent speech may be similarly diverse when
token size is small (e.g., less than 400) but at high token sizes
contingent speech may be less diverse than non-contingent
speech. The complexity gap we observe between the word
diversity of caregiver speech which is coordinated around
infants’ vocalizations and non-contingent speech is
harmonious with findings from adult conversations. In adult
turn taking conversation, initial responses to conspecific’s
speech turn typically consist of much more simple speech
content than speech which comes non-contingently and
speakers have time to decide how to frame their next thought
[24].
To compare our sampling results to the raw subject data,
in the bottom left corner of Figure 4 we plotted the respective
subjects’ type and token counts of speech from their
contingent and non-contingent utterances (small dots). It is
clear that the counts of both types and tokens are much lower
than the curves generated by the random sampling. The
reason for this difference lies in the coherence of contiguous
speech content of any given speaker compared to the
incoherence obtained from random sampling. As caregivers
speak, in order to form coherent speech, they must repeat
words at a much higher rate than would be observed in a
random sampling of an equivalent size of words from a
pooled distribution of all the caregivers’ speech. The
usefulness of this raw data, however, is limited because they
are confounded by sample size, a problem that is
circumvented by our sampling approach.
Control Sample Results. Figure 5 depicts the average count
of unique word types as a function of the word tokens
sampled from contingent words and non-contingent words at
90%, 60% and 30% eligibility (see Figure 3b for a visual
depiction of our size-reduced random control sample
technique). Because contingent speech contains fewer total
words to sample from in general, we derived non-contingent
TTR curves which test the effects of incrementally
decreasing the size of the eligible sample pool from which
the curves are derived to test the effects of corpus size on
TTR curve outcomes. The extent of differences from the
contingent curve to the 30% eligibility non-contingent curve
suggest the effect size of the difference between the word
distributions of contingent and non-contingent speech. It is
important to note that the contingent word corpus is .31 times
the size of the non-contingent corpus, so 30% eligibility
sampling is conservative in its estimate of non-contingent’s
TTR curve at a size comparable to the contingent corpora.
Comparing the number of word types in pairs of contingent
and non-contingent samples at token size 100 results in 54
out of 100 pairs of random samples which had more
contingent unique word types than non-contingent. Making
the same comparison at token size 300 results in 9 out of 100
pairs of random samples which had more contingent unique
word types than non-contingent. At every token size, the
range for contingent and non-contingent unique word types
overlap. By this estimation, when restricting the eligibility of
the non-contingent corpora to more closely resemble the size
of contingent corpora, the divergence between the two TTR
curves is vastly reduced. We interpret this to mean that when
ignoring a potential source of variation, such as amount of
talk, it is possible that contingent and non-contingent talk
only differs by a small amount. However, in our view, size-
matched control samples, which utilize all of the data points
available in a given experiment, offer distinct advantages
which the size-reduced control samples lack (Figure 3a). In
previous simulations, we calculated differences between
TTR curves generated from test samples and size-matched
random control samples. This was useful because we could
estimate effects due to sample size differences alone and
compare those effects against those found in our test samples
[20]. Further details on the results of size-matched random
control samples can be found in our previous study [20].
Figure 5. Average counts of word types (number of unique words) as
related to the total count of words (tokens) taken from random samples
of words which were contingent and non-contingent on infants’
vocalizations. Non-contingent samples were pulled from corpora where
90%, 60% and 30% of the words were eligible for sampling.
100
500 1000 1500 2000 2500 3000
0
0
200
400
300
500
600
Types (Unique Words)
Tokens (Total Words)
Contingent (Random Test Samples)
60% Eligible Non-contingent Corpus (Random Samples)
90% Eligible Non-contingent Corpus (Random Samples)
30% Eligible Non-contingent Corpus (Random Samples)
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Transactions on Cognitive and Developmental Systems
IV. STATISTICAL MONTE CARLO TESTS
The data presented above show differences in lexical
diversity between contingent and non-contingent speech. It
would be helpful if we can replicate those results in an
independent simulation to verify our interpretation of the
sampling results. The goal of the simulation below is to
estimate the probability that the sampling results can happen
even though there is no difference in lexical diversity
between contingent and non-contingent speech. It is
generally accepted that word frequency and word frequency
rank follow a statistical trend known as Zipf’s law.
Therefore, we can simulate caregivers’ speech in caregiver-
infant conversation by sampling words from a dictionary of
caregiver speech, while adhering to Zipf’s law. If we assume
that the dictionary sizes for contingent and non-contingent
speech are same, we can count the number of unique tokens
in the simulated dialogues. If we repeat this many times and
count the occurrences when the number of unique tokens is
same with the experiment, we can estimate the probability
that the experiment result can happen even though there is
no lexical diversity between contingent and non-contingent
speech.
The distribution of parents’ talk which is contingent on
infants’ vocalizations is characterized by a TTR curve which
is shaped differently than the curve produced by parents' talk
which is non-contingent. The importance of this finding is
the demonstration that parent talk has special properties as a
function of its timing within a turn-taking context. A key
point of emphasis is that even over long timescales, the
frequency of word types which characterize different kinds
of talk does not relate to the amount of talk under scrutiny in
a deterministic manner. Indeed, in a sample from Montag
and colleagues (2015) which compared a corpus of words
found in several picture books (total word counts were
approximately 70,000) against words in the CHILDES
corpus (total word counts were about 6.5 million), it is clear
from simulation that the picture book (smaller token count)
has a higher diversity of words [22,25]. However, in our
sample, the contingent speech (smaller token count), has a
lower diversity of words. We now turn to computational
experiments which replicate the results of this paper with
functions that relate a range of presumptive caregiver
vocabulary sizes to observe how contingent unique words
accumulate as new words are uttered.
Models and Assumptions. We used Monte Carlo
simulations to test the generalizability and boundary
conditions of our findings. The simulations tested the effects
of a range of randomly selected caregiver vocabulary sizes
on contingent and non-contingent lexical diversity. First, we
assume that the vocabulary size of caregivers follows a
Gaussian distribution. We denote the distribution of
vocabulary size for contingent conversation as
𝒩
!(𝜇!, 𝜎!)
and
𝒩
"!(𝜇"! , 𝜎"!)
for non-contingent conversation. After
we randomly sample vocabulary sizes for contingent and
non-contingent conversation, we set the probability of
selecting each word in this vocabulary following a near-
Zipfian distribution as shown in Eq 1. If we rank each word
according to its frequency of occurrence, the frequency of
the word with rank r,
𝐹𝑟𝑒𝑞(𝑤#)
is proportional to the inverse
of its rank [26,27]. The probability of selecting word
𝑤#
,
𝑃[𝑤#]
can be derived by normalizing the probabilities of all
words as shown in Eq. 2 [28]. Mandelbrot introduced the
parameters
/𝛼
and
/𝛽
to improve the fit of the frequency
distribution of actual languages across contexts and sample
sizes [13]. However, the parameters of a near-Zipfian
distribution are also different among participants, and we
model this with the assumption that
𝛼
and
𝛽
themselves
follow Gaussian distributions (where
𝛼
is the y-intercept of
the distribution and
𝛽
is the slope). Finally, a conversation is
built by randomly sampling words from this vocabulary
which is characterized by a near-Zipfian distribution.
In this simulation, we estimate the near-Zipfian
parameters from the conversation data and use it to estimate
the vocabulary size distribution. Using these parameters, we
calculate the probability of a null-hypothesis that the
experimental results might happen by chance across a range
of simulation results. Figure 6 shows the overall process of
this approach.
Eq. 1
Eq. 2
Step 1: Estimating Zipfian parameters. We begin by
estimating the near-Zipfian parameters from the
experimental results because it is independent from other
factors and affects all subsequent estimations. Zipf's law is
an empirical observation and the parameters for distribution
are different across individual languages and contexts.
Piantadosi, 2014, estimated that
𝛼
is 1.13, and
/𝛽
is 2.73 for
a general English-speaking adult corpus but also showed that
these parameters change according to the time and category.
We used curve fitting methods with least square loss,
where we estimated
𝛼
and
𝛽
for all participants for
contingent and non-contingent conversation. The mean
𝛼
obtained was 0.88 with a standard deviation of 0.035.
𝛽
has
sample mean of 2.21 and standard deviation of 0.378. We
used a Gaussian distribution for
𝛼
and
/𝛽
with these mean
and standard deviation in the following simulation.
Step 2: Estimating the vocabulary size distribution.
We estimated the Gaussian distributions
𝒩
!/
and
𝒩
"!/
of the
vocabulary sizes. The main assumption in this process is that
the number of unique word types in the conversation of a
Figure 6: Overall process of null-hypothesis testing using Monte Carlo
Simulation.
Corpus
parameter (⍺,
β) estimation
by Curve
fitting
Vocabulary
Size
Distribution
Estimation
N(µ, σ)
Estimate most
likely
vocabulary
size for Null
Hypothesis H0
Calculate
Probability of
Null
Hypothesis
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Transactions on Cognitive and Developmental Systems
certain length is predicted by a caregivers’ vocabulary size.
We set
𝜇$
and
𝜎$
as the mean and the standard deviation of
the number of unique types in the conversation, and
𝜇%/
and
𝜎%
as parameters for the vocabulary size which follows the
Gaussian distribution. To find optimal
𝜇%/
and
𝜎%
, we
estimate the parameters iteratively. First, we fix
𝜎%/
and then
find the
𝜇%,
which will most likely produce the actual
experiment data,
𝜇$/
and
𝜎$
. After finding the optimal
𝜇%
,
we fix it and find the optimal
𝜎%
using the same methods.
Then we use the optimal
𝜎%
value in the next iteration and
search for an optimal
𝜇%
again. We repeat this simulation
until the
𝜇%
and
𝜎%
converge to the specified threshold.
Given µV and σV, we utilize simulation to estimate the
expected µU and σU. We sample a vocabulary size estimate
from the
𝒩(𝜇%, 𝜎%)
. Then we sample α and β from Gaussian
distribution we estimated in Step 1 and use it to build a
vocabulary with near-Zipfian distribution. Then we construct
a random conversation by sampling from this vocabulary.
We generated 30 contingent and non-contingent
conversation pairs using the conversation length of the actual
participants. We calculated the expected number of unique
word types by repeating this process.
When we use the mean (84.3) and standard deviation
(41.2) of the number of unique types in the contingent
conversation, we can estimate the
𝜇!/𝑎𝑠
206.0 and
𝜎!
as
90.2. Similarly, we estimated the non-contingent vocabulary
distribution parameter
𝜇"!
as 275.8 and
𝜎"!
as 101.3 by
using the mean (181.1) and the standard deviation (57.4) of
non-contingent conversation.
This computational simulation approach provides
complimentary evidence to the findings in the Control
Sample Results section if there is a low probability that the
vocabulary size of contingent and non-contingent
conversation are the same (null hypothesis). If this is the case,
the null hypothesis is rejected. In this section, we will
calculate the probability that the result obtained occurred
when the mean of the vocabulary size is the same across
contingent and non-contingent conversation.
Null Hypothesis testing. Our null hypothesis
Η&
is that
the mean of the vocabulary size distribution for the contingent
and non-contingent conversation is same. We denote this
vocabulary size distribution as
𝒩
&(𝜇&, 𝜎&)
.
We define the event
𝑍!/
as obtaining less than 2528 unique
types from 30 conversations with the length from the actual
experiment. The event
𝑍"!
is obtaining more than 5434
unique types from the 30 contingent conversations.
What is the probability that
𝑍!
and
𝑍"!
were drawn from
the same vocabulary distribution
𝒩
&(𝜇&, 𝜎&)
by chance?
Because the two events are independent from each other, we
can get
𝑃[𝐻&]
by multiplying the probability of the events by
each other.
The
𝜎&/
value affects the
𝑃
[
𝐻&
]
/
such that the larger
𝜎&//
value is, the higher
/𝑃
[
𝐻&
]
/
is estimated. For the
conservative estimation of the Null-Hypothesis test, we use
the higher value between
𝜎!/𝑎𝑛𝑑/𝜎"!
which was 101.3.
Similarly,
𝑃
[
𝐻&
] is affected by the
𝜇&
. Smaller values of
𝜇&
make the event
𝑍!
more likely. Higher
𝜇&
values make the
event
𝑍"!
more likely. When we search for the
𝜇&
that
maximizes
𝑃
[
𝐻&
] by monte carlo simulation, we get
𝜇&/
=
246 (Figure 7).
When we calculate the
𝑃
[
𝐻&
] probability that
𝑍!
and
𝑍"!
happened when the vocabulary size was from
𝒩
&(𝜇&=
246, 𝜎&=101.3)
, we obtain
𝑃
[
𝐻&
] = 0.35%. Therefore, we
can reject the null-hypothesis with 1% significance and
conclude that the vocabulary size for the contingent context
is smaller than the non-contingent context (Figure 8).
V. DISCUSSION
Our simulated environments make three main
contributions. First, the content of caregivers’ contingent and
non-contingent speech are different, showing that immature
infant behavior functions to influence their learning
environment. Infants’ prelinguistic vocalizing may promote
language learning because it facilitates parental behavior that
contains simplified, more easily learned information. In our
view, the coordination of caregivers’ speech content around
infant immature vocalizations is an emergent property of
𝑷[𝑯𝟎]= 𝑷[𝒁𝑪]𝑷[𝒁𝑵𝑪]
Eq. 3
Figure 7: P[ZC], P[ZNC], and P[H0] as the mean of the vocabulary size
changes. We can see that we get maximum P[H0] around when the
vocabulary size is about 246. We used 𝜎! = 101.3 for this simulation.
Figure 8: The histogram of ZC and ZNC when the vocabulary size is
sampled from N(246; 101.3). The orange colored region represents the
trials where the results were as extreme as the outcomes in the actual
experiment.
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Transactions on Cognitive and Developmental Systems
early vocal turn-taking between caregivers and infants which
facilitates the development of communication and early
language. Second, our estimates demonstrate that the
divergence of word diversity between contingent and non-
contingent speech was exacerbated at larger word counts. At
larger scales, our estimates suggest that contingent talk to
infants remains simplified while non-contingent talk
continues to increase in complexity. Third, our simulations
demonstrate that the simplification of talk is not necessarily
caused by smaller samples of talk and that non-contingent and
contingent talk are two distinct distributions of words in the
infants’ early learning environment. The lexical complexity
of contingent talk will not ‘catch up’ with that of non-
contingent talk. This is because the contingent and non-
contingent talk follow different curves describing their lexical
complexity as a function of lexical activity.
A. Methodological contribution
The limitations inherent in simple TTR metrics need not
dissuade researchers from utilizing TTR curves. On the
contrary, by demonstrating theoretically motivated
applications of these curves, we hope to promote additional
novel approaches to better understand the early ambient
language learning environment of prelinguistic infants. It has
been well documented that TTR are tightly linked to sample
size. Our simulations point out, however, that there are
techniques to minimize the effects of sample size. Size-
reduced random control samples may not yield as many
insights as size-matched random control samples. Through
size-matched control samples, we can test whether TTR curve
differences persist when we artificially create a single
distribution of words and resample new corpora at matching
sizes to the original. By forcing TTR curve generation from a
single word distribution, we observe the true effects of sample
size differences from a single word distribution. Results
obtained by reducing the size of one corpus to compare the
resulting curve against a similarly-sized corpus may be
difficult to interpret. The main disadvantage of size-reduced
sampling is that it does not provide evidence pertaining to
whether the original corpora were drawn from the same
distribution of words. Crucially, distributions of words can be
compared to one another even when the size of the datasets
are not equivalent. TTR curves can give rise to unique
insights when used alongside size-matched control curves
that illuminate whether sample size determines the nature of
the distribution. A limitation of the present work is that our
estimations do not incorporate any information about change
in caregivers’ lexical diversity over the course of infant
development. Together with our previous research, we
provide evidence that a) individual caregivers contingent
lexical diversity is simplified and b) this simplification
phenomenon exists above and beyond what is expected due
to sample size differences in contingent and non-contingent
speech [10].
However, visual inspection of the estimates becomes
more challenging as vocabulary size differences become
smaller. Prior research utilized the size-reduced random
sampling technique to investigate the difference between
word diversity in a picture book corpus and the CHILDES
corpus [25]. When we employ the same technique, the
observed differences between contingent and non-contingent
conversation are small. Similarly, the size-matched random
control sampling would show less of a difference between the
lexical diversity of contingent and non-contingent talk as the
vocabulary size difference becomes narrower. Monte Carlo
simulation studies provide another framework for estimating
the difference in vocabulary size between contingent and non-
contingent talk. Monte Carlo simulation studies rely on many
assumptions and corresponding parameters. Therefore, the
results should not be accepted as a conclusion, rather as
additional supporting evidence. Among many parameters,
our conjecture is that the standard deviation of the vocabulary
size between individuals will be the key factor affecting the
simulation result. Our Monte Carlo simulation estimates the
chances of obtaining our results when vocabulary sizes for
contingent and non-contingent speech are the same. As a
concrete example, we used 101.3 as the standard deviation
because it was the largest number from the fit in the
experimental data. In this case, the P[H0] was 0.35% meaning
that it is unlikely that vocabulary sizes for the contingent and
non-contingent speech are the same. However, when we use
larger standard deviation such as 160, the P[H0] was 6.5%
which will not pass a 5% significance level for rejection of
this null hypothesis. A more reliable estimate of the standard
deviation of individual vocabulary sizes would give our
simulation more predictive power. Estimating individual
vocabulary size, however, is still a challenging problem
especially given the diversity of the social contexts.
B. Developmental contribution
Functions of simplified caregiver speech. Over long
timescales, our simulation estimates that caregivers’ speech
which is organized around infants’ vocalizations will
generally contain a higher amount of repeated lexical items.
The evidence on the influence repetition has on language
development is mixed over longer time scales (6 to 12
months); repetitive language input has been linked to both
lower [29,16] and greater [6] vocabulary sizes later in
development. The extent to which caregivers organize less
repetitive speech around infants’ vocalizations predicts
infants’ vocal maturity [10]. Caregivers naturally use similar
words and phrases in contiguous utterances, these quasi-
repetitive adjacent utterances are called variation sets [31].
For example, a caregiver might say “Is that a spoon? Where’s
your spoon? Get your spoon!”. Variation sets facilitate
learning in adults and similarly guide early linguistic learning
in infants [30,31]. Repetition is not isolated to infants’
language environment. For example, during meal times
infants’ encounter iconic objects that are labeled reliably by
caregivers, creating recurrent visual and linguistic cues
coupled closely in time. Caregiver speech, organized around
daily routines, is part of a constellation of cues which
facilitate word learning from everyday activities [32,33,34].
The earliest words infants learn could arise out of
prelinguistic turn-taking interactions, such as when an infant
points at an object and vocalizes, then the parent utters the
object’s label. Indeed, infants in experimental settings learn
word-object mappings when caregivers respond to infants’
object-directed vocalizations with object-label utterances
[35].
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Transactions on Cognitive and Developmental Systems
Caregivers’ contiguous speech is highly coherent and
therefore repetitive, but over long time scales, continuous
speech will change topic or dive deeper into a single topic and
therefore elicit a greater diversity of words. However,
because it takes speakers time to plan more elaborate and
diverse utterances in production, contingent speech will
always be relatively simplified compared to non-contingent
speech. We do not hypothesize that the more parents simplify
their speech, the better the opportunities for infants’ learning.
Evidence suggests that infants who hear more lexical
diversity spoken contingently on their vocalizations have a
greater capacity for producing syllables that include
consonants [10]. Thus, increased contingent caregiver lexical
diversity may facilitate infants’ vocal learning.
Evidence suggests that stable speech sounds might be
better targets for infants to base refinement of their vocal
repertoires on. Simplified caregiver speech might be useful
because it does not overtax infants’ limited working memory
at the moments they are ready to learn. In addition to the
perception of mature adult speech, infants’ own vocal
productions can serve as a source of stability in the input.
Recent findings suggest that infants who have a stable
phonological pattern in their vocal repertoire are better at
segmenting the speech stream in perception [36]. One
interpretation of these findings is that when stable
representations in infants’ phonological memory are present
(from either within or without), the processing load for
similar phonological structures is eased. It is possible that
early stability in infants’ production is useful for similar
reasons in perception. When caregivers produce similar
sound forms, infants could discover underlying structure by
examining the input’s redundancy.
Why is the speech content of caregivers’ responses to
infants’ vocalizations simplified? We propose two testable
hypotheses which can guide future work on this question. The
altriciality effects hypothesis suggests that the source of
change between contingent and non-contingent lexical
diversity is infants’ vocal altriciality. Human infants are
altricial – they depend on caregivers for survival over an
extended period of development. Characteristics of
immaturity (e.g., neotenic appearance) may serve as cues that
facilitate caregiving behavior [37]. Infants’ early
vocalizations may serve as salient cues of immaturity. Even
when infants are capable of engaging in sophisticated social
behavior (e.g., smiling and pointing) their prelinguistic
vocalizations are still immature and do not resemble words or
language. Such immaturity may drive the observed
simplification of adults’ contingent speech, and explain why
non-contingent speech is not simplified.
An alternative hypothesis is that caregivers respond to
infants’ vocalizations with simplified speech because of the
reduced processing time allotted them. The processing time
hypothesis suggests that the source of change between
contingent and non-contingent lexical diversity is the small
increment of time between infants’ vocalization and
caregivers’ speech in response. Two pieces of evidence
would speak to these hypotheses. First, adults’ lexical
diversity should be measured in adult-adult turn-taking as a
function of contingency. If adults’ speech complexity differs
across responses to adult speech and infant vocal turns, this
would provide evidence in favor of the altriciality effects
hypothesis. Second, if the reduced processing time hypothesis
holds, then the latency between infants’ vocalizations and
caregiver speech responses should correlate positively with
caregivers’ speech complexity. If there is no correlation
between latency and speech complexity, this would provide
evidence in favor of the altriciality effects hypothesis. These
analyses are beyond the scope of the present paper, but future
work in our lab will shed light on these hypotheses.
The length of infant vocalizations may have also
influenced the nature of caregiver responses. As infants age,
they begin to string together multiple prelinguistic
vocalizations closely in time, structuring vocal bouts into
syllable sequences [38]. In the current study we considered
parents’ responses to non-cry vocalizations to investigate the
influence of these vocalizations on caregiver speech.
However, it is possible that the complexity of caregivers’
speech changes in response to infant vocalizations that extend
further in time. In the future, there is a need to study the
influence of infants’ vocalizations which span multiple
syllables to investigate whether infant vocal sequences
change caregiver responding. It is possible that one pathway
for infants to increase the lexical diversity of their caregivers’
speech is by organizing their vocalizations with sequential
structure within conversational turn-taking contexts.
Our findings have important implications for data
collection at large scales and language development
intervention studies. Home recording efforts can reveal the
extent to which there are changes in linguistic structure within
parent-child vocal turn-taking bouts over time [39]. The main
focus in several interventions for at-risk families surrounds
the number of words produced by caregivers (e.g.,
Providence Talks; http://www.providencetalks.org) or turn-
taking with infants [40]. Evidence suggests that interventions
are effective at promoting early language development when
caregivers’ increase their lexical activity that is organized
around infants [41]. Future research should seek to better
illuminate how caregivers might attempt to continually adapt
their contingent talk to match their infants’ current
communicative capacities.
Our findings point to the role of infants’ immature
vocalizations in shaping infants’ own language learning
environment. Computational models of vocal learning utilize
mechanisms of accurate prediction of environmental
changes; such a mechanism may also support infants in
contexts of social learning [42, 43]. Theoretical frameworks
have postulated that discrepancies between predictions and
observed outcomes may elicit a learner’s curiosity. Models
centered around curiosity select to learn from information
from which they can diminish the error of their own
predictions at maximum rates. When infants vocalize they
create opportunities to learn the effects of their own
vocalizations on their caregivers’ behavior. During their first
12 months of life, infants rapidly learn that their own
prelinguistic vocalizing elicits responses from their
caregivers [5]. Eliciting mature speech sounds from
caregivers may become the target of infants’ curiosity and
subsequently guide their vocal development. For a more
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Transactions on Cognitive and Developmental Systems
advanced understanding of early infant learning, future large-
scale observational, computational and experimental research
should investigate the effects infants have on the temporal and
distributional properties of parents’ speech.
ACKNOWLEDGMENTS
Jessica Montag and Felix Thoemmes provided helpful critical
discussion. We thank the families who participated in the study.
Sofia Carrillo, Shelly Zhang, Kexin Zheng and SoYoung Kwon
transcribed parent speech and coded infant vocalizations.
REFERENCES
[1] S. Carouso-Peck, and M. Goldstein. "Female social feedback reveals
non-imitative mechanisms of Vocal Learning in Zebra Finches," Curr.
Bio., vol 29, pp. 1-6, 2019.
[2] Y. Gultekin, and S. Hage, “Limiting parental interaction during vocal
development affects acoustic call structure in marmoset monkeys,” Sci
Advances, vol 4, eaar4012, 2018.
[3] M. Goldstein, and J. Schwade, “Social feedback to infants' babbling
facilitates rapid phonological learning,” Psych. Sci., vol 19(5), pp.
515–523, 2008.
[4] P. Kuhl, F. Tsao, and H. Lui, “Foreign-language experience in
infancy: Effects of short-term exposure and social interaction on
phonetic learning,” PNAS, vol 100, pp. 9096–9101, 2003.
[5] M. Goldstein, J. Schwade, and M. Bornstein, “The value of vocalizing:
five‐month‐old infants associate their own noncry vocalizations with
responses from caregivers,” Child Dev., vol 80(3), pp. 636-644, 2009.
[6] R. Newman, M. Rowe and N. Ratner, “Input and uptake at 7 months
predicts toddler vocabulary: the role of child-directed speech and
infant processing skills in language development,” J. of Child Lang.,
vol 43, pp. 1158-1173, 2016.
[7] C. S. Tamis-LeMonda, M. H. Bornstein, and L. Baumwell, “Maternal
Responsiveness and Children’s Achievement of Language
Milestones,” Child Development, vol. 72, no. 3, pp. 748–767, 2001
[8] E. D. Thiessen, E. A. Hill, and J. R. Saffran, “Infant-Directed Speech
Facilitates Word Segmentation,” Infancy, vol. 7, no. 1, pp. 53–71,
2005.
[9] L. Smith, S. Jayaraman, E. Clerkin, and C. Yu, “The developing infant
creates a curriculum for statistical learning,” Trends in Cognitive
Sciences, vol. 22(4), pp. 324-336, 2018.
[10] S. Elmlinger, J. Schwade, and M. Goldstein, “The ecology of
prelinguistic vocal learning: parents simplify the structure of their
speech in response to babbling,” J. of Child Lang., 2019.
[11] J. Montag, M. Jones, and L. Smith, “Quantity and diversity:
Simulating early word learning environments,” Cog Sci., vol 42, pp
375-412, 2018.
[12] E. Bergelson, M. Casillas, M. Soderstrom, A. Seidl, A. S.
Warlaumont, and A. Amatuni, “What Do North American Babies
Hear? A large-scale cross-corpus analysis,” Developmental Science,
vol. 22, no. 1, p. e12724, 2018.
[13] S. Piantadosi, “Zipf’s word frequency law in natural language: A
critical review and future directions,” Psych. Bull. & Rev., vol 21(5),
pp. 1112-1130, 2014.
[14] E. Clerkin, E. Hart, J. Rehg, C. Yu, L. Smith, "Real-world visual
statistics and infants' first-learned object names." Phil. Trans. R. Soc.
B 327, 20160055.
[15] W. Johnson, “Studies in language behavior: A program of
research,” Psych. Monographs, vol 56(2), pp. 1-15, 1944.
[16] J. Schwab, M. Rowe, N Cabrera, C. Lew-Williams, “Fathers’
repetition of words is coupled with children’s vocabularies.” J of Exp.
Child Psych., vol 166, 437-450, 2018.
[17] B. Richards, “Type/Token ratios: what do they really tell us?” J. of
Child Lang., vol 14(2), pp. 201-209, 1987.
[18] M. Goldstein, A. King, and M. West, “Social interaction shapes
babbling: Testing parallels between birdsong and speech,” PNAS vol
100(13), pp. 8030-8035, 2003.
[19] A. Warlaumont, J. Richards, J. Gilkerson, and D. Oller, “A social
feedback loop for speech development and its reduction in autism,”
Psych. Sci., vol 25(7), pp. 1314-1325, 2014.
[20] S. Elmlinger, J. Schwade, and M. Goldstein, “Babbling elicits
simplified caregiver speech: Findings from natural interaction and
simulation,” ICDL-EpiRob, pp. 1-6. 2019.
[21] C. Venker, D. Bolt, A. Meyer, H. Sindberg, S. Weismer, and H. Tager-
Flusberg, “Parent telegraphic speech use and spoken language in
preschoolers with ASD,” J. of Speech, Lang. and Hear. Res., vol 58(6),
pp. 1733-1746, 2015.
[22] B. MacWhinney, “The childes project: The database”, vol. 2.
Psychology Press, 2000.
[23] L. Van Egeren, M. Barratt, and M. Roach, “Mother-infant
responsiveness: Timing, mutual regulation, and interactional context.”
Dev Psych., voc 37.5, pp. 684, 2001.
[24] J. Du Bois, “Towards a dialogic syntax,” Cog. Ling., vol 25(3), pp.
359-410, 2014.
[25] J. Montag, M. Jones, and L. Smith, “The words children hear: Picture
books and the statistics for language learning.” Psych. Sci., vol 26(9),
pp. 1489-1496, 2015.
[26] G. K. Zipf, “The psychobiology of language (rout-ledge, london),”
1936.
[27] G. K. Zipf, “Human behavior and the principle of least effort.” 1949.
[28] B. Mandelbrot, “An informational theory of the statistical structure of
language,” Communication theory, 1953.
[29] E. Newport, H. Gleitman, and L. Gleitman, “Mother, I’d rather do it
myself: some effects and non-effects of maternal speech style.” in
Talking to Children: Language input and acquisition, Cambridge:
Cambridge University Press, 1977, pp. 109–149.
[30] J. Schwab, C. Lew-Williams, "Repetition across successive sentences
facilitates young children’s word learning." Developmental
Psychology, vol. 52, p. 879, 2016.
[31] L. Onnis, H. Waterfall, and S. Edelman, “Learn locally, act globally:
Learning language from variation set cues,” Cognition, vol 109, pp.
423-430, 2008.
[32] M. Casillas, P. Brown, S. Levinson, “Early language experience in a
Tseltal Mayan village,” Child Dev., vol. 90, pp. 1819-1835, 2020.
[33] C. Tamis-LeMonda, S. Custode, Y. Kuchiro, K. Escobar and T. Lo,
“Routine language: Speech directed to infants during home activities.”
Child Dev., vol. 90, pp. 2135-2152, 2019.
[34] C. Yu, and L. Smith, “Embodied attention and word learning by
toddlers.” Cognition, vol 125.2, pp. 244-262, 2012.
[35] M. Goldstein, J. Schwade, J. Briesch, S. Syal, “Learning while
babbling: Prelinguistic object-directed vocalizations indicate a
readiness to learn.” Infancy, vol. 15, pp. 362-391, 2010.
[36] M. Hoareau, H. Yeung, T. Nazzi, “Infants’ statistical word
segmentation in an artificial langauge is linked to both parental
speech input and reported production abilities.” Developmental
Science, vol 22, p.e12803, 2019.
[37] L. Zebrowits, S. Brownlow, K. Olson, “Baby talk to the babyfaced.”
J Nonverbal Behav, vol 16, pp. 143-158, 1992.
[38] D. Lipkind, G. Marcus, D. Bemis, K. Sasahara, N. Jacoby, M.
Takahsi, … & O. Tchernichovski, “Stepwise acquisition of vocal
combinatorial capacity in songbirds and human infants,” Nature, vol
498, pp. 104-108. 2013.
[39] M. VanDam, A. Warlaumont, E. Bergelson, A. Cristia, M.
Soderstrom, P. De Palma, and B. MacWhinney, “HomeBank: An
online repository of daylong child-centered audio recordings,”
in Seminars in speech and language, NIH Public Access, p. 128,
2016.
[40] K. Leffel, and D. Suskind, “Parent-directed approaches to enrich the
early language environments of children living in poverty,” Sems. in
Speech & Lang., vol 34, pp. 267–278, 2013.
[41] M. McGillion, J. Pine, J. Herbert, D. Matthews, “A randomised
controlled trial to test the effect of promoting caregiver contingent
talk on language development in infants from diverse socioeconomic
status backgrounds,” Journal of Child Psychology and Psychiatry,
vol. 58, pp. 1122-1131, 2017.
[42] C. Kidd, B. Hayden, “The psychology and neuroscience of
curiosity,” Neuron, vol 88(3), pp. 449–460, 2015.
[43] C. Moulin-Frier, S. Nguyen, and P. Oudeyer, “Self-organization of
early vocal development in infants and machines: the role of intrinsic
motivation,” Fntiers in Psych., vol 4, p. 1006, 2014.
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