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Modeling Individual Differences in Children’s
Information Integration During Pragmatic
Word Learning

Manuel Bohn1

, Louisa S. Schmidt2

, Cornelia Schulze2,3

, Michael C. Frank4

and Michael Henry Tessler5,6

1Department of Comparative Cultural Psychology, Max Planck Institute for Evolutionary Anthropology, Leipzig, Allemagne
2Leipzig Research Center for Early Child Development, Leipzig University, Leipzig, Allemagne
3Department of Educational Psychology, Faculty of Education, Leipzig University, Leipzig, Allemagne
4Département de psychologie, Université de Stanford, Stanford, Etats-Unis
5DeepMind, Londres, ROYAUME-UNI
6Department of Brain and Cognitive Sciences, Massachusetts Institute of Technology, Cambridge, Etats-Unis

Mots clés: pragmatics, language development, individual differences, cognitive modeling

ABSTRAIT

Pragmatics is foundational to language use and learning. Computational cognitive models have
been successfully used to predict pragmatic phenomena in adults and children – on an aggregate
level. It is unclear if they can be used to predict behavior on an individual level. We address this
question in children (N = 60, 3- to 5-year-olds), taking advantage of recent work on pragmatic
cue integration. In Part 1, we use data from four independent tasks to estimate child-specific
sensitivity parameters to three information sources: semantic knowledge, expectations about
speaker informativeness, and sensitivity to common ground. In Part 2, we use these parameters
to generate participant-specific trial-by-trial predictions for a new task that jointly manipulated
all three information sources. The model accurately predicted children’s behavior in the
majority of trials. This work advances a substantive theory of individual differences in which the
primary locus of developmental variation is sensitivity to individual information sources.

INTRODUCTION

A defining feature of human communication is its flexibility. Conventional languages – signed
and spoken – allow for expressing a near-infinite number of messages. In the absence of a
shared language, humans can produce and understand novel signals which can rapidly be
transformed into structured communication systems (Bohn et al., 2019; Brentari & Goldin-
Meadow, 2017; Fay et al., 2018). The flexibility stems from a powerful social-cognitive infra-
structure that underlies human communication (Levinson & Holler, 2014; Sperber & Wilson,
2001; Tomasello, 2008). Interlocutors can recruit and integrate a range of different information
sources – conventional language being one of them – to make so-called pragmatic inferences
about the speaker’s intended meaning in context (Grice, 1991). They play an important role
during everyday language use (Clark, 1996; Schulze & Buttelmann, 2021) and during lan-
guage acquisition (Bohn & Frank, 2019; Clark, 2009; Tomasello, 2009).

Decades of developmental research have shown that children readily make pragmatic infer-
ences in a wide variety of contexts and starting at an early age (Bohn & Frank, 2019; Schulze &

un accès ouvert

journal

Citation: Bohn, M., Schmidt, L. S.,
Schulze, C., Frank, M.. C., & Tessler,
M.. H. (2022). Modeling Individual
Differences in Children’s Information
Integration During Pragmatic Word
Apprentissage. Open Mind: Discoveries
in Cognitive Science, 6, 311–326.
https://doi.org/10.1162/opmi_a_00069

EST CE QUE JE:
https://doi.org/10.1162/opmi_a_00069

Supplemental Materials:
https://doi.org/10.1162/opmi_a_00069;
https://osf.io/pa5x2;
https://github.com/manuelbohn
/spin-within

Reçu: 13 Juillet 2022
Accepté: 29 Octobre 2022

Intérêts concurrents: The authors
declare no conflict of interest.

Auteur correspondant:
Manuel Bohn
manuel_bohn@eva.mpg.de

droits d'auteur: © 2022
Massachusetts Institute of Technology
Publié sous Creative Commons
Attribution 4.0 International
(CC PAR 4.0) Licence

La presse du MIT

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Modeling Individual Differences in Developmental Pragmatics

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Tomasello, 2015). Par exemple, already early in the second year of life, children use their
emerging semantic knowledge (word-object mappings) to infer that a speaker uses a novel word
to refer to a novel object (Bion et al., 2013; Clark, 1988; Halberda, 2003; Lewis et al., 2020;
Markman & Wachtel, 1988; Merriman et al., 1989; Pomiechowska et al., 2021). Around the
same age, children start to use common ground (shared knowledge) in communication (Akhtar
et coll., 1996; Bohn & Köymen, 2018; Bohn et al., 2018; Diesendruck et al., 2004; Ganea &
Saylor, 2007). From age three onwards, they expect speakers to communicate in an informative
and context-sensitive way (Frank & Homme bon, 2014; Schulze et al., 2022; Schulze et al., 2013).

Theoretical accounts of language use and learning postulate that these pragmatic inferences
require integrating various sources of information but often fail to specify how exactly the
information integration happens. This theoretical paucity is a special case of a more general
issue in psychology and – specifically — in developmental science, where there is a lack of
fort, explicit theories that predict and explain behavior (Muthukrishna & Henrich, 2019).
Computational cognitive modeling is one way to overcome this issue (van Rooij & Baggio,
2021; Simmering et al., 2010). Cognitive models formalize the computational processes that
generate the observed behavior (Ullman & Tenenbaum, 2020; van Rooij, 2022). The modeling
process forces researchers to state explicitly their assumptions and intuitions, which can result
in stronger theories (Guest & Martine, 2021).

The field of pragmatic language comprehension has been particularly active from a com-
putational modeling perspective (Cummins & de Ruiter, 2014), including work on common
ground (Anderson, 2021; Heller et al., 2016), politeness ( Yoon et al., 2020); over-
informativeness (Degen et al., 2020); implicature (Franke & Bergen, 2020), and generic lan-
guage (Tessler & Homme bon, 2019). The Rational Speech Act (RSA) framework has been one
productive framework for modeling pragmatic inference, construing language understanding
as a special case of Bayesian social reasoning (Frank & Homme bon, 2012; Homme bon & Frank,
2016; Scontras et al., 2021). RSA models are distinguished by their recursive structure in
which a listener reasons about a cooperative speaker – sensu Grice (1991) – who reasons
about a literal listener who interprets words according to their literal semantics. These models
have been successfully applied to predict aggregate behavior – the average judgment proba-
bility across a large group of participants, for example – for a range of different pragmatic phe-
nomena (reviewed in Frank & Homme bon, 2012; Homme bon & Frank, 2016).

Computational cognitive models – including RSA – are mostly used as summary descrip-
tions and explanations of well-known effects from the literature or in pre-existing data. Encore, pour
a comprehensive theory, models should also be able to predict new data (Hofman et al., 2021;
Shmueli, 2010; Yarkoni & Westfall, 2017). Recent work using RSA models has begun to
address this issue. Par exemple, Bohn et al. (2021) studied young children’s information inte-
gration during pragmatic word learning (see also Bohn et al., 2022b). They measured chil-
dren’s developing sensitivity to three different sources of information about meaning in context
and used an RSA model to generate predictions about situations in which these information
sources need to be integrated. Newly collected data aligned closely with what the model pre-
dicted, in the sense that the model predictions were numerically similar to the average level of
performance across a large sample of children. This line of work tested the scope and validity
of models of pragmatic reasoning and the results offered support for the theoretical assump-
tions around which the model was built in comparison to alternative models.

These prior studies only explained and predicted behavior on an aggregate level, cependant.
The models were assessed following the assumption that the “average person” behaves like the
prototypical agent whose cognitive processes are being simulated by the model (Estes & Todd

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Maddox, 2005). Yet it is an open question if everybody – or in fact anybody – really behaves like
this prototypical agent. Most likely, there are differences between individuals. Par exemple,
Franke and Degen (2016) studied quantity implicatures and found that participant data was best
captured by a model that assumes a population in which individuals differ in the depth of their
Theory of Mind reasoning. A central question is, donc, whether models that accurately pre-
dict group-level results can also be used to predict individual differences. Par exemple,
although Griffiths and Tenenbaum (2006) showed that groups of participants in the aggregate
could correctly make optimal judgments about the conditional probability of everyday events,
Mozer et al. (2008) argued that this pattern could emerge from an aggregate of individual agents
with far simpler and more heuristic strategies (cf. Griffiths & Tenenbaum, 2011). Ainsi, the fit of
cognitive models to aggregate patterns of data may not always support the inference that the
cognitive model describes individuals’ patterns of reasoning or inference.

In the present study, we address this issue in the domain of pragmatic word learning, en utilisant
RSA models to predict individual differences between children. Our study builds on Bohn et al.
(2021) and measures how children integrate different information sources. We focused on how
children’s semantic knowledge interacts with their expectations about informative communica-
tion and sensitivity to common ground. Following the previous study, we formalized this inte-
gration process in a model derived from the RSA framework. Surtout, cependant, the current
model was designed to capture individual differences, which we conceptualize as differences
between children in sensitivity to the different information sources. In Part 1, we collected data
in four tasks from which we estimated child-specific sensitivity parameters. In Part 2, we used
these parameters to predict – on a trial-by-trial basis – how the same children should behave in
a new task that required information integration. The critical contribution of this work is thus
to test whether a successful model of aggregate judgments holds at the individual level.

PART 1: SENSITIVITY

Methods

Methods, sample size, and analyses were pre-registered at: https://osf.io/pa5x2. All data, anal-
ysis scripts, model code, and experimental procedures are publicly available in the following
online repository: https://github.com/manuelbohn/spin-within.

Participants. We collected complete data for 60 enfants (mage = 4.11, rangeage: 3.06–4.93, 30
girls) during two experimental sessions each. As per our pre-registration, children who provided
valid data for fewer than half of the test trials in any of the three experiments were excluded from
the analysis. This was the case for five additional children (two 3-year-olds, three 4-year-olds)
due to disinterest in the experiments (n = 2), parental interference due to fussiness (n = 2), ou
withdrawal from the study after the first testing session (n = 1). Children came from an ethnically
homogeneous, mid-size German city (∼550,000 inhabitants, median income A1,974 per
month as of 2020), were mostly monolingual, and had mixed socioeconomic backgrounds.
The study was approved by an internal ethics committee at the Max Planck Institute for Evolu-
tionary Anthropology. Data was collected between March and July of 2021.

Measures. Children were recruited via a database and participated with their parents via an online
conferencing tool. The different tasks were programmed as interactive picture books in Java-
Script/HTML and presented on a website. During the video call, participants would enter the
website with the different tasks and share their screens. The experimenter guided them through the
procedure and told caregivers when to advance to the next task. Children responded by point-
ing to objects on the screen, which their caregivers would then select for them via mouse click.

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Schematic overview of the study and the model. Pictures on the left show screenshots from the four sensitivity tasks. Arrows
Chiffre 1.
indicate which tasks informed which parameter in the model (grey area). Based on the data from the sensitivity tasks, child-specific parameter
distributions for each information source were estimated. These sources were integrated via an RSA model, which generated predictions for
each trial of the combination task. These predictions were then evaluated against new data from the combination task.

For the word production task, the experimenter shared their screen and presented pictures in a slide
show. For the mutual exclusivity, discourse novelty, and combination tasks (Part 2), pre-recorded
sound files were used to address the child. Chiffre 1 shows screenshots from the different tasks.

The discourse novelty task assessed children’s sensitivity to common ground (voir la figure 1).
Children saw a speaker (cartoon animal) standing between two tables. On one table, there was
a novel object (drawn for the purpose of this study), while the other was empty (side counter-
équilibré). The speaker sequentially turned to both sides (order counterbalanced) and either
commented on the presence or absence of an object (without using any labels, voir
supplementary material for details). Alors, the speaker disappeared, and – while the speaker
was gone – another novel object appeared on the previously empty table. Suivant, the speaker
re-appeared and requested one of the objects using a novel non-word as the label. Nous
assumed that children would take the novel word to refer to the object that was new to the
conférencier. Children received 12 trials, each with a new pair of novel objects.

The mutual exclusivity task was used to assess children’s semantic knowledge and expec-
tations about speaker informativeness (voir la figure 1). Children again saw a speaker and two
tables. On one table, there was a novel object while on the other there was a (potentiellement)
familiar object (side counterbalanced). The speaker used a novel non-word to request one
of the objects. We assumed that children would take the novel word to refer to the novel
objet. In line with previous work (Bohn et al., 2021; Grassmann et al., 2015; Lewis et al.,
2020) we assumed this inference would be modulated by children’s lexical knowledge of
the familiar object. Children received 16 trials, each with a new pair of novel and familiar
objets. Both the discourse novelty as well as the mutual exclusivity tasks showed good

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re-test reliability (r > .7 for both tasks) in a previous study and seem well-suited for individual-
level measurement (Bohn et al., 2022un).

The word production task assessed children’s semantic knowledge (voir la figure 1). Le
experimenter showed the child each of the 16 familiar objects from the mutual exclusivity task
and asked them to name them. We used a pre-defined list of acceptable labels per object to
categorize children’s responses as either correct or incorrect (see supplementary material).

The word comprehension task was also used to assess semantic knowledge (voir la figure 1).
The child saw four slides with six objects. Four objects per slide were taken from the 16 famil-
iar objects that also featured in the mutual exclusivity and word production tasks. Two objects
were unrelated distractors. The experimenter labeled one familiar object after the other and
asked the child to point to it.

Data collection for the entire study (Part 1 et 2) was split into two sessions which took
place around one week apart (min: 1 day, maximum: 2 weeks). On day one, children completed the
mutual exclusivity and the discourse novelty tasks. On day two, they completed the combi-
nation task (Part 2) followed by the word comprehension and production tasks.

Analysis

The goal of the analysis of Part 1 was to estimate participant-specific sensitivity parameters
based on the tasks described above. Parameter estimation happens in the context of the
modeling framework we used to generate predictions for the novel task in Part 2. In the fol-
lowing, we first describe the general modeling framework and then continue with the
participant-specific parameter estimation.

Modeling Framework. We adopted the modeling framework used by Bohn et al. (2021). Notre
models are situated in the Rational Speech Act (RSA) framework (Frank & Homme bon, 2012;
Homme bon & Frank, 2016). RSA models treat language understanding as a special case of
Bayesian social reasoning. A listener interprets an utterance by assuming it was produced
by a cooperative speaker who has the goal to be informative. Being informative is defined
as producing messages that increase the probability of the listener inferring the speaker’s
intended message. The focal rational integration model, including all data-analytic parameters,
is formally defined as:

(cid:4)

(cid:1)
PL1 r j u; ρi; ai; θij

(cid:5)
(cid:3)

(cid:4)

(cid:1)

∝ PS1 u j r; ai; θij

(cid:3)

(cid:5) :

P r j ρi
ð

(1)

The model describes a listener (L1) reasoning about the intended referent of a speaker’s (S1)
utterance. This reasoning is contextualized by the prior probability of each referent P(r j ρi).
This prior probability is a function of the common ground ρ shared between speaker and lis-
tener in that interacting around the objects changes the probability that they will be referred to
plus tard. We assume that individuals vary in their sensitivity to common ground which, captured
in participant-specific parameters ρi. Note that this view ignores that there might be other
aspects of a referent (such as perceptual salience or familiarity) that might influence the prior
probability of it being the referent. While we do think that these aspects might matter, we tried
to minimize their influence by way of carefully designing and selecting the stimuli used in the
experiments.

To decide between referents, the listener (L1) reasons about what a rational speaker (S1)
would say given an intended referent. This speaker is assumed to compute the informativity
for each available utterance and then choose an utterance in proportion to its informativity

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raised to the power of the parameter α. En tant que tel, α reflects how informative the listener expects
the speaker to be (with values above 1 speaking for a stronger expectation). This expectation
may vary between individuals, leading to a participant-specific parameter αi:
(cid:1)

(cid:1) (cid:3)

(cid:5)
(cid:3)

(cid:4)

PS1 u j r; αi θij

(cid:4)
∝ PL0 r j u; θij

(cid:5)ai

(2)

The informativity of each utterance is given by imagining which referent a literal listener
(L0), who interprets words according to their lexicon L, would infer upon hearing the utter-
ance. This reasoning depends on what kind of semantic knowledge (word–object mappings, je)
the speaker thinks the literal listener has. For familiar objects, we take semantic knowledge to
be a function of the degree-of-acquisition of the associated word, which we assume to vary
between individuals (θij).

(cid:4)

(cid:1) (cid:3)

(cid:5)

PL0 r j u; θij

(cid:4)
∝ L u; r j θij

(cid:5)

(3)

This modeling framework describes how different information sources are integrated and
how individuals might differ from one another. More specifically, we assume individual differ-
ences to arise from varying sensitivities to the three information sources (captured in the
participant-specific parameters ρi, ai, and θi, j). The process by which information is integrated
is thought to follow the same rational (Bayesian) procedure for all participants. Given
participant-specific values for the three sensitivity parameters, this model allows us to generate
participant-specific predictions for situations in which information needs to be integrated.
Suivant, we describe how we estimated these participant-specific parameter values based on
the data collected in Part 1.

Parameter Estimation. Models to estimate parameters were implemented in the probabilistic
programming language webppl (Homme bon & Stuhlmüller, 2014). As noted above, the three
information sources were: sensitivity to common ground ( ρi), expectations about speaker infor-
mativeness (ai), and semantic knowledge (θij). Chiffre 1 shows which tasks informed which
parameters. All parameters were estimated via hierarchical regression (mixed-effects) models.
C'est, for each parameter, we estimated an intercept and slope (fixed effects) that best
described the developmental trajectory for this parameter based on the available data.
Participant-specific parameters values (random effects) were estimated as deviations from
the value expected for a participant based on their age (standardized so that minimum age
était 0). Details about the estimation procedure can be found in the supplementary material
and code to run the models can be found in the associated online repository.

The parameters for semantic knowledge (θij) were simultaneously inferred from the data
from the mutual exclusivity, the comprehension, and the production experiments. To leverage
the mutual exclusivity data, we adapted the RSA model described above to a situation in
which both objects (novel and familiar) had equal prior probability (c'est à dire., no common ground
information). In the same model, we also estimated the parameter for speaker informativeness
(see below).

For the comprehension experiment, we assumed that the child knew the referent for the
word with probability θij. If θij indicated that they knew the referent (a coin with weight θij
comes up heads) they would select the correct picture; if not they would select the correct
picture at a rate expected by chance (1/6). De même, for the production experiment, nous
assumed that the child knew the word for the referent with probability θij. If θij indicated that
they knew the word (a coin with weight θij comes up heads), we assumed the child would be
able to produce it with probability γ. This successful-production-probability γ was the same for

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all children and was inferred based on the data. This adjustment reflects the finding that chil-
dren’s receptive vocabulary for nouns tends to be larger than the productive (Clark & Hecht,
1983; Frank et al., 2021). Taken together, for each child i and familiar object j there were three
data points to inform θ: one trial from the mutual exclusivity, one from the comprehension and
one from the production experiment.

As noted above, the participant- and object-specific parameter (θij) was estimated in the
form of a hierarchical regression model: θij = logistic(βθ
1;j); each word’s lexical devel-
opment trajectory (the intercept βθ
1;j of the regression line for each object) était
estimated as a deviation from an overall trajectory of vocabulary development. The intercept
and slope for each item were sampled from Gaussian distributions with means μθ
1 and var-
∼ N(μθ
iances σθ
1 represented the overall vocabulary
development independent of particular familiar word–object pairings, and σθ
0 and σθ
1
represented the overall variability of intercepts and of slopes between items.

0;j and slope βθ

0;j + i · βθ

0) and βθ
1;j

0 and μθ

∼ N(μθ

1: βθ
0;j

1). μθ

0, σθ

1, σθ

0, μθ

The parameter representing a child’s expectations about how informative speakers are (ai),
was estimated based on the data from the mutual exclusivity experiment. As mentioned above,
this was done jointly with semantic knowledge in a RSA model adopted to a situation with
equal prior probability of the two objects (novel and familiar). Ainsi, for each child, there were
16 data points to inform α.

To estimate the participant specific parameter, we used the same approach as for semantic
connaissance. C'est, αi was estimated via a linear regression – αi = βα
0 et
βα
1 defined a general developmental trajectory. Encore, we assumed that children might deviate
from their expectations about speaker informativeness based on their numerical age and so we
estimated i as a deviation from the child’s numerical age k: i ∼ N (k, σα
je ).

1 – in which βα

0 + i · βα

We estimated children’s sensitivity to common ground (ρi) based on the 12 data points from
the discourse novelty experiment. We used a logistic regression model to estimate the average
developmental trajectory: ρi = logistic(βρ
1). To generate participant specific values for ρ
we again estimated i as a deviation from the child’s numerical age k: i ∼ N (k, σρ
je ).

0 + i · βρ

Results

Chiffre 2 visualizes the results for the four sensitivity tasks and the participant-specific model
parameters estimated from the data. In all four tasks, we saw that children performed above
chance (not applicable in the case of word production), suggesting that they made the alleged
pragmatic inference or knew (quelques) of the words for the objects involved. With respect to age,
performance in raw test scores seemed to increase with age in the three tasks relying on
semantic knowledge (mutual exclusivity, word production and word comprehension). Perfor-
mance in these tasks was also correlated (see supplementary material). For discourse novelty,
performance did not increase with age.

The hierarchical nature of the parameter estimation procedure in our model allowed us to
take an aggregate look at these results in what they indicate about the development of sensi-
tivity to the different information sources. For this, we extracted the posterior distributions for
intercepts and slopes for the parameter estimates corresponding to the different information
sources (un, r, and θ) based on which the participant-specific estimates were sampled. These
values can be taken to describe the average developmental trajectory for the respective param-
eter and with that, the sensitivity to the respective information source. For expectations about
speaker informativeness, the intercept was larger than 1 (mode = 1.56; 95% HDI = 0.66–2.38)

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Chiffre 2. Results for the sensitivity tasks. (UN) Proportion of correct responses in each task by age. Colored dots show the mean proportion of
correct responses (avec 95% CI) binned by year. Regression lines show fitted generalized linear models with 95% CIs. (B) Posterior distributions
for each parameter (information source) and participant, ordered by mean value, separate for each parameter. Color shows age group. (C)
Average developmental trajectories for the three sensitivity parameters based on the hyper-parameters extracted from the model.

and the slope was positive (mode = 1.18; 95% HDI = 0.73–2.12) suggesting that already the
youngest children (age was standardized so that minimum age was 0) were expecting the
speaker to be informative and this expectation increased with age. For sensitivity to common
ground, the intercept was positive (mode = 1.96; 95% HDI = 1.32–2) while the slope was
negative (mode = −0.43; 95% HDI = −0.84 – −0.17) showing that sensitivity to common
ground was very high at 3 years of age (probability to select the discourse-novel object =
logistic (1.96) = 0.88) and slightly decreased with age. For semantic knowledge, the intercept
and slope represent the overall vocabulary development independent of particular familiar
word–object pairings (conditional on the familiar objects involved in the study). À 3 années
of age, the average probability to know the label for a word was 0.23 (logistic (−1.21); inter-
cept estimate: mode = −1.21; 95% HDI = −2.47–0.01), which substantially increased with age
(slope estimate: mode = 1.10; 95% HDI = 0.28–1.83). To contextualize the semantic knowl-
edge of the different familiar objects, we correlated the probability to know a word (averaged
across participants) with age-of-acquisition ratings for English translations these words
obtained by Kuperman et al. (2012)1. We found a strong negative correlation of r = −0.59,

1 German ratings were not available for all words.

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suggesting that participants (German children) had less semantic knowledge of words that
were rated (by adult English-speakers) to be acquired later in development.

Le plus important, cependant, we saw considerable variation in raw scores between individ-
uals (voir la figure 2). When focusing on the participant-specific parameter estimates (Figure 2B),
we saw that parameters that were estimated based on more data (sensitivity to common
ground – 12 trials, and expectations about speaker informativeness – 16 trials) had better
defined posterior distributions in comparison to the semantic knowledge parameters, lequel
were based on fewer data (3 trials per object).

Discussion

In Part 1, we estimated participant-specific parameters representing each individual’s sensitiv-
ity to the three information sources. We found that, as a group, children were sensitive to the
different information sources we measured. En outre, there was substantial variation
between individuals in how sensitive they were to each information source. These results pro-
vided a solid basis for studying information integration in Part 2.

PART 2: INTEGRATION

Methods

The study was pre-registered and all data, analysis script and materials are publicly available
(see Part 1 for more information).

Participants. Participants were the same as in Part 1.

Procedure. The task was implemented in the same environment as the tasks in Part 1. Chaque
child completed the combination task in the second testing session. The general procedure
followed that of the discourse novelty task, cependant, only one of the objects was unknown
while the other was familiar. The combination task had two conditions. In the congruent con-
dition, the unfamiliar object was also new to discourse. Par exemple, at the beginning of the
trial, a familiar object (par exemple., a lock) was on one table while the other table was empty. Quand
the agent disappeared, a novel object appeared. When the experimenter returned and used a
novel nonce-word both the mutual exclusivity and discourse inferences pointed to the novel
object as the referent of the novel word (see also Figure 1). In the incongruent condition, le
familiar object was new to discourse and thus the two inferences pointed to different objects
(the mutual exclusivity inference would suggest the novel object but the common ground
would suggest the familiar object). The idea behind having these different conditions was to
increase variability in children’s responses to test the scope of the model. We created matched
pairs for the 16 familiar objects and assigned one object of each pair to one of the two con-
ditions. Ainsi, there were eight trials per condition in the combination task in which each trial
was with a different familiar object. We counterbalanced the order of conditions and the side
on which the discourse-novel object appeared. Responses were coded from a mutual exclu-
sivity perspective (choosing novel object = 1). All children received the same order of trials.
There was the option to terminate the study after 8 trials (two children).

Analysis

We used the rational integration model described above to generate predictions for each partic-
ipant and trial in the combination task based on the participant-specific parameters estimated in

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Part 1. C'est, for each combination of ρ, un, and θ for participant i and familiar object j, the model
returned a distribution for the probability with which the child should choose the novel object.

We contrasted the predictions made by the rational integration model described above to
those made by two plausible alternative models which assume that children selectively ignore
some of the available information sources (Gagliardi et al., 2017). These models generated
predictions based on the same parameters as the rational integration model, the only differ-
ence lay in how the parameters were used.

The no speaker informativeness model assumed that the speaker does not communicate in
an informative way. This corresponds to αi = 0, which causes the likelihood term to always be
1. As a consequence, this model also ignores semantic knowledge (which affects the likeli-
hood term) and the predictions of this model correspond to the prior distribution over objects:

Pno si
L1

r j u; ρif g
ð

Þ ∝ P r j ρi
ð

(4)

On the other hand, the no common ground model ignores common ground information, ρi.
This model takes in object-specific semantic knowledge and speaker informativeness but uses
a prior distribution over objects that is constant across alignment conditions and uniform (par exemple.,
[0.5, 0.5]). This model corresponds to a listener who only focuses on the mutual exclusivity
inference and ignores the common ground manipulation. As a consequence, the listener does
not differentiate between the two common ground alignment conditions.

(cid:4)
P no cg
L1

(cid:1)
r j u; αi θij

(cid:3)

(cid:5)

(cid:4)

(cid:1)

(cid:3)

(cid:5)

∝ PS1 u j r; ai; θij

(5)

We evaluated the model predictions in two steps. D'abord, we replicated the group-level results
of Bohn et al. (2021). C'est, we compared the three models in how well they predicted the
data of the combination task when aggregated across individuals. For this, we correlated
model predictions and the data (aggregated by trial and age group) and computed Bayes Fac-
tors comparing models based on the marginal likelihood of the data given the model.

Deuxième, and most importantly, we evaluated how well the model predicted performance on
an individual level. For each trial, we converted the (continu) probability distribution
returned by the model into a binary prediction (the structure of the data) by flipping a coin
with the Maximum a posteriori estimate (MAP) of the distribution as its weight2. For the focal
and the two alternative models, we then computed the proportion of trials for which the model
predictions matched children’s responses and compared them to a level expected by random
guessing using a Bayesian t-test. Enfin, for each child, we computed the Bayes Factor in favor
of the rational integration model and checked for how many children this value was above 1
(log-Bayes Factors > 0). Bayes Factors larger than 1 present evidence in favor of the rational
integration model. We evaluated the distribution of Bayes Factors following the classification
of Lee and Wagenmakers (2014).

Results

On a group-level, the results of the present study replicated those of Bohn et al. (2021). Le
predictions made by the rational integration model were highly correlated with children’s
responses in the combination task. The model explained around 74% of the variance in the
data and with that more compared to the two alternative models (Figure 3A). Bayes Factors

2 Note that this procedure is not deterministic and the results will slightly vary from one execution to the next
(see also Figure 4).

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Chiffre 3. Group-level model comparison. (UN) Correlation between model predictions and data (aggregated across individuals and binned by
year with 95% HDI) for each trial in the combination experiment. (B) Log-likelihood for each model given the data.

computed via the marginal likelihood of the data (Figure 3B) strongly favored the rational inte-
gration model in comparison to the no common ground (BF10 = 9.1e+53) as well as the no
speaker informativeness model (BF10 = 1.2e+44).

Suivant, we turned to the individual-level results. When looking at the proportion of correct
prédictions (for one run of the coin-flipping procedure), we saw that the rational integration
model correctly predicted children’s responses in the combination task in 72% of trials, lequel
was well above chance (BF10 = 2.15e+14) and numerically higher compared to the two alter-
native models (Figure 4A). Note that the alternative models also predicted children’s responses
at a level above chance (no common ground: 61%, BF10 = 220251; no speaker informative-
ness: 60%, BF10 = 55.4), emphasizing that they constitute plausible alternatives. In the
supplementary material we also compared models with respect to the situations in which they
did or did not correctly predict children’s responses.

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Individual-level model comparison. (UN) Proportion of correct predictions for each model. Solid colored dots show mean with 95%
Chiffre 4.
CI for one run of the coin flip procedure. Light dots show aggregated individual data for the same run. Violins show the distribution of means
pour 1000 runs of the procedure. (B) Distribution of log-Bayes Factors for each individual. Dashed lines show Bayes Factor thresholds of 3, 10
et 100.

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When directly comparing the models on an individual level, we found that the rational
integration model provided the best fit for the majority of children. In comparison to the no
common ground model, 62% of Bayes Factors were larger than 1 et 35% were larger than
10. In comparison to the no speaker informativeness model, 68% of Bayes Factors were larger
que 1 et 45% were larger than 10 (Figure 4B).

Discussion

The results of Part 2 show that the rational integration model accurately predicted children’s
responses in the combination task. Surtout, this was the case not just on a group level, mais
also on an individual level where the model correctly predicted children’s responses in the
majority of trials. En outre, it was more likely to be correct and provided a better expla-
nation of the data compared to two alternative models that assumed that children selectively
ignored some of the information sources.

GENERAL DISCUSSION

Probabilistic models of cognition are often used to describe human performance in the aggre-
gate, but these successes do not necessarily imply that they correctly describe individuals’
judgments. Plutôt, individual judgments could be produced via the operation of simpler heu-
ristics. We investigated this study using rational speech act models of children’s pragmatic
reasoning as a case study, using a computational cognitive model to make out-of-sample pre-
dictions about individual children’s behavior on a trial-by-trial basis. In Part 1, we used data
from four tasks to estimate child-specific sensitivity parameters capturing their semantic
connaissance, expectations about speaker informativeness, and sensitivity to common ground.
In Part 2, we used these parameters to predict how the same children should behave in a new
task in which all three information sources were jointly manipulated. We found strong support
for our focal rational integration model in that this model accurately predicted children’s
responses in the majority of trials and provided a better fit to individuals’ performance
compared to two alternative heuristic models. Taken together, this work provides a strong test of
the theoretical assumptions built into the model and both replicates and extends prior research
that showed pragmatic cue integration in children’s word learning in the aggregate (Bohn
et coll., 2021).

The rational integration model was built around three main theoretical assumptions. D'abord, it
assumes that children integrate all available information sources. The model comparison, dans
which we compared the focal model to two models that selectively ignored some of the infor-
mation sources, strongly supported this assumption. For the majority of individuals – as well as
on a group level – this model provided the best fit. Zooming out, this result strengthens the
assumption that language learning and comprehension are social inferences processes during
which listeners integrate different information sources to infer the speaker’s intention (Bohn &
Frank, 2019; Clark, 2009; Tomasello, 2009). At any given moment, different pathways may lead
to the same goal, and the lack of one type of information source might be compensated by the
availability of another. This view highlights the resilience of human communicative abilities.

Cependant, for some individuals, one of the alternative models provided a better fit. Many of the
Bayes Factors in these cases were relatively close to zero, but in a few cases, there was substan-
tial evidence for the alternative models. Finding out why this is the case and what characterizes
these individuals (e.g. if support for a lesioned model can be linked to other psychological con-
structs like attention or memory abilities) would be an interesting avenue for future research.

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The second assumption built into the model is that the integration process does not change
with age. We did not probe this assumption in the present study because, in order to do so
on an individual level, it would require longitudinal data – an interesting extension for
future work. Enfin, the model assumes that children differ in their sensitivity to the different
information sources but not in the way they integrate information. Even though a model using
this assumption predicted the data well, it would also be interesting to explore structural
differences between individuals. Par exemple, Franke and Degen (2016) conceptualized
individual differences in pragmatic reasoning in terms of mind-reading abilities or “depth of
recursion” (Camerer et al., 2004). In modeling terms, this corresponded to adding additional
layers of speakers and listeners to the RSA model. This approach implies that individual differ-
ences are qualitative (c'est à dire., individuals engage in qualitatively different reasoning processes) et
not merely quantitative as in the model presented here. It would be interesting for future
research to identify situations in which these two approaches could be directly compared to
one another (see Rouder & Haaf, 2021 for a discussion of quantitative vs. qualitative individual
differences).

Although our model explains and predicts data, we should be careful with granting the
processes and parameters in it too much psychological realism. Nevertheless, we think that
when studying individual differences, the model parameters can be interpreted as candidate
latent measures of the psychological processes – this interpretation is not necessarily worse
than using raw performance scores as a description of individuals (Borsboom, 2006).

In further support of the idea that model parameters can capture individual variation, notre
model parameters are estimated by taking into account the structure and the different pro-
cesses involved in the task. This estimation process means that individual parameters can
be based on data from multiple tasks, comme, Par exemple, semantic knowledge was estimated
based on the mutual exclusivity, comprehension and production tasks. Support for such an
approach comes from a recent study that used an RSA-type model to estimate a single param-
eter that captured children’s pragmatic abilities based on data from three tasks (Bohn et al.,
2022un, 2022b). Taken together we think that computational modeling can make an important
contribution to studying individual differences on a process level.

Our study is limited in terms of generalizability because we tested only one sample of chil-
dren growing up in a western, affluent setting. Cependant, the modeling approach put forward
here provides an interesting way of studying and theorizing about cross-cultural differences.
Following Bohn and Frank (2019), our prima facie assumption is that children from different
cultural settings might differ in terms of their sensitivity to different information sources – just
like individuals differ within cultural settings – but the way that information is integrated is
hypothesized to be the same across cultures. This prediction could be tested by comparing
alternative models that make different assumptions about the integration process.

In sum, we have shown that children’s pragmatic word learning can be predicted on a trial-
by-trial basis by a computational cognitive model. Together with previous work that focused
on aggregated developmental trajectories (Bohn et al., 2021), these findings suggest that the
same computational processes – a pragmatic inference process that integrates sources of infor-
mation in a rational manner – can be used to predict group- and individual-level data.

CONTRIBUTIONS DES AUTEURS

Manuel Bohn: Conceptualisation, Analyse formelle, Méthodologie, Visualisation, En écrivant -
brouillon original, Rédaction – révision & édition. Louisa S. Schmidt: Conceptualisation, Enquête,
Méthodologie, Rédaction – ébauche originale, Rédaction – révision & édition. Cornelia Schulze:

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Conceptualisation, Méthodologie, Rédaction – révision & édition. Michael C. Frank: Conceptual-
ization, Rédaction – révision & édition. Michael Henry Tessler: Conceptualisation, Formal anal-
ysis, Méthodologie, Rédaction – révision & édition.

INFORMATIONS SUR LE FINANCEMENT

M.. H. Tessler was funded by the National Science Foundation SBE Postdoctoral Research Fel-
lowship Grant No. 1911790. M.. C. Frank was supported by a Jacobs Foundation Advanced
Research Fellowship and the Zhou Fund for Language and Cognition. The funders had no role
in study design, data collection and analysis, decision to publish, or preparation of the
manuscript.

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