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Developmental Differences in the Structure of Executive Function in Middle Childhood and Adolescence Fen Xu1,2*, Yan Han2*, Mark A. Sabbagh3, Tengfei Wang4, Xuezhu Ren4, Chunhua Li5
1 Department of Psychology, Zhejiang Sci-Tech University, Hangzhou, China, 2 State Key Laboratory of Cognitive Neuroscience and Learning, Beijing Normal University,
Beijing, China, 3 Psychology Department, Queen’s University, Kingston, Canada, 4 Goethe University Frankfurt, Frankfurt a.M., Germany, 5 Beijing No. 12 High School,
Beijing, China
Abstract
Although it has been argued that the structure of executive function (EF) may change developmentally, there is little empirical research to examine this view in middle childhood and adolescence. The main objective of this study was to examine developmental changes in the component structure of EF in a large sample (N = 457) of 7–15 year olds. Participants completed batteries of tasks that measured three components of EF: updating working memory (UWM), inhibition, and shifting. Confirmatory factor analysis (CFA) was used to test five alternative models in 7–9 year olds, 10–12 year olds, and 13–15 year olds. The results of CFA showed that a single-factor EF model best explained EF performance in 7–9-year-old and 10–12-year-old groups, namely unitary EF, though this single factor explained different amounts of variance at these two ages. In contrast, a three-factor model that included UWM, inhibition, and shifting best accounted for the data from 13–15 year olds, namely diverse EF. In sum, during middle childhood, putative measures of UWM, inhibition, and shifting may rely on similar underlying cognitive processes. Importantly, our findings suggest that developmental dissociations in these three EF components do not emerge until children transition into adolescence. These findings provided empirical evidence for the development of EF structure which progressed from unity to diversity during middle childhood and adolescence.
Citation: Xu F, Han Y, Sabbagh MA, Wang T, Ren X, et al. (2013) Developmental Differences in the Structure of Executive Function in Middle Childhood and Adolescence. PLoS ONE 8(10): e77770. doi:10.1371/journal.pone.0077770
Editor: Amanda Bruce, University of Missouri-Kansas City, United States of America
Received February 15, 2013; Accepted September 5, 2013; Published October 29, 2013
Copyright: � 2013 Xu et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Funding: The present study was supported by grants from the National Natural Science Foundation of China (30528027, 31028010, and 31170996) and Zhejiang Provincial Natural Science Foundation of China (Y2110369). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Competing Interests: The authors have declared that no competing interests exist.
* E-mail: [email protected] (YH); [email protected] (FX)
Introduction
Executive function (EF) is the ability to monitor and regulate
different types of cognition and behavior to achieve specific
internal goals [1–2]. EF serves as an umbrella term that includes
multiple processing components, such as attentional control,
cognitive flexibility, set-shifting, inhibition, intentional control,
purposive action, set maintenance, working memory, and plan-
ning [3–5]. Among these components, updating working memory
(UWM), inhibition, and shifting are the most widely researched EF
processes [2,6–8], because they are lower-level (i.e., supposedly
implicated in complex executive components, such as planning),
and relatively well-defined [2]. UWM (often termed working
memory by most authors) refers to the processes involved in
monitoring and updating representations in working memory by
adding new relevant information and deleting no-longer-relevant
information [9,2]. Inhibition is the ability to deliberately suppress
the prepotent (i.e., habitual, dominant, autonomic) responses when
those actions run counter to goal achievement [10,2]. Shifting is
the ability to flexibly switch between mental sets, mental
operations or different task rules [11,2].
Although theoretically dissociable, these three aspects of EF
may share some cognitive substrates. Over the last decade, a
number of studies have investigated the EF structure with respect
to these three components with the goal of determining whether
they are indeed separable, or they are best thought of as a mostly
unitary cognitive process. For adult, these investigations have
concluded that though moderately correlated, UWM, inhibition,
and shifting can vary independently which suggests that they may
indeed be separable. This pattern has been called the full three-
factor structure [2,12–13]. However, in childhood, especially
during middle childhood and adolescence, not all studies
replicated this finding [14–22]. Furthermore, few studies, if any,
investigated whether the factor structure of EF changes across age
groups. Thus, the main goal of this study was to investigate the
developmental differences of the structure of these three EF
components during middle childhood and adolescence.
The three-factor structure of UWM, inhibition, and shifting was
first proposed by Miyake et al. based upon data from adults [2]. In
order to examine the distinctiveness of these three EF components
in college students, Miyake et al. used relatively simple tasks that
were thought to tap each of the three main factors of EF
separately, such as running memory, Stroop, number-letter, to
index UWM, inhibition, and shifting respectively. Performance on
these tasks was then submitted to confirmatory factor analysis
(CFA), to extract latent variables capturing the unique covariances
among the tasks in each factor battery. Using CFA, they compared
models with one, two, or three factors. The results indicated that
the full three-factor model was the best fit model relative to models
with fewer factors. They concluded that UWM, inhibition, and
shifting were indeed distinguishable, yet correlated EF compo-
nents, namely diversity of EF. Since then, evidences from both
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behavior studies [12–13] and neuroimaging studies [23–24] have
supported the claim that UWM, inhibition, and shifting are
diverse.
Intriguingly, the three-factor structure obtained in adults has
not been replicated in young children [14–17]. A series of studies
conducted by Wiebe and colleagues found that in a sample of
children between 2 and 6 years of age, the tasks tapping inhibition
and working memory loaded on a single latent factor, that is,
inhibition and working memory were not separable [14–16].
Similar to the findings of Wiebe and colleagues, Hughes, Ensor,
Wilson, and Graham found that a single-factor structure best
captured the relationship among working memory, inhibition, and
planning at the ages of 4 and 6 in a longitudinal study [17].
Contrary to the studies with young children, previous research
focused on middle childhood and adolescence has reported mixed
results [18–22]. In a group of 7–9-year-old children, Brydges,
Reid, Fox, and Anderson observed that a single-factor model was
sufficient to account for performances on a battery of tasks tapping
UWM, inhibition, and shifting [18]. However, some researchers
found that with slightly older children, two of the three executive
components might be distinguishable [19–20]. For example, in
children aged 9 to12 years, a two-factor model including UWM
and shifting best accounted for EF performance after controlling
for what they called non-executive factors (i.e., naming factor,
participants were required to rapidly name geometrical figures,
digits, or letters in tasks loading the naming factor) [19]. A two-
factor model was also suggested for 11–12 year olds by St Clair-
Thompson and Gathercole who used exploratory factor analysis to
identify two executive factors: inhibition and UWM [20]. Finally,
some research that included still older children has provided
evidence for a three-factor model [21–22]. For instance, the study
by Wu et al. supported the three-factor structure including UWM,
inhibition, and shifting in 7–14-year-old children [21]. Similar
results were reported by Lehto, Juujärvi, Kooistra, and Pulkkinen
in a sample of children aged 8 to 13 years [22].
From this brief review of the developmental work, it appears
that one potential reason for the mixed results is because the
studies used participants from different age spans [18–20]. The
studies that find for one-factor structure tend to include much
younger children than the studies that find evidence for three-
factor structure. To date, studies have not been able to address the
possibility that there may be developmental changes in the factor
structure of EF. Most of the research with school-aged children
collapsed participants across the age range they studied, for
example, from middle childhood to post-adolescence [19,21–22].
Doing so may have obscured important developmental changes in
the factor structure of EF that we might predict to be present
based upon findings. Moreover, UWM, inhibition, and shifting
have different developmental trajectories during that period,
specifically improve quickly during middle childhood, and
gradually mature through adolescence [25–28]. A second possible
reason for the mixed results is that different studies used different
measures to assess the same latent factor. For example, the latent
factor inhibition was indicated by Eriksen Flankers task and Go/
no-go task in some studies [18], but by Tower of London and
Matching Familiar Figures Test in other studies [22].
Given the developmental differences [25–28], it is necessary to
examine the factor structure of EF across age groups. To date,
there have been just two studies along these lines, with disparate
findings. In one, Huizinga, Dolan, and van der Molen selected
four age groups (7 years old, 11 years old, 15 years old, and 21
years old) to investigate the relationships of UWM, inhibition, and
shifting. They did not find that the factor structure of EF changed
with age in their study, only UWM and shifting were separable in
all age groups, even in the adult group [28]. In the second, Shing,
Lindenberger, Diamond, and Davidson divided children and
adolescents into three age groups (4–7 years, 7–9.5 years, and 9.5–
14.5 years), and found that the factor structure of EF gradually
separated with age. More specifically, memory maintenance and
inhibitory control were not separable in 4–7 year olds and 7–9.5
year olds, but they were separable in 9.5–14.5 year olds [29].
Their results are difficult to integrate with others, because they
used memory maintenance rather than UWM.
Thus, in the current study, we examined the developmental
differences of the structure of UWM, inhibition, and shifting in
middle childhood and adolescence. Recently, some researchers
argued that the degree of unity or diversity of EF structures may be
different at different age groups [26,30]. According to this view
and previous findings [18–22,29–30], we hypothesized the
developmental trend in the factor structure of EF may be from a
one- or two-factor model to a three-factor model across
development. Specifically, on the basis of previous findings found
in 7–9 year olds [18,29] and adult sample [2,12], we hypothesized
a one-factor model of EF (that incorporates UWM, inhibition, and
shifting) might best explain the performance of 7–9 year olds, but
that the full three-factor model may best explain the performance
of older children aged 13–15 years old.
Following the approach of Miyake and his colleagues [2,12], we
used tasks that were designed to tap a single EF component while
placing minimal demands on other EF components. Performance
on these tasks was then submitted to CFA to characterize the fit of
five possible models, which include the traditional three-factor
model proposed by Miyake and colleagues, one one-factor model,
and three two-factor models (see Table 1). To characterize
developmental changes in the factor structure of EF, EF tasks were
administrated to children and adolescents aged 7–15 years old
who were divided into three age groups (7–9 years old, 10–12
years old, and 13–15 years old). This age range and group division
was chosen because it captures the period over which previous
studies have suggested that the factor structure of EF changes from
having a one-factor structure (7–9 years old) [18,29] to a more
diverse structure [25,29]. Finally, because CFA is a large sample
technique (sample size should be at least 100), and the use of larger
samples tend to provide more precise and stable factor structure,
the sample size in each age group was relatively large in
comparison to other studies (n = 140–165).
Methods
Ethics Statement Guardians and teachers were given a letter explaining the
purpose of this study. Written informed consent was obtained from
each participant’s guardian. All procedures were approved by the
ethics committee of the State Key Laboratory of Cognitive
Neuroscience and Learning, Beijing Normal University.
Participants A total of 457 children and adolescents were recruited from
three primary schools and three junior middle schools of a large-
sized town located in east China. All participants received a
notebook as gift for their participation. According to the previous
findings [18,25,29], the sample was divided into three age groups:
7–9 years (M = 8.78 years, SD = 0.57, 73 boys, n = 140), 10–12
years (M = 11.59 years, SD = 0.88, 84 boys, n = 165), and 13–15
years (M = 14.41 years, SD = 0.86, 76 boys, n = 152). Most
participants came from rural areas of China, where most families
belonged to low to middle socioeconomic status (SES) group.
The highest education level of their parents was as follows:
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approximately 4.3% of parents had earned an undergraduate
education degree, 3.3% had received a junior college education
degree, 18.5% had gotten a high/technical secondary school
diploma, 59.8% had received a junior high school diploma, and
14.3% had a diploma of primary school. We used the non-verbal
Raven Standard Progressive Matrices (China Revised edition,
SPM-CR, 1989) [31] to assess participants’ intelligence. Based on
the norm of the Chinese version for each age group, raw scores of
the SPM-CR were converted to standardized scores. All partic-
ipants had normal intelligence on the basis of the standardized
scores of the SPM-CR, with mean standardized scores between
70.23 and 84.98 (SD, between15.36 and 26.51) in 7–9 year olds,
between 60.58 and 72.09 (SD, between 15.36 and 26.51) in 10–12
year olds, and between 60.25 and 73.80 (SD, between 18.41 and
29.77) in 13–15 year olds.
EF Measures All participants completed a battery of EF tasks to tap the three
EF components. The tasks were selected based on two principles.
First, tasks chosen in the present study should be sensitive to the
development differences of UWM, inhibition, and shifting during
middle childhood and adolescence. Second, we used relatively
simple tasks that were designed to especially tap one of the three
executive components while placing minimal demands on others
to avoid the problem of task impurity. Specifically, n-back tasks
and running memory tasks were employed to measure UWM.
Both tasks involve constantly monitoring and updating informa-
tion in working memory. The tasks used to tap inhibition were the
go/go-go task and color-word Stroop task. Both tasks require
deliberately inhibiting prepotent responses. The tasks used to tap
shifting were number-pinyin task and dots-triangles task. Both
tasks require shifting between mental sets. Because of possible
cultural differences between western in which these tasks were
originally developed, and the current context (rural China), we
adapted those classic tasks as necessary to ensure that they were
suitable for Chinese children. All EF tasks were computerized, and
were programmed in E-Prime (Version 1.2, Psychological
Software Tools).
Measures of UWM. N-back task. There were two conditions
in the n-back task, 1-back and 2-back, using the same stimulus
materials (adapted from Jaeggi, Buschkuehl, Jonides and Perrig,
2008) [32]. In each condition, a small purple square was presented
at one of eight different locations within a bigger white square. In
the 1-back condition, the participants were told to press the
‘‘same’’ key if the location where the small purple square appeared
was the same as the stimulus shown immediately prior to this
square and to press the ‘‘different’’ key if the location at which the
small purple square was presented was different from the one
prior. In the 2-back condition, participants were instructed to press
the ‘‘same’’ button whenever the stimulus at hand matched the
one presented 2 positions back in the sequence and to press
‘‘different’’ whenever the locations were mismatched. In each
condition, there were 16 practice trials followed by 42 target trials.
Each stimulus was presented for 3000 ms, followed by an 800-ms
interstimulus interval (ISI). The main dependent variable was the
proportion of correct responses.
Running memory task. This task was adapted from Van der
Sluis et al. [19]. In this task, participants were presented with
series of digits successively, which varied in length from 3, 5, 7, to 9
digits. Participants were asked to constantly recall the last 3 digits
presented to them. To ensure continuous updating, participants
were asked to say aloud the last 3 digits they had seen, regardless of
where they were in the sequence. Participants achieved this by
adding the latest digit to a cluster and dropping the oldest one, and
then saying the new cluster of 3 digits out loud. For example, if the
digits presented were ‘‘5, 7, 3, 1, 6’’, the participants should have
read ‘‘5…57… 573…731…316’’, and then recalled ‘‘316’’ at the
end of the trial. The length of the sequences varied unpredictably
for the participants. The task consisted of 12 target sequences (3
lists of each sequence length), resulting in 84 clusters of digits to be
recalled. Before the target list began, there were 3 practice
sequences (1 of length 3, 5, 9). Digits within a sequence were
presented serially with 1000-ms per digit, followed by 1000-ms
blank screen. The score was the proportion of digit clusters
recalled correctly.
Measures of inhibition. Go/no-go task. This task was
adapted from Eigsti et al. [33]. Participants were instructed to
press the spacebar as quickly as possible whenever a target (go)
stimulus (a square with a left diagonal) was presented (75% of
trials) but to inhibit the response when the non-target (no-go)
stimulus (a square with a vertical line in the middle) appeared on
the screen (25% of trials). To measure the development of
inhibition in the sample whose age was older than 6 years, the task
included three conditions: the number of go trials before a no-go
trial varied as either 2, 4, or 6. The more go trials that precede a
no-go trial, the more difficult it is to inhibit the preponderant
response generated by go trials. The duration of each stimulus was
500 ms with an ISI ranging from 800 to 1200 ms. This task
consisted of 96 experimental trials and 15 practice trials. The
proportion of successfully inhibited no-go stimuli was the
dependent measure.
Color-word Stroop task (Chinese character version) [34]. In this
task, the four keys (Z, X, N, M) on the keyboard represent the four
colors (red, yellow, blue, and green). Participants were required to
name the color of a stimulus by pressing the key corresponding to
the color on each trial. There were three conditions: (1) in the
Table 1. Five alternative models tested in this study.
Models
1. Full three-factor Three EF components are separable, though correlated
2. One-factor Three EF components are not separable. All tasks tapping UWM, inhibition, and shifting load on a single latent factor
Two-factor models
3. UWM & Inhibition-Shifting collapsed UWM is separable from inhibition and shifting; inhibition and shifting are not distinguished
4. Shifting & Inhibition-UWM collapsed Shifting is separable from inhibition and UWM; inhibition and UWM are not distinguished
5. Inhibition & Shifting-UWM collapsed Inhibition is separable from shifting and UWM; shifting and UWM are not distinguished
Note. UWM, updating working memory. doi:10.1371/journal.pone.0077770.t001
The Structure of Executive Function
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baseline condition, participants must name the ink color of patches
colored red, blue, yellow, or green; (2) in the incongruent
condition, there is a mismatch in the semantic and the color of
Chinese characters (e.g., Chinese character for ‘‘red’’ shown in
green ink), and the participants were asked to judge the printed
color of a word while ignoring its meaning; (3) in the congruent
condition, the color-words were printed in congruent ink colors
(e.g., Chinese character for ‘‘red’’ shown in red ink), and
participants also need to judge the name of color of a word. This
task included 24 baseline trials in block 1, and 24 incongruent
trials with 6 congruent trials in block 2. The participants also
received two blocks of 20 trials (8 baseline trials in block 1, 10
incongruent trials and 2 congruent trials in block 2) for practice.
Stimuli were presented for 3500 ms, and the ISI was 800 to
1200 ms. The dependent variable was the reaction time (RT)
difference between the trials in the baseline condition and the trials
in the incongruent condition.
Measures of shifting. Number-pinyin task. This task was
derived from number-letter task used by Rogers and Monsell [35]
and Miyake et al [2]. In the original number-letter task,
participants switched between classifying numbers (2, 4, 6, and 8
for even; 3, 5, 7, and 9 for odd) and classifying English letters (G,
K, M, and R for consonant; A, E, I, and U for vowel). In the
current study, we replaced English letters with Chinese pinyins (b,
p, m, and f for the initial consonant of a Chinese syllable; a, e, i, and ü for the simple vowel of a Chinese syllable) since Chinese
pupils are not familiar with the vowels and consonants in English.
A number-pinyin pair (e.g., 3e) was presented in one of the four
quadrants on the screen. The participants were instructed to judge
whether the number was odd or even when the number-pinyin
pair was presented in one of the bottom quadrants whereas they
were asked to judge whether the pinyin was a consonant or vowel
when the pair was presented in one of the top quadrants. This task
consisted of three blocks. The number-pinyin pair was always
presented in one of the bottom quadrants for the first block (30
target trials, 12 practice trials), always in the top quadrants for the
second block (30 target trials, 12 practice trials), and in the
clockwise rotation around all four quadrants for the third block (60
target trials, 20 practice trials) in which the participants had to shift
between the number task and the pinyin task. The duration of
each number-pinyin pair was 6500 ms. After a response was given,
the next number- pinyin pair was presented. The time interval
between the response and the next pair was 1000 ms. The
dependent variable was the difference between the average RTs
on alternation trials in the third block and the average RTs of the
trials from the first two blocks.
Dots-triangles task. This task was adopted from Huizinga et al.
[28]. Different numbers of red dots or green triangles were
presented in a 464 grid, and there were three to eight dots or triangles per half of this grid. In the dots task, the participants were
instructed to decide whether there are more dots in the right or left
(in block 1, 30 target trials and 10 practice trials). During the
triangles task, the participants had to judge whether there are more
triangles in the top or bottom (in block 2, 30 target trials and 10
practice trials). In the third block, four ‘‘dots’’ tasks and four
‘‘triangles’’ tasks appeared alternately (72 target trials and 16
practice trials). Each dot or triangle pattern was presented in the
middle of the screen for 3500 ms until a response was given and
was then followed by 1000 ms ISI. Similar to the Number-Pinyin
task, the dependent variable was the difference between the
average RTs of the alternative trials in the third block and the
average RTs of the trials from the first two blocks.
Procedures All tasks were administered in a quiet classroom. All participants
were tested for non-verbal Raven standard progressive matrices in
groups of 8–30 students for 30–40 minutes. The running memory
task was administered individually for all participants. The
remaining EF tasks were tested individually for 7 and 8 year olds
and simultaneously in groups of two for 9–15 year olds.
Participants sat at separate tables and used different computers
during simultaneously testing procedures. EF measures took place
in two sessions. Each session lasted approximately 30–40 minutes
for a total of 60–80 minutes. The tasks administered in Session 1
included the Stroop, dots-triangles, 1-back, and 2-back. Tasks in
Session 2 included the go/no-go, number-pinyin, and running
memory. The interval time of the two sessions was approximately
1 week. The order of the two sessions was counterbalanced across
participants. Psychology graduate students who were trained prior
to testing administered the tests.
Outliers In each executive task, missing data were identified for any
accuracies and RTs that exceeded 3 standard deviations in each
age group. We also performed bivariate outlier analyses on the
correlations among these tasks designed to tap the three EF
components. Specifically, outliers were identified by computing
leverage, student t, and Cook’s D values. Three participants were
removed due to these analyses (i.e., levers values.0.05, t values.
|3.00|, or Cook’s D values .1.00). Moreover, we performed a
two-stage trimming procedure for three tasks (Stroop, number-
pinyin, and dots-triangles) in which RT acted as the dependent
variable. First, all incorrect trials and trials shorter than 150 ms
(too fast to be meaningful) were excluded from the analysis for
each participant. Second, we followed the same procedures used in
previous studies [28,35]. If the accuracy of performance was less
than 55% in one of the conditions in these three tasks, the
corresponding dependent variables of those tasks were coded as
missing (baseline condition and incongruent condition in Stroop
task, alternative condition and repetition condition in dots-
triangles task and number-pinyin task). After the trimming
procedures above, the missing values amounted to 7.4% for 7–9
year olds, 4.2% for 10–12 year olds, and 3.6% for 13–15 year olds.
Statistical Analysis Analysis of covariance (ANCOVA) was used to assess age effects
on each measure with gender as a covariate. To assess the
structure of UWM, inhibition, and shifting, CFA was performed in
Mplus version 6.0 [36] with the maximum likelihood method.
According to past studies, we used multiple fit indices to evaluate
the fit of each theoretical model, including chi-square (x 2 ), x
2 /df,
root-mean-square error of approximation (RMSEA), comparative
fit index (CFI), and Akaike Information Criterion (AIC) [37].
Models were considered to be good fits with non-significant x 2
values at the 0.05 level, x 2 /df of less than 2, CFI of more than
0.90, RMSEA of less than 0.08, and smaller AIC values [38]. In all
of the following analyses, the directionality of the dependent
variables on the basis of RT was reversed so that higher scores
indicated better performance.
Results
Descriptive Statistics and Significance Test of Development for each Task
The mean scores, standard deviations, skewness, and kurtosis
for performance on each executive task for each age group were
listed in table 2. All variables showed normal distributions in each
The Structure of Executive Function
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age group (i.e., absolute value of skewness ,2 and kurtosis ,7)
[39]. Cronbach’s alpha or the split-half (odd–even) correlation was
computed as index of internal consistency for each of the variables.
As is shown in table 2, all estimates were higher than 0.78,
indicating reasonable reliability. The zero-order correlations
among these executive tasks were generally low (r = 0.36 or lower)
in each age group (see Appendix).
For the 2-back, preliminary analyses suggested that the gender
difference reached a significant level, though the effect size was
small. Moreover, gender did not interact with age on any tasks.
Even so, we used gender as a covariate in follow-up analysis to
ensure that the effect of age would not be affected by gender.
Analysis of covariance (ANCOVA) with gender as a covariate
resulted in significant main effects of age on all executive tasks,
F = 3.17,85.92, all p,0.05, g2 = 0.01,0.28 (see table 2). The findings showed that all executive tasks used in the present study
were sensitive to the developmental differences in EF across the
three age groups. In addition, post-hoc Bonferroni tests showed
that the performance for the 1-back, 2-back, running memory, go/
no-go, and Stroop tasks was better in 13–15 year olds than in 10–
12 year olds, and better in 10–12 year olds than in 7–9 year olds.
However, for the performance on the number-pinyin and dots-
triangles tasks 7–9 year olds did not differ from 10–12 year olds,
but 13–15 year olds significantly outperformed 10–12 year olds.
Confirmation Factor Analysis Multi-group CFA was carried out to evaluate whether the factor
structure of EF performance was the same across the three age
groups. Guided by existing research, we first established the best
fitting model for the entire sample (7–15 year olds). The results of
CFA showed that the fit of the full three-factor model was better
than the one-factor model and two-factor models (see table 3),
suggesting that these three executive components were distin-
guishable from each other in 7–15 year olds. Next, to assess
whether the three-factor construct was applicable to each age
group (7–9 year olds, 10–12 year olds, and 13–15 year olds), multi-
group CFA models were established in the three age groups. First,
a configural invariance model was established as the baseline
model for the multi-group comparison. In this baseline model, the
configuration of factor loading was set to be identical for each age
group, while parameters (e.g., specific factor loadings, factor
variance, etc.) were free to vary across age groups. This baseline
model, however, was not successful and the minimum requirement
of multi-group comparison was not met. This suggested that the
three-factor construct may be appropriate for one of the three age
groups but not for every age group.
According to our hypothesis that the factor structure of EF may
be different at different age groups, the five alternative models
were tested for each age group separately using CFA. Table 4
presents the fit results of these models in each age group. In 7–9
year olds, both the one-factor model and full three-factor model
were acceptable models according to the fit indexes (see table 4). In
that case, we should select the simpler model based on parsimony
principle [14,37], so the one-factor model (Model 2) was preferred.
Furthermore, according to AIC which can be used to compare
competing models [40], the one-factor model is preferred because
it has smaller AIC than the full three-factor model (see table 4).
The results suggested that UWM, inhibition, and shifting were not
statistically dissociable in 7–9 year olds, that is, the structure of EF
was unitary in this age range (see figure 1 A). The same was true
for 10–12 year olds where the CFA results again suggested that a
one-factor model (model 2) provided the most parsimonious
account of EF performance (see table 4), which suggested that the
unitary construct was still appropriate for describing the relation-
ship of the three components in 10–12 year olds (see figure 1B).
The single latent factor was named Executive Function. For the
Table 2. Descriptive statistics and age group differences on all executive tasks in each age group.
7–9 years old 10–12 years old 13–15 years old ANCOVA
Tasks M(SD) Ske Kur M(SD) Ske Kur M(SD) Ske Kur F P g 2
Reliability
1-back (%) 86.21(10.58) 21.42 1.90 91.12(6.36) 21.18 2.09 93.41(4.69) 2.51 2.06 33.13 ,.001 .13 .82 a
2-back (%) 58.64(13.68) .44 2.32 66.30(13.83) .08 2.70 71.22(13.77) 2.28 2.76 29.52 ,.001 .12 .78a
Running Memory (%) 69.99(12.36) .04 2.47 80.90(10.21) 2.25 2.85 86.66(9.81) 2.69 2.20 85.92 ,.001 .28 .84 a
Go/no-go (%) 50.21(15.62) 2.02 2.69 58.42(18.06) 2.12 2.68 69.37(17.85) 2.46 2.52 43.10 ,.001 .16 .91 b
Stroop (ms) 415.47(190.62) .18 2.41 309.48(185.82) .58 2.01 230.29(115.01) .55 .36 41.57 ,.001 .16 .94b
Number-pinyin (ms) 782.88(307.07) .04 .90 722.03 (284.28) .46 .19 608.42(236.76) .88 .20 15.28 ,.001 .01 .83 b
Dots-triangles (ms) 611.46 (328.82) .48 2.07 591.55(284.37) .65 .19 543.05(289.69) .74 .20 20.59 ,.001 .08 .92 b
Note. Ske,Skewness, Kur, kurtosis. a Reliability was calculated using Cronbach’s alpha.
b Reliability was calculated by adjusting split-half (odd–even) correlations with the Spearman-Brown prophecy formula.
doi:10.1371/journal.pone.0077770.t002
Table 3. Goodness of fit indices for alternative CFA models for total sample.
Models x 2
df P x 2
/df RMSEA CFI AIC
1. Full three-factor model
19.89 11 .05 1.81 .04 .97 71.74
2. One-factor 62.04 14 .00 4.43 .09 .86 104.04
Two-factor
3. UWM & Inhibition- Shifting collapsed
28.08 13 ,.01 2.16 .05 .96 100.98
4. Shifting & Inhibition- UWM collapsed
37.16 13 ,.01 2.86 .06 .93 100.31
5. Inhibition & Shifting - UWM collapsed
29.02 13 ,.01 2.23 .09 .78 98.52
Note. The best fitting model is indicated in bold. UWM, updating working memory, RMSEA, root-mean-square error of approximation; CFI, comparative fit index; AIC, Akaike Information Criterion. doi:10.1371/journal.pone.0077770.t003
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13–15 year olds, however, there was a shift for them, the three-
factor model (model 1) provided the best fit of the five models (see
table 4). These findings suggest that the latent variables of UWM,
inhibition, and shifting each constituted statistically separable
component of 13–15 year old children’s EF performance. In other
words, for the older group, the three EF components were clearly
distinguishable, though they are moderately correlated with each
other for children aged 13 and older (see figure 1 C).
We further examined whether the regression coefficients (factor
loadings) of the observed indicators of Executive Function (the
single latent factor) were identical in both 7 to 9 years of age and
10 to12 years of age. To address this issue, multi-group CFA was
conducted. We first established a configural invariance model. The
fit of this model displayed acceptable fit to the data, x 2
= 29.90,
x 2 /df = 1.07, CFI = 0.98, RMSEA = 0.02. Then, we nested within
the configural invariance model, a metrical measurement invari-
ance model in which the factor loadings were constrained to be
equal across the two groups in addition to the loading patterns.
The fit of the metrical measurement invariance model was not
satisfactory, particularly with respect to the value of CFI,
x 2
= 42.96, x 2 /df = 1.21, CFI = 0.87, RMSEA = 0.04. A direct
chi-square comparison also indicated that there was a significant
difference between the configural invariance model and the
metrical measurement invariance model (Dx 2
= 13.06, Ddf = 6, p,0.05), suggesting that the factor loadings differed between the
two younger age groups (see figure 1A and figure 1B). Executive
Function (the single latent factor) explained 30%, 23%, 25%,
12%, and 26% of the variance in the 1-back, 2-back, running
memory, go/no-go, and number-pinyin, respectively, in 7–9 year
olds, but only 15%, 16%, 21%, 7%, and 10% of the variance in
10–12 year olds.
Discussion
The present study investigated the developmental changes in
the factor structure of EF. We administrated a battery of
appropriate measures tapping UWM, inhibition, and shifting in
a large sample of Chinese children and adolescents, and then used
CFA to characterize the latent factor structure of EF among three
age groups: 7–9 years, 10–12 years, and 13–15 years. The results
of CFA indicated that over development, the factor structure of EF
changed from a one-factor to a full three-factor model. Specifi-
cally, a single factor accounted for EF performance in both 7–9
years and 10–12 years, though even between these periods there
was some development in the specific factor loading patterns. For
the oldest group, however, a three-factor model best accounted for
the performance of UWM, inhibition, and shifting. That is, the
three EF components separated into three distinct components at
13–15 years of age. Put another way, the results of CFA indicated
that the structure of the three components developed from unity to
diversity. Our findings provide evidence for the age differentiation
hypothesis which postulates that the structure of cognitive abilities
develops from a relatively unified, general ability to more
differentiated, specific cognitive abilities with child development
[41–42].
Our results are similar to those of Shing et al. [29], who also
found that the specific executive components gradually separated
across age groups. However, Shing et al. only examined the
separation of memory maintenance and inhibitory control, and
found that they were separable in 9.5–14.5 years. In the current
study, we found that the constructs of UWM, inhibition, and
shifting were distinct at 13–15 years of age but not earlier. The
slight inconsistency between these results may come from the
different tasks chosen in the two studies. Specifically, the tasks used
in the study by Shing et al. only assessed set maintenance whereas
Table 4. Goodness of fit indices for alternative CFA models in each age group.
Models x 2
df P x 2
/df RMSEA CFI AIC
7–9 years old *1. Full three-factor 14.38 12 .37 1.20 .03 .96 59.34
2. One-factor 15.65 14 .34 1.12 .03 .95 56.64
Two-factor
3. UWM & Inhibition-Shifting collapsed 23.87 13 .03 1.84 .08 .68 67.87
4. Shifting & Inhibition- UWM collapsed N.A.
5. Inhibition & Shifting -UWM collapsed 16.27 13 .24 1.25 .04 .89 60.27
10–12 years old 1. Full three-factor 22.10 11 .02 2.01 .08 .81 68.15
2. One-factor 19.24 14 .30 1.37 .05 .95 57.44
Two-factor
3. UWM & Inhibition-Shifting collapsed 26.80 13 .01 2.06 .08 .71 70.80
4. Shifting & Inhibition- UWM collapsed 19.71 13 .11 1.52 .06 .90 61.86
5. Inhibition & Shifting -UWM collapsed 28.10 13 .01 2.16 .08 .68 67.74
13–15 years old 1. Full three-factor 15.72 11 .15 1.43 .05 .95 63.72
2. One-factor 32.51 14 .00 2.32 .09 .74 74.51
Two-factor
3. UWM & Inhibition-Shifting collapsed 24.05 13 .03 1.85 .08 .85 68.05
4. Shifting & Inhibition- UWM collapsed 24.95 13 .03 1.88 .08 .83 68.49
5. Inhibition & Shifting -UWM collapsed 29.02 13 .01 2.23 .09 .78 73.02
Note. The best fitting model is indicated in bold. UWM, updating working memory, RMSEA, root-mean-square error of approximation; CFI, comparative fit index; AIC, Akaike Information Criterion. N. A., not admissible. *not positive definite residual covariance matrix. doi:10.1371/journal.pone.0077770.t004
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Figure 1. Best fit model in each age group. RM = running Memory, G/NG = go/no-go, N–P = number-Pinyin, D–T = dots – triangles. All standardized parameters were significant (P,0.05) except the loading of the Stroop task (dotted line) in 7–9 year olds. A for 7–9 years old, B for 10–12 years old, C for 13–15 years old. doi:10.1371/journal.pone.0077770.g001
The Structure of Executive Function
PLOS ONE | www.plosone.org 7 October 2013 | Volume 8 | Issue 10 | e77770
ours included the requirement to actively update working memory
representations. It is well known that active updating of working
memory has a protracted developmental time course relative to
maintenance [43], which may delay the differentiation of EF
structure in our study.
However, the specific timing of our findings dovetails nicely
with documented changes in cortical functioning that are
happening around the same time in development. EF is often
linked to the functioning of the prefrontal cortex (PFC) [8–9], and
the development of EF appears to be closely linked to the
development of PFC [29]. The PFC goes through dynamic
structural and functional changes around the age of 12. From the
structural perspective, longitudinal neuroimaging studies have
demonstrated that gray matter in the PFC increased throughout
childhood with a maximum size occurring at approximately 12
years, followed by a sharp loss after 12 years of age [44]. At the
functional level, there are critical changes in the patterns of PFC
activation that are elicited during EF performance, including
enhanced activation in critical regions and attenuation in others
between 9 years and 12 years [45]. These changes usually result in
more focal and less diffuse PFC activation as children transition
from childhood to adolescence. The structure and function of PFC
change around 12 years old may be associated with the
separability of EF structure found in present study.
The results of this study run counter to those of Huizinga et al.
[28] who found evidence of only the two latent factors (UWM and
shifting) which were distinguishable in children as well as adults.
The discrepancy between those findings and our own could be
attributed to the characteristics of the three inhibitory tasks. The
three inhibition tasks used in their study (stop-signal, Eriksen
flanker, and smiley pictures) measured three different types of
inhibitory abilities, so a common inhibition factor could not be
extracted, which also led to the inconsistent results in the adult
sample between their study and past adult studies [2]. However,
the two tasks (go/no-go, color-word Stroop) used in our study were
specifically designed to rely on proponent response inhibition and
little else [46], so a common inhibition factor can be extracted in
13–15 years. Also, the age divisions used by Huizinga et al.
differed from ours, and, perhaps most important, the sample size
in each age group in the study of Huizinga et al. was limited,
especially the youngest age group (n = 71).
There were some limitations of our study that should be
addressed in future research. One limitation concerns the missing
data, especially in the young age group. After following standard
practices for data trimming, 7.4% of 7–9 year olds data was
missing. This result may be because the three EF components
undergo rapid improvements during childhood and adole-
scence, so individual differences were considerable. Second, the
participants in the present study came from lower SES families.
Recent evidence has shown that children from low SES families
experience slower EF development relative to children in higher
SES categories, especially in working memory and inhibitory
control [47–48]. The slow development of cognitive abilities may
delay the extent to which those abilities are statistically separable
from a single EF factor [41]. In any case, studies with children
from diverse SES backgrounds may help to establish the
generalizability of the patterns we reported here. Finally, for the
youngest group, performance on the Stroop task did not load on
the single latent factor (Executive Function) in 7–9 year olds,
which was not expected. However, the Stroop task loaded on the
single latent factor in one-factor model for the 10–12 year olds,
and inhibition factor in the three-factor model for the 13–15 year
olds. Given these limitations, it would be worthwhile to confirm
the findings using different tasks, and extend this work with
different EF components in future study.
To conclude, using a relatively large sample, the present study
found that the factor structure of EF changed with children’s
transition from middle childhood to adolescence. In particular, a
single-factor model better accounted for younger children’s EF
performance, whereas a three-factor model considering UWM,
inhibition, and shifting as separate latent variables provided the
best fit for older children’s performance. Our findings further
confirmed the view that the underlying nature of children’s EF
skills vary with age, and suggest that the neurocognitive systems
that support different aspects of EF become increasingly specific
and dissociated with age.
Supporting Information
Table S1 Correlations between executive tasks for each group. Note. * p,.05, **p,.01.
(DOC)
Acknowledgments
We thank all the participants involved in this study for their kindly
cooperation. We are also grateful to those six schools for permitting to do
this research. We also would like to express our gratitude to anonymous
reviewers for their helpful comments.
Author Contributions
Conceived and designed the experiments: FX YH XR. Performed the
experiments: YH TW. Analyzed the data: YH MS TW CL XR.
Contributed reagents/materials/analysis tools: YH MS. Wrote the paper:
FX YH MS TW XR.
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