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Running Head: AFFECT WORKING MEMORY COUPLINGS 1
Momentary Working Memory Performance is Coupled with Different Dimensions of Affect
for Different Children: A Mixture Model Analysis of Ambulatory Assessment Data
Andreas B. Neubauer1,2, Judith Dirk1,2, & Florian Schmiedek1,2,3
1German Institute for International Educational Research (DIPF), Frankfurt am Main,
Germany
2Center for Research on Individual Development and Adaptive Education of Children at Risk
(IDeA), Frankfurt am Main, Germany
3Goethe University, Frankfurt am Main, Germany
Author Note
Andreas B. Neubauer, Department of Education and Human Development, German
Institute for International Educational Research (DIPF), Frankfurt am Main, Germany and
Center for Research on Individual Development and Adaptive Education of Children at Risk
(IDeA), Frankfurt am Main, Germany; Judith Dirk, Department of Education and Human
Development, German Institute for International Educational Research (DIPF), Frankfurt am
Main, Germany and Center for Research on Individual Development and Adaptive Education
of Children at Risk (IDeA), Frankfurt am Main, Germany; Florian Schmiedek, Department of
Education and Human Development, German Institute for International Educational Research
(DIPF), Frankfurt am Main, Germany, Center for Research on Individual Development and
Adaptive Education of Children at Risk (IDeA), Frankfurt am Main, Germany, and Goethe
University, Frankfurt am Main, Germany.
AFFECT WORKING MEMORY COUPLINGS 2
Correspondence concerning this article should be addressed to Andreas B. Neubauer,
Education and Human Development, German Institute for International Educational Research
(DIPF), Frankfurt am Main, Germany. E-Mail: neubauer.andreas@dipf.de
Acknowledgments
This research was part of the FLUX project at the IDeA-Center in Frankfurt am Main,
Germany, which was funded by the Hessian Initiative for the Development of Scientific and
Economic Excellence (LOEWE). We thank Heiko Rölke and the Technology Based
Assessment Group at the DIPF for developing and providing the software to assess children’s
performance and experiences via smartphones. We owe special thanks to Verena Diel, Tanja
Könen, Jan Kühnhausen, Anja Leonhardt, Philipp Wiesemann, and a team of highly
committed student assistants for their important roles in conducting the FLUX project. FS and
ABN further acknowledge support from the Jacobs Foundation (grant number 2016-1245-00).
© 2018, American Psychological Association. This paper is not the copy of record and may not
exactly replicate the final, authoritative version of the article. Please do not copy or cite without
authors' permission. The final article will be available, upon publication, via its DOI:
10.1037/dev0000668
AFFECT WORKING MEMORY COUPLINGS 3
Abstract
Elementary school children’s working memory performance (WMP) fluctuates from moment
to moment and day to day, yet the underlying mechanisms are not well understood. In the
present study, affective states were investigated as predictors of these fluctuations. Inter-
individual differences in the intra-individual affect-WMP associations were expected, and
their structure was explored. One hundred nine children (8-11 years) were investigated in an
ambulatory assessment. Affective states (positive affect, negative affect, activation,
deactivation) and WMP were assessed three times daily for up to 31 consecutive days. In the
whole sample, WMP was lower at occasions with higher negative affect or deactivation,
while there was no overall effect of positive affect or activation. Results of a mixture model
analysis revealed meaningful heterogeneity in these effects: Approximately half of the
children showed comparably weaker effects of affect on WMP, while the other three groups
showed (a) comparably stronger negative effects of negative affect and deactivation; (b) a
comparably stronger positive effect of activation; or (c) comparably stronger negative effects
of negative affect and deactivation and stronger positive effects of positive affect and
activation. Findings emphasize the importance of explicitly considering inter-individual
differences in intra-individual associations. They are discussed in the context of current
frameworks of inter-individual differences in environmental sensitivity.
Keywords: ambulatory assessment; within-person processes; working memory;
differential susceptibility; environmental sensitivity; intra-individual variability
AFFECT WORKING MEMORY COUPLINGS 4
Momentary Working Memory Performance is Coupled with Different Dimensions of
Affect for Different Children: A Mixture Model Analysis of Ambulatory Assessment
Data
Executive functions (EF) describe a set of cognitive processes involved in everyday tasks that
require top-down control (Diamond, 2013). Inter-individual differences in EF in childhood
have been related to positive adjustment throughout the human life span, with better EF
associated with better achievement in school (Gathercole, Pickering, Knight, & Stegmann,
2004) as well as various indicators of psychological adjustment up to 20 years later (e.g.,
physical health and financial situation; Moffitt et al., 2011). Importantly, these studies
conceptualized EF as a more or less stable, person-level (trait) variable, while intra-individual
(day-to-day or moment-to-moment) fluctuations of EF components have only recently
received some attention in research with children and adolescents (Dirk & Schmiedek, 2016;
Riediger, Wrzus, Schmiedek, Wagner, & Lindenberger, 2011). In the present work, we
examine momentary affective experiences as predictors of intra-individual fluctuations in
working memory performance (WMP). WMP requires simultaneous storage and processing
of several elements and thereby requires and encompasses central components of EF (Miyake
et al., 2000). Investigating the antecedents of ups-and-downs in cognitive functioning in
children’s daily lives allows for better understanding the processes that lead to better vs.
worse cognitive functioning in everyday contexts, and thereby potentially opens up
possibilities to improve WMP via interventions targeting these predictors.
Prior research has shown that intra-individual fluctuations in sleep (Könen, Dirk, &
Schmiedek, 2015) and perceived disturbance (Dirk & Schmiedek, 2017) are systematically
“coupled” with intra-individual fluctuations in WMP in elementary school children. In the
present work, we focus on current affective states as potential predictors of WMP.
Specifically, our focus lies on inter-individual differences in intra-individual couplings of
AFFECT WORKING MEMORY COUPLINGS 5
affective experiences and WMP in elementary school children. That is, we investigate if
children differ in the degree to which their WMP is associated with their current affective
state. The next sections will be organized as following: First, we will summarize prior
research that investigated the association between affective states and EF / WMP. We will
primarily focus either on research with children or on research that has specifically
investigated intra-individual associations of these two constructs. Next, we will introduce
environmental sensitivity (Pluess, 2015) as a framework to investigate the structure of inter-
individual differences in these intra-individual couplings. We then present findings from an
ambulatory assessment study with 109 elementary school children.
Associations Between Affect and WMP
Associations between affective states and cognitive functioning have received
substantial attention in the literature. Due to the scarcity of studies specifically targeting
WMP (especially in children) we provide a non-exhaustive overview of studies investigating
either WMP or EF components. Negative affect (NA) has often been negatively associated
with cognitive performance (Ellis, Moore, Varner, A. Ottaway, & S. Becker, 1997), but the
processes underlying this association remain largely unknown. One explanation proposed is
that NA interferes with resources available to work on cognitive tasks, and is therefore related
to poorer EF (Ashcraft & Kirk, 2001; Ellis & Ashbrook, 1988; Ilkowska & Engle, 2010).
Other mediating mechanisms have been proposed as well, such as decreases in serotonin
(Mitchell & Phillips, 2007) or motivational decrements (Brose, Schmiedek, Lövdén, &
Lindenberger, 2012). Furthermore, the hypothalamic–pituitary–adrenal (HPA) axis might also
play an important role in this association, since previous research found that its end product
(cortisol) can have detrimental effects on cognitive performance (Lupien, Gillin, & Hauger,
1999). While the proposed mechanisms for the effect of NA on cognitive performance concur
in predicting a negative association, the role of positive affect (PA) for EF is less clear. Some
AFFECT WORKING MEMORY COUPLINGS 6
(Ashby, Isen, & Turken, 1999) suggest that mild levels of PA should be associated with
slightly elevated dopamine levels and—as a consequence—with better EF. Others argue that
elevated PA occupies cognitive resources as well and should therefore be associated with
diminished performance in EF tasks (Mitchell & Phillips, 2007).
Previous research points toward a deteriorating effect of NA on EF (Patel et al., 2016),
while findings regarding the effects of PA are more inconsistent with some reporting a
positive effect on EF (Palmiero, Nori, Rogolino, D'Amico, & Piccardi, 2015; Yang, Yang, &
Isen, 2013), and others reporting a negative effect (Martin & Kerns, 2011). Most of previous
research has, however, targeted these associations in adult samples and research in children is
comparatively sparse. Investigating the dynamics of EF / WMP in this population would,
however, be highly important because the development and maturation of EF and WMP is
ongoing from birth well into the teen years (Diamond, 2013; Gathercole et al., 2004), and a
better understanding of the processes involved in this developmental phase could hint towards
promising interventions and policy implications.
Two experimental studies revealed similar findings in children as studies among
adults. In one study on children between 9 and 12 years (Fartoukh, Chanquoy, & Piolat,
2014), a negative mood induction lead to decreasing performance in a letter–number
sequencing task (an indicator of WMP), while no effect of a positive mood induction could be
observed (relative to a neutral control condition). Similarly, Pnevmatikos and Trikkaliotis
(2013) showed that an anxiety induction led to poorer inhibitory control (a facet of EF) in
children between 8 and 12 years. That is, these studies suggest that negative affect is
associated with poorer EF in children, while no effect for PA could be observed.
The vast amount of the aforementioned studies has exclusively focused on between-
person associations of affect and EF / WMP. While this approach is certainly informative
when the core focus lies on determining inter-individual differences, it cannot uncover intra-
AFFECT WORKING MEMORY COUPLINGS 7
individual processes, unless unrealistic assumptions are being made (Molenaar, 2004).
Crucially, models explaining the associations between affect and EF such as the resource
allocation model (Ellis & Ashbrook, 1988) target effects that unfold within individuals over
time. Taking a within-person perspective with regard to both study design and data analysis is
paramount to investigate these intra-individual processes (Hamaker, 2012). A few studies
have targeted intra-individual effects of affective states on WMP, and all of these have been
conducted with adults or adolescents. With regard to NA, some studies revealed a negative
intra-individual effect on WMP (Brose et al., 2012; Riediger et al., 2011), while others
(Sliwinski, Smyth, Hofer, & Stawski, 2006; Stumm, 2016) did not find significant intra-
individual associations. Previous findings regarding the intra-individual effect of PA on WMP
are also mixed with some (Brose, Lövdén, & Schmiedek, 2014) reporting a positive
association, others a quadratic association, indicating elevated performance at medium levels
of PA (Riediger et al., 2011), or no association (Stumm, 2016).
Part of the inconsistency in previous research might be attributed to the existence of
meaningful inter-individual differences in the intra-individual coupling of affect and WMP:
While there may be some individuals who exhibit meaningful intra-individual couplings
between PA / NA and WMP, others might not. Aggregating across individuals could therefore
result in a small coupling which could not be detected in these studies because it was masked
by inter-individual differences. In the present study, we specifically target these inter-
individual differences in the intra-individual affect-WMP couplings in children. We now
introduce the theoretical framework of environmental sensitivity (ES), which we utilize to
better understand the structure of inter-individual differences in the intra-individual affect-
WMP couplings in elementary school children.
Environmental Sensitivity and Inter-Individual Differences in Affect-WMP Couplings
AFFECT WORKING MEMORY COUPLINGS 8
The environmental sensitivity framework (Pluess, 2015) considers inter-individual
differences in environmental sensitivity as the core determinant of inter-individual differences
in reactivity that is, the degree to which current experiences affect physiological,
psychological, and behavioral outcomes. According to this view, individuals differ in their
ability to register and process external stimuli (=environmental sensitivity), and these
differences are associated with inter-individual differences in the degree to which they are
affected by their environment (=reactivity). This framework is intended as an integration of
various related theoretical accounts. Among others, these include differential susceptibility
theory (Belsky & Pluess, 2009), vantage sensitivity (Pluess & Belsky, 2013), the diathesis-
stress model (Zuckerman, 1999), the biological sensitivity to context model (Boyce & Ellis,
2005), and the adaptive calibration model (Del Giudice, Ellis, & Shirtcliff, 2011). In a
nutshell, all of these accounts aim to explain inter-individual differences in the effects of
environmental inputs on physiological, psychological, and behavioral outcomes. They differ,
for example, in whether they focus on the effects of positive (VS) or negative environmental
inputs (DS), or both (DST; BSC; ACM), as well as in the origins of these differences (genetic
vs. environmental) and their postulated mechanisms (Ellis, Boyce, Belsky, Bakermans-
Kranenburg, & van IJzendoorn, 2011; Pluess, 2015). On the most general level, however,
they all converge on the prediction that individuals differ in the degree to which
physiological, psychological, and behavioral outcomes are affected by environmental
conditions.
Subsuming these prior accounts in the ES framework, Pluess (2015) identified four
(mutually exclusive) sensitivity types: low sensitivity individuals are characterized by
attenuated responses to environmental inputs. That is, these individuals are barely affected by
either positive or negative environmental conditions. A second group, referred to as
vulnerability group, is hypothesized to respond particularly strongly to negative
AFFECT WORKING MEMORY COUPLINGS 9
environments. Hence, these individuals can be characterized as vulnerable for the impact of
negative environmental effects (sensu a diathesis stress model; Zuckerman, 1999), while they
do not necessarily exhibit a pronounced reaction to positive environmental conditions. The
third group, which Pluess (2015) called vantage sensitivity group, shows the reversed pattern
with enhanced effects specifically of positive environments. Vantage sensitivity is defined as
“the general proclivity of an individual to benefit from positive and presumptively well-being-
and competence-promoting features of the environment” (Pluess & Belsky, 2013), and can
therefore be seen as a tendency to profit from positive environmental conditions. The fourth
group, referred to as general sensitivity, combines elements of the vulnerability group and the
vantage sensitivity group: These individuals are strongly affected by both positive and
negative environmental inputs. Hence, general sensitivity is close to the concept of
differential susceptibility which has been defined as the proclivity to be affected by both
adverse and supportive environmental conditions in a “for-better-and-for-worse” manner
(Belsky & Pluess, 2009).
There has been a vast amount of research investigating differences in the effects of
environmental conditions, most of which has targeted questions related to human
development, in particular development in childhood. Almost exclusively, this research has
measured environmental conditions more or less directly (e.g., as parenting quality, physical
abuse, socioeconomic status, experimentally induced stress) and has targeted a plethora of
outcomes (e.g., academic achievement, attachment style, inhibitory control; see (Belsky
& Pluess, 2009). In the present work, we do not measure positive or negative environmental
conditions and examine their differential effects on WMP or affect. Thus, we do not test
predictions directly derived from the ES framework. We rather utilize central concepts of this
account to examine inter-individual differences in the intra-individual coupling of affect and
WMP in children.
AFFECT WORKING MEMORY COUPLINGS 10
How can the framework of ES, which targets inter-individual differences in reactivity
to the environment, inform hypotheses about the structure of inter-individual differences in
the intra-individual affect-WMP couplings in children? Conceptually, environmental
influences on both affect and WMP can be expected. That is, we can understand both affect
and WMP as outcomes of a common cause: environmental input. Further, we can understand
both of these variables as outcomes in the ES framework. For example, children in the general
sensitivity group will be more strongly affected by environmental inputs (both positive and
negative) in their affect and their WMP compared to children in the low sensitivity group.
Assuming that differences between children in the effect of environment on affect are related
to the same cause (e.g., the same genetic predispositions) and of the same size as differences
in the effect of environment on WMP1, children in the general sensitivity group will show
larger affect-WMP couplings compared to children in the low sensitivity group. Hence, under
these conditions inter-individual differences in affect-WMP couplings can be interpreted as
indicators of differences in ES.
The Present Study
The aim of the present study was to investigate intra-individual couplings of current
affective states and WMP in elementary school children’s everyday lives using ambulatory
assessment (Trull & Ebner-Priemer, 2013). Previous research investigating intra-individual
fluctuations in affect among elementary school children showed that children of this age
report affect in a differentiated fashion. Specifically, Leonhardt, Könen, Dirk, and Schmiedek
(2016) demonstrated that a six-factor model describing the three affect dimensions valence,
energetic arousal, and tense arousal best described the affective experiences reported in a
sample from this population. As discussed by Leonhardt et al. (2016), this three-dimensional
1 We note that, according to Pluess (2015), so far “it remains to be determined whether an individual’s
environmental sensitivity varies across different domains of functioning (e.g., cognitive, emotional, social) or
whether differences in sensitivity affect all domains equally” (p.142). For the interpretation of our findings in
light of the ES framework, we assume the latter.
AFFECT WORKING MEMORY COUPLINGS 11
affect space concurs with the three-dimensional model of affect by Steyer, Schwenkmezger,
Notz, and Eid (1994) and can be related to alternative models of affect such as the two-factor
model (Watson & Tellegen, 1985) and the pleasure-arousal model (Russell & Barrett, 1999).
In the present study, we assessed two of these three dimensions of affective experience—
valence and energetic arousal—by two scales each: Positive affect (PA) and negative affect
(NA) represented the two poles of the valence dimension, activation and deactivation
represented the two poles of the energetic arousal dimension.
Based on previous studies investigating the within-person effects of NA with cognitive
functioning, we hypothesized that indicators of negative affectivity (NA; deactivation) would
show a negative within-person association with WMP. Predictions regarding the effects of
positive affectivity (PA; activation) were less clear, given the inconsistency in previous
research. However, we expected that everyday experiences in our sample would—in many
cases—not exceed mild levels of elevated PA, yielding a positive association between
positive affective sates and WMP.
Given the somewhat heterogeneous findings in previous studies, we further expected
that there would be meaningful inter-individual differences in the intra-individual couplings
of all affect indicators with WMP. To better understand these differences, we utilized central
ideas from the ES framework. This framework allows deriving the expectation that these
differences might be structured into four distinct groups. Specifically, there should be one
group of children who are virtually unaffected by affective experiences in their cognitive
performance (low sensitivity group). A second group of children is expected to show strong
negative effects of negative affective experiences (vulnerability group), while a third group
should exhibit pronounced positive effects of positive affective experiences (vantage
sensitivity group). Finally, a fourth group is expected that is strongly affected by both positive
and negative affective experiences (general sensitivity group).
AFFECT WORKING MEMORY COUPLINGS 12
Method
The present study comprised an ambulatory assessment (AA) phase during which
children repeatedly worked on cognitive tasks and reported on potential covariates of their
cognitive performance. Before and after the AA, extensive pre- and post-test measures were
obtained in a classroom setting. The focus of the present work is on the AA phase.
Participants
The sample comprised 110 children that attended the third (n = 50) and fourth grade (n
= 60), respectively, of an elementary school. The present research is conducted on an already
existing data set (Dirk & Schmiedek, 2016). Hence, sample size was not planned with regard
to the specific aims of the present study. One child was discarded for the analyses because he
did not provide any concurrent measures of WMP and affective experiences at the same
measurement occasion. The analyses are therefore based on the remaining 109 children (45
girls; 8-11 years; Mage = 9.88, SDage = 0.61). We chose to include only children of Grades 3
and 4 (but not younger) because children participating in this study needed to possess
elementary reading and arithmetic skills in order to understand and perform the cognitive
tasks. Notably, a recent review on ecological momentary assessment (EMA) in children and
adolescents concluded that self-report EMA studies are feasible with children of seven years
or older, but it is unclear whether they can be used with younger children (Heron, Everhart,
McHale, & Smyth, 2017). Both children and their parents provided informed consent.
Participation was voluntary and could be terminated at any point during the study. Children
and parents received money or a gift certificate as remuneration.
Procedure
The study started with 4.5 hours of training and pretesting, distributed across six
school lessons. Among other variables, baseline measures of fluid intelligence, WMP, trait
affect, and school achievement were assessed during this phase. The testing took place as
AFFECT WORKING MEMORY COUPLINGS 13
group testing in the class rooms. In addition to these measurements, children were also trained
in operating the study smartphones for the AA phase. These touchscreen based smartphones
(Dell Streak 5 with Android 2.2 operating system) were programmed with an application that
was specifically developed for this study. All other functionalities of the smartphones (e.g.,
internet browser, cellular reception, microphone, application menu) were disabled; it was
further ascertained that children could not exit or terminate the study application. Hence, the
smartphones could only be used for the intended purposes of the present study. During the
training session, the smartphones were distributed and detailed instructions were given by
qualified research assistants. They instructed the children how to operate the smartphones and
demonstrated each of the tasks and questions of the daily assessments. After that,
smartphones were collected by the research assistants and redistributed at the beginning of the
AA phase which started one week after the training session.
The AA phase lasted for 31 consecutive days and was conducted during the middle of
the spring term (May / June 2012). During that time, four assessments per day were signaled
by the smartphone, of which two took place during school hours (Occasion 1 at 8:50 am;
Occasion 2 at 11:25 am). The third assessment started around 3:00 pm; the exact timing was
individually adapted, depending on each child’s schedule within a four hour window. The
fourth session started around 7:00 pm (again +/- 2 hours to allow for individual schedules).
This session is not relevant for the present study, since no WMP assessments were taken at
the fourth occasion. Each assessment lasted approximately between 10 and 15 minutes.
Assessments during school lessons (Occasions 1 and 2 during school days) were supervised
by teachers and trained research assistants to ascertain that participating children were not
distracted by their fellow students who did not participate (since not all students of a class
participated in the study, non-participating students were provided with coloring books to
work on during the assessments). Across all days and children, at least one valid data point on
AFFECT WORKING MEMORY COUPLINGS 14
the five relevant study variables (see below) was present in 6,753 of the 10,137 occasions
(109 children x 31 days x 3 measurement occasions per day), yielding an overall compliance
rate of 66.6%. Split up into the three occasions, compliance was slightly higher at Occasion 1
(68.9%) and Occasion 2 (69.4%) than at Occasion 3 (61.6%). These compliance rates are
slightly below the average, yet in the typical range of, compliance rates in comparable AA
studies with children and adolescents reported in a recent review (Heron et al., 2017).2 The
study protocol for the project FLUX (Assessment of Cognitive Performance FLUctuations in
the School ConteXt) was approved by the ethics committee of the Faculty of Psychology and
Sport Sciences at Goethe University in Frankfurt am Main, Germany (protocol number 2011-
25 R2).
Measurements
Momentary Measures (Ambulatory Assessment).
Affect. Previous research in elementary school children has shown that the four scales
PA, NA, activation, and deactivation, although correlated, are psychometrically distinct and
should therefore be considered separately (Leonhardt et al., 2016). In the present study, each
scale was assessed with three items each. Specifically, at each measurement occasion children
were asked to indicate to what extent they felt each state right now (“Right now, I feel …”) on
a five-point Likert scale ranging from 1 (“not at all”) to 5 (“very much”). The items were
good, fantastic, content (PA), unhappy, miserable, afraid (NA), active, interested,
concentrated (activation), and exhausted, tired, faint (deactivation), respectively. The three
items belonging to the same factor were averaged, resulting in four affect variables used for
further analyses. A multilevel confirmatory factor analysis with four factors on the between-
person level and four factors on the within-person level revealed adequate model fit in the
2 We examined whether individual compliance rates were associated with mean levels in our study variables.
Results showed that compliance rates were unrelated to gender, age, or any of the four affect scales, |r| < .13, p >
.19 for all. There was a small but significant association with mean working memory performance, r = .21, p =
.03, indicating that children with worse average performance tended to comply less with the measurement
procedure.
AFFECT WORKING MEMORY COUPLINGS 15
present sample, comparative fit index (CFI) = .926, root mean square error of approximation
(RMSEA) = .032, standardized root mean square residual (SRMR) = .043 (within) / .073
(between). Estimated reliabilities of the four scales were obtained as multilevel ω (Geldhof,
Preacher, & Zyphur, 2014). The respective estimates suggested good internal consistency on
the between-person level, ω = .85 (PA), ω = .99 (NA), ω = .90 (activation), and ω = .97
(deactivation), respectively, and adequate internal consistency on the within-person level, ω =
.70 (PA), ω = .75 (NA), ω = .65 (activation), and ω = .70 (deactivation), respectively.
Working memory performance. At each measurement occasion, children worked on
two memory updating tasks of working memory. In the numerical updating task, children
were presented two (Load 2 task) or three (Load 3 task) digits (0-9) on the screen of the
smartphone. After that, three (Load 2 task) or four (Load 3 task) updating operations were
presented in the same place where the digits had appeared. These operations were subtractions
and additions ranging from -2 to +2. Children had to apply these operations to the digits that
were presented in the corresponding location. After all operations had been presented, the two
(Load 2 task) or three (Load 3 task) end results had to be entered within 20000ms. During
each measurement occasion (i.e., three times per day) four Load 2 tasks and four Load 3 tasks
were administered. Each of the total 20 responses (4 x 2 results in the Load 2 tasks and 4 x 3
results in the Load 3 tasks) was coded as 1 if the correct response was given within the
20000ms response window (0 otherwise). Mean accuracy of the 8 (Load 2) and 12 (Load 3)
responses per measurement occasion was computed.
In the spatial memory updating task, children were presented a 4x4 grid on the
smartphone screen. Two (Load 2 task) or three (Load 3 task) cartoon creatures were
simultaneously presented, each in one of the 16 squares. Three (Load 2 task) or four (Load 3
task) updating operations were sequentially presented. These operations were represented as
colored arrows positioned at the center of the grid. These arrows indicated movements of the
AFFECT WORKING MEMORY COUPLINGS 16
cartoon creature with the corresponding color (e.g., if a red arrow facing downward appeared
this indicated that the red creature had moved one square downward). After all updating
operations had been shown, children had to indicate the position of the two or three creatures
by tapping the respective square within 30000ms. Four blocks of the Load 2 task and four
blocks of the Load 3 task were presented and the average accuracy across the 8 (Load 2) and
12 (Load 3) responses per measurement occasion was computed.
Previous research using the same data3 as the present study (Dirk & Schmiedek, 2016)
showed that the four performance indicators (numerical Load 2, numerical Load 3, spatial
Load 2, and spatial Load 3) load on one common factor on both the between-person and the
within-person level. We therefore aggregated the four indicators into one accuracy score per
measurement occasion. For detailed information on the tasks and psychometric properties of
this assessment see Dirk and Schmiedek (2016) and Galeano Weber, Dirk, and Schmiedek
(2018).
Data Analysis
In a first step, four multilevel models were run in which WMP was predicted by one
affect scale (PA, activation, NA, deactivation) each. To control for retest effects, a linear
effect of measurement occasion was added in the model. Random effects were estimated for
the intercept, the focal predictor (affect) and time. That is, child i’s WMP at measurement
occasion t (WMPti) was predicted by this child’s affect at the same measurement occasion
(affti) and time (timeti):
Level 1:
=
β0 +β1 ∙time +β2 ∙aff +ε
(1)
Level 2:
β0 =
γ00 +υ0
(2)
3 We note that we excluded one child from the present analyses that had been included in the previous
publication.
AFFECT WORKING MEMORY COUPLINGS 17
β1 =
γ10 +υ1
(3)
β2 =
γ20 +υ2
(4)
Affect was centered on the respective person mean to obtain an unbiased estimate of
the intra-individual effect (Wang & Maxwell, 2015); time was centered on the 50th
measurement occasion and raw scores were divided by ten. Correlations between random
effects were estimated. In a next step, intra-individual couplings were extracted as estimates
(specifically, best linear unbiased predictors, or BLUPs) of person specific regression
coefficients (β2 ). Couplings between NA and WMP and between deactivation and WMP,
respectively, were multiplied by -1 in order to facilitate interpretation: Positive coupling
estimates represent an association between affect and WMP in the expected direction (i.e.,
positive association of WMP with PA and activation, negative association with NA and
deactivation). Person means of the five variables of interest (four affect scales and WMP)
were computed as each child’s arithmetic mean across all observations. These mean scores
and the four coupling estimates were then subjected to a mixture model analysis (MMA).
Since the variances of these nine variables were substantially heterogeneous and unequal
variances affect the solution of the MMA (Steinley & Brusco, 2011), we transformed them
prior to the analyses. Specifically, we standardized the variables via a variance-to-range
weighting procedure which has been shown to be superior to traditional transformations such
as the z-standardization (Steinley & Brusco, 2008). Within-class variances of the nine
indicators were constrained to equality across classes. Correlations between the couplings of
WMP with PA and activation, the couplings of WMP with NA and deactivation, mean PA
and activation, and mean NA and deactivation, respectively, were estimated within each class.
This MMA allows for examining whether the multivariate distribution of the study variables
might represent a mixture of different distributions arising from distinct subgroups in the
population. That is, in these models we examined whether the total sample might consist of
AFFECT WORKING MEMORY COUPLINGS 18
various subsamples (classes) that differ in their distributions of the nine study variables (five
person means and four couplings). Utilizing concepts derived from the theoretical account of
ES, it can be expected that four classes can be identified that differ in the extent to which their
members’ affect is coupled with WMP.
The MMA was conducted in Mplus version 8 (Muthén & Muthén, 2017), all other
analyses using R version 3.4.0 for Windows (R core team, 2017). Multilevel models were
estimated using the lme4 package (Bates, Mächler, Bolker, & Walker, 2015); 95% bootstrap
confidence intervals for multilevel model parameters were obtained via the confint.merMod
function of the lme4 package. A conventional α-level of .05 was set for all analyses.
Results
Table 1 depicts descriptive statistics on the person level. PA correlated positively with
activation, r = .79, p < .001, and negatively with NA, r = -.30, p = .002, and deactivation, r = -
.23, p = .016, respectively. Activation was not significantly related to both NA, r = -.17, p =
.077, and deactivation, r = -.18, p = .061. Deactivation and NA were strongly positively
correlated on the person level, r = .90, p < 001. Average WMP was negatively associated with
average NA, r = -.33, p < .001, and deactivation, r = -.29, p = .002, and positively associated
with average PA, r = .27, p = .005.
Multilevel Models
We estimated separate models for each of the four predictors of interest. Table 2
depicts the results. Fixed effects were statistically significant for NA and deactivation, but not
PA and activation. Importantly, random effects for the focal predictors were statistically
significant for all predictors. That is, although the effect of PA (activation) on WMP was not
statistically significant for the average sample, there were statistically meaningful inter-
individual differences in the strength of the intra-individual association of PA (activation) and
WMP. This was evident by both significant likelihood ratio tests (comparing models with vs.
AFFECT WORKING MEMORY COUPLINGS 19
without random effects for the predictors), χ²(3) > 22.77, p < .001 for all, and lower bounds of
the confidence intervals for the random effect standard deviations markedly above 0 (see
Table 2).4
Structure of Within-Person Couplings
From the multilevel models shown in Table 2, we extracted each child’s estimated
couplings (see Data Analysis for details). Table 3 shows the correlations of these person-
specific within-person couplings. All correlations were positive and (with the exception of the
coupling of activation and deactivation) statistically significant. Correlations for the couplings
of PA and activation, r = .67, and NA and deactivation, r = .69, were substantial. The upper
bounds of the 95% bootstrap confidence intervals for these two correlations were, however,
markedly smaller than 1, suggesting that these couplings are distinct from one another.
We then subjected these four variables, as well as the person means of the four
predictors (PA, activation, NA, deactivation) and the person mean of WMP across all
observations to a MMA. Models with two to six latent classes were estimated; only models
with two, three, and four classes successfully converged and only these were examined in
detail. Model comparisons are depicted in Table 4. Based on these results, a four-class model
provided the best description of the data. The four classes were made up of 16, 51, 19, and 23
children, respectively. Average latent class probabilities for the four classes were .97, .95, .97,
and .99, respectively, suggesting good classification of individuals into the four latent classes.
Figure 1 depicts the means of the nine variables (i.e., the four couplings and the person
means of WMP and the four affect scales) separately for the four latent classes (note that for
better interpretability, Figure 1 depicts z-standardized values). The largest class (Class 2) was
4 In post-hoc analyses, we investigated whether including a quadratic time trend (as fixed and random effect)
would alter the conclusions. Results revealed a significant positive quadratic trend in all four models (indicating
that the change in working memory performance was decelerated towards the end of the study period), b >
0.001, p < .025 for all. When including the quadratic time trend, the fixed effect for PA was significant, b =
0.009, p = .036. All other results remained unaltered (this also applies to the results reported later in the
manuscript).
AFFECT WORKING MEMORY COUPLINGS 20
characterized by above-average WMP and PA, as well as below-average NA and
deactivation. Couplings in this group were all around or slightly below the sample average.
We interpreted this class as representing the group of children with low sensitivity. Class 1
was characterized by below-average WMP, NA, and deactivation, as well as above-average
mean PA and activation. Children in this class exhibited above-average couplings of WMP
with PA, activation, and NA, as well as deactivation (descriptively). The above average
couplings for all four predictors in this class are consistent with the notion of a general
sensitivity group. Children in Class 3 were characterized by below-average WMP, mean NA,
and mean activation, but above-average activation-WMP couplings; this pattern is broadly in
line with a group of children high in vantage sensitivity. Finally, Class 4 also had below-
average mean levels in WMP and, additionally, below-average mean PA. Mean NA and
deactivation were markedly above the sample average. WMP couplings with PA and
activation were around average for children in this class, but couplings with NA and
deactivation were about .75 SDs above the sample average, as would be expected for a
vulnerability group.
Figure 2 depicts each child’s intra-individual couplings (separately for the four
predictors; please note again that couplings with NA and deactivation were multiplied by -1).
Children with couplings one or more standard errors away from zero are marked in black. The
mean couplings together with their associated 95% confidence interval are reported in Table
5. Figure 2 and Table 5 show that (a) couplings in Class 2 (low sensitivity group) were close
to zero, (b) children in Class 3 (vantage sensitivity group) showed overall a positive
association of activation (and to a lesser extent a negative association of NA) with WMP, (c)
in Class 4 (vulnerability group), the associations of NA and deactivation, respectively, with
WMP were negative, while no overall association between PA/activation and WMP could be
observed, and (d) Class 1 (general sensitivity) showed negative effects of NA and
AFFECT WORKING MEMORY COUPLINGS 21
deactivation, respectively, on WMP, and positive effects of PA and activation, respectively,
on WMP.
Discussion
WMP reliably fluctuates within children (Dirk & Schmiedek, 2016), yet little is known
about the predictors of these fluctuations. Why do children sometimes perform better or worse
on the same tasks? In the present study, we focused on one group of predictors: affective
experiences in everyday lives in a sample of elementary school children. Building on previous
research, we expected that momentary states characterized by positive affective experiences
(positive valence, high energetic arousal) would be associated with better WMP, while
negative affective experiences (negative valence, low energetic arousal) would be associated
with worse WMP. Regarding the average associations with indicators of negative affectivity
(NA, deactivation), our findings are consistent with the greatest portion of prior research that
has reported a negative effect of NA on cognitive performance (Brose et al., 2014; Fartoukh et
al., 2014; Patel et al., 2016; Pnevmatikos & Trikkaliotis, 2013): At occasions when children
reported higher NA or higher deactivation, their WMP was worse compared to occasions with
lower NA / deactivation. This finding is consistent with theoretical accounts such as the
resource allocation model (Ellis & Ashbrook, 1988) which proposes that the regulation of
negative affective states takes up resources that cannot be simultaneously engaged for
cognitive tasks requiring working memory resources. We note that, although the average
effects across the whole sample were statistically significant, there were meaningful inter-
individual differences in the intra-individual association between NA / deactivation and
WMP, indicating that children differed in the magnitude of this association. Further
investigating these heterogeneities via mixture models showed that there were two groups of
children (latent Classes 1 and 4) who exhibited particularly strong NA-/deactivation-WMP
couplings.
AFFECT WORKING MEMORY COUPLINGS 22
Positive affective states (PA / activation) were, on average, not significantly coupled
with WMP. However, our results showed that there were substantial inter-individual
differences in the intra-individual association of PA / activation with WMP. Mixture model
analyses suggested that in two groups of children (latent Classes 1 and 3), the (positive)
association of activation with WMP was statistically significant: That is, these children
showed better performance on the working memory tasks at occasions when they reported
higher perceived energetic arousal. Children in latent Class 1 further also exhibited
pronounced (positive) intra-individual PA-WMP couplings.
Taken together, our findings emphasize the importance of considering inter-individual
differences when investigating intra-individual affect-WMP couplings: Had we only
considered the average (fixed) effects, we would have concluded that there was a negative
association of NA/deactivation with WMP, and no association between PA/activation and
WMP. The picture seems to be a bit more nuanced, however: While the negative association
between NA and WMP primarily differed in magnitude between children (larger in Classes 1
and 4), differences in the PA/activation/deactivation associations with WMP were more
complex: For some children (latent Class 2), all these within-person associations were close to
zero. Other children (Classes 1 and 4) showed pronounced couplings between deactivation
and WMP. We note that these were the same children who exhibited particularly strong NA-
WMP couplings as well. In order to better understand the structure of these inter-individual
differences, we interpret these groups along the terminology proposed in the ES framework.
Inter-Individual Differences in Affect-WMP Couplings
Individuals differ in the degree to which they are affected by their environment. While
the processes accounting for these differences are largely unknown (see below for a brief
discussion), the assumption of the existence of such differences is shared among various
theoretical frameworks (Aron, Aron, & Jagiellowicz, 2012; Belsky & Pluess, 2009; Boyce
AFFECT WORKING MEMORY COUPLINGS 23
& Ellis, 2005; Del Giudice et al., 2011; Pluess & Belsky, 2013). According to the ES account
(Pluess, 2015), individuals differ in the effect of the environment on physiological,
psychological, and behavioral outcomes, and these differences can be structured in four
groups: low sensitivity, vulnerability, vantage sensitivity, and general sensitivity. These four
groups resemble the four latent classes identified in the present work: Class 1 consisted of
children with particularly strong couplings for all four affect variables with WMP, and
therefore paralleled the idea of a general sensitivity group. These children showed a strong
(positive) effect of PA and activation on WMP, but also a strong (negative) effect of NA and
deactivation on WMP. Hence, cognitive performance of these children is associated with
current affective states in a “for-better-and-for-worse” manner (Belsky & Pluess, 2009).
Children’s WMP in Class 2 was substantially less affected by their current affective state.
More specifically, couplings in this group were smaller than in Class 1 (NA) or close to zero
(PA, activation, deactivation) in line with the idea of a low sensitivity group. Notably, since
genetic predispositions towards heightened ES, such as the dopamine D4 receptor (DRD4)
gene 7-repeat allele (Bakermans-Kranenburg, van IJzendoorn, Pijlman, Mesman, & Juffer,
2008) or the serotonin transporter-linked polymorphic region (5-HTTLPR) short allele (van
Ijzendoorn, Belsky, & Bakermans-Kranenburg, 2012), are expected to be prevalent in a
minority of the population only (Wolf, van Doorn, & Weissing, 2008), it can be expected that
the largest proportion of children should not demonstrate pronounced responsiveness. This is
in line with our results which revealed that approximately half (47%) of the children in our
sample were categorized into the low sensitivity group (Class 2).
Latent Classes 3 and 4 further emphasize that inter-individual differences in
responsivity to positive and negative experiential influences, respectively, might not
necessarily be consequences of the same mechanism. Specifically, children in Class 3 on
average exhibited positive couplings between activation and WMP, coinciding with the
AFFECT WORKING MEMORY COUPLINGS 24
proposal of a vantage sensitivity group. Class 4, on the other hand, was characterized by
particularly strong (negative) couplings of WMP with NA and deactivation, paralleling the
pattern of a vulnerability group. These results, when interpreted in the ES framework, can
provide important information with regard to potential mechanisms accounting for inter-
individual differences in the effects of environmental influences.
Potential Mechanisms Accounting for Inter-Individual Differences in Reactivity
Previous theorizing on potential mechanisms accounting for inter-individual
differences in the effect of environmental inputs has often not differentiated between the
impacts of positive vs. negative environments. For example, the BSC (Boyce & Ellis, 2005)
and its later refinement as the ACM (Del Giudice et al., 2011) propose that differences in the
sensitivity to environmental influences are a consequence of differences in physiological
stress reactivity. According to this view, individuals differ in the sensitivity of various
subsystems of the stress response system (SRS; i.e., the sympathetic and parasympathetic
systems and the HPA axis) and these differences account for differences in the effects of
environmental inputs on behavioral outcomes. Evidence for this proposition comes from
research examining inter-individual differences in physiological stress reactivity. For
example, in a study by El-Sheikh, Keller, and Erath (2007) inter-individual differences in skin
conductance reactivity (a marker for reactivity of the sympathetic nervous system) moderated
the longitudinal association between parental marital conflict and internalizing problems
among girls (but not boys). This finding is in line with the assumption that differences in SRS
drive differences in environmental effects. So far, however, whether differences in
physiological stress reactivity can account for an “organism’s adjustment to both positive and
negative events”, as postulated by Del Giudice et al. (2011; p. 1572) remains an open
question. Our findings suggested a separation between vantage sensitive children and
vulnerable children, hence challenging the assumption that a single mechanism underlies
AFFECT WORKING MEMORY COUPLINGS 25
environmental sensitivity to both positive and negative input. Nevertheless, it could be that
differences in the responsivity of various subsystems of the SRS interact in giving rise to the
observed structure of inter-individual differences in the intra-individual couplings of affective
states and WMP. Based on our findings, a more fine-grained analysis of interactive effects of
these subsystems, as well as their interaction with serotonergic and dopaminergic pathways
seems to be a promising avenue for future research.
Another mechanism that has been discussed to underlie differences in ES is sensory
processing sensitivity (SPS)—the tendency to be “more or less responsive, reactive, flexible,
or sensitive to the environment” (Aron et al., 2012). Recent advances in the measurement of
inter-individual differences in SPS in adults (Lionetti et al., 2018) and children (Pluess et al.,
2018) have shown that this construct can be further divided into three subscales, of which one
(aesthetic sensitivity) has been related to positive emotionality and vantage sensitivity, and
two (ease of excitation; low sensory threshold) have been more closely related to negative
emotionality and vulnerability (Pluess et al., 2018). These findings are concordant with the
observation of the present study that differences in sensitivity to positive contexts and
sensitivity to negative contexts seem to be not necessarily two sides of the same coin. An
interesting agenda for future research would be to examine differences in SPS between the
latent classes identified by intra-individual couplings in the present study: Building on prior
psychometric work, suggesting some discriminant validity among the three SPS subscales
(Lionetti et al., 2018; Pluess et al., 2018) it might be expected that children in the
vulnerability group (latent Class 4 in the present research) show elevated levels in SPS, ease
of excitation, and low sensory threshold, whereas children from the vantage sensitivity group
(latent Class 3 in the present research) show higher levels in SPS and aesthetic sensitivity than
less responsive children. Children in the general sensitivity group (Class 1) might exhibit
higher levels in SPS and all three subscales (aesthetic sensitivity, ease of excitation, and low
AFFECT WORKING MEMORY COUPLINGS 26
sensory threshold). Ultimately, investigating the mechanisms underlying inter-individual
differences in ES is beyond the scope of the present work, but our results point towards
potentially interesting directions for future research, emphasizing the importance of
accounting for mechanisms that can explain evidence of both convergence (general sensitivity
group) and divergence (vulnerability group; vantage sensitivity group) between responsivity
to positive and negative states, respectively.
Limitations
In interpreting the results, a number of limitations have to be considered. First,
although fairly large for an AA study in the school context, the number of participants in the
study has to be considered rather small for a mixture model analysis. The sample size might
have been too small to reveal a further differentiation into more latent classes. Specifically,
models with more than four latent classes failed to converge, and we therefore cannot
conclude that the reported four latent classes might not be divided further into smaller groups.
Second, the tense arousal dimension of affective experiences that has been shown to be
relevant in elementary school children’s everyday affective experiences (Leonhardt et al.,
2016) was not assessed in the present research. Negative tense arousal (such as stress) has
been related to intra-individual fluctuations in cognitive performance (Sliwinski et al., 2006)
and future research needs to determine if vulnerability to stress co-varies with vulnerabilities
to the other two negative affectivity dimensions assessed in the present study (NA,
deactivation). Third, relevant covariates and predictors of membership in the latent classes
remain unknown. As discussed above, physiological stress reactivity and sensory processing
sensitivity would be prime candidates for this purpose and should be explored in future
research. Fourth, our research primarily targeted inter-individual differences in the intra-
individual coupling of affective states and WMP and we utilized the ES framework to better
understand the structure of these inter-individual differences. In order to interpret our findings
AFFECT WORKING MEMORY COUPLINGS 27
in light of the ES framework, we need to make one of the following two assumptions: Either
(a) children’s momentary affective experiences are interpreted as proxy measures for positive
and negative environmental input, or (b) both affective states and WMP are considered as
outcomes of the common cause environmental input. With regard to the first possibility,
affective states are most likely only distal indicators for environmental inputs that are central
to ES. In fact, children might already differ in the extent to which they respond to positive /
negative environmental input (e.g., the occurrence of stressors or uplifting events) in terms of
PA and NA. However, as long as assumption (b) holds true, meaning that inter-individual
differences in PA / NA reactivity (i.e., difference in the degree to which PA / NA are affected
by positive / negative environmental input) are predicted by the same characteristics as are
inter-individual differences in WMP reactivity (i.e., difference in the degree to which WMP is
affected by positive / negative environmental input), this does not pose a threat to the
conclusions drawn in the present research. We note, however, that this assumption needs to be
examined in future research (Pluess, 2018). No concurrent assessments of such events and
WMP were available in the present study, precluding us from directly assessing the effect of
events on WMP. Future research should consider implementing both stressor events and
uplifting events together with concurrent WMP assessments to more directly assess the
impact of environmental input on cognitive performance and inter-individual differences
therein.
Conclusions
Intra-individual fluctuations in elementary school children’s WMP were associated
with concurrently measured fluctuations in affective states. Across the whole sample, higher
negative affect and higher deactivation were associated with poorer performance, while no
overall associations of WMP with positive affect and activation could be detected. Children
differed in the degree to which their performance was associated with their affective states: In
AFFECT WORKING MEMORY COUPLINGS 28
approximately half of the sample, WMP was more or less unrelated to current affect. One
group of children showed pronounced decrements in performance when negative affect or
deactivation were higher than usual, while another group exhibited elevated performance in
situations of high energetic arousal (activation). One further group showed positive
associations with positive affective experiences and negative associations with negative
affective experiences. Differences between the four groups might be a result of genetic by
early environment interactions that are mediated by differences in ES.
AFFECT WORKING MEMORY COUPLINGS 29
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AFFECT WORKING MEMORY COUPLINGS 36
Table 1
Descriptive Statistics
Mean
(SD)
ICC
Range
2
3
4
5
6
7
1 Age
9.88
(0.61)
-
8.1-11.2
-.18
.02
.00
-.04
.00
.23*
2 Gendera
0.42
(.50)
-
0-1
.04
-.06
-.02
.03
.08
3 Positive Affect
4.05
(0.77)
.435
1.76-5.00
.79*
-.30*
-.23*
.27*
4 Activation
3.69
(0.94)
.538
1.21-5.00
-.17
-.18
.09
5 Negative Affect
1.54
(0.60)
.367
1.00-3.53
.90*
-.33*
6 Deactivation
1.70
(0.63)
.371
1.00-3.55
-.29*
7 Working memory
0.61
(0.21)
.522
0.13-0.97
Note. Table depicts descriptive statistics on the person-level. ICC = intra-class correlation.
a0=male; 1= female. *p < .05. N = 107 (age); N = 108 (gender); N = 109 (other variables).
Table 2
Multilevel Models (Predicting Working Memory Performance)
Positive Affect
Activation
Negative Affect
Deactivation
Fixed Effects
Intercept
0.636*
[0.596, 0.674]
0.639*
[0.601, 0.677]
0.638*
[0.599, 0.675]
0.637*
[0.599, 0.676]
Time
-0.019*
[-0.023, -0.015]
-0.018*
[-0.022, -0.014]
-0.019*
[-0.023, -0.014]
-0.019*
[-0.023, -0.015]
Predictor
0.008
[-0.001, 0.018]
0.008
[-0.002, 0.017]
-0.023*
[-0.034, -0.013]
-0.011*
[-0.020, -0.002]
Random Effects
(Standard Deviations)
Intercept
0.199
[0.172, 0.227]
0.199
[0.171, 0.226]
0.199
[0.171, 0.226]
0.198
[0.171, 0.226]
Time
0.019
[0.016, 0.022]
0.018
[0.015, 0.021]
0.019
[0.016, 0.022]
0.019
[0.016, 0.023]
Predictor
0.032
[0.023, 0.041]
0.035
[0.025, 0.044]
0.034
[0.024, 0.044]
0.028
[0.017, 0.036]
Level-1 Residual Standard
Deviation 0.170
[0.167, 0.173]
0.169
[0.165, 0.172]
0.169
[0.165, 0.172]
0.170
[0.167, 0.173]
Pseudo-R² (Level 1)
21.5%
22.1%
22.2%
21.3%
Note. Table depicts point estimates (95% bootstrap confidence intervals in parentheses). Pseudo-R² was estimated as the proportion of residual
(Level 1) variance explained by the model (compared to a baseline model which includes no predictors). *p < .05
N = 109.
Table 3
Intercorrelations of Intra-Individual Couplings
2
3
4
1 Positive Affect
.67*
[.55, .76]
.31*
[.06, .52]
.35*
[.09, .57]
2 Activation
.25*
[.02, .45]
.23
[-.01, .45]
3 Negative Affect
.69*
[.52, .82]
4
Deactivation
Note. Couplings involving negative affect and deactivation have been multiplied by -1 to facilitate interpretation; high values on all estimates
correspond to a strong coupling in the hypothesized direction. 95% bootstrap confidence intervals are depicted in parentheses.
*p < .05. N = 109.
Table 4
Model Comparisons
Number of latent
classes
Log likelihood
Number of free
parameters
Scaling
correction
factor
BIC
Entropy
2
-1699.233
36
1.367
3567.355
0.858
3
-1655.427
50
1.233
3545.422
0.887
4
-1619.981
64
1.144
3540.209
0.923
Note. BIC = Bayesian information criterion.
Table 5
Person-Specific Couplings Separated by Latent Class
Class 1 (N = 16)
General Sensitivity
Class 2 (N = 51)
Low Sensitivity
Class 3 (N = 19)
Vantage Sensitivity
Class 4 (N = 23)
Vulnerability
Positive Affect
0.0215
[0.0069, 0.0362]
0.0050
[0.0014, 0.0086]
0.0075
[-0.0030, 0.0179]
0.0070
[-0.0066, 0.0205]
Activation
0.0268
[0.0133, 0.0402]
-0.0022
[-0.0059, 0.0015]
0.0248
[0.0138, 0.0357]
0.0035
[-0.0103, 0.0173]
Negative Affect
0.0386
[0.0290, 0.0483]
0.0128
[0.0097, 0.0159]
0.0138
[0.0057, 0.0218]
0.0427
[0.0303, 0.0552]
Deactivation
0.0179
[0.0094, 0.0264]
0.0041
[0.0012, 0.0071]
0.0068
[-0.0014, 0.0149]
0.0250
[0.0158, 0.0343]
Note. Table depicts means (95% confidence intervals in brackets). Bold values indicate means statistically significant larger than zero (p < .05).
Note that couplings with negative affect and deactivation have been multiplied by -1 to facilitate interpretation; high values on all estimates
correspond to a strong coupling in the hypothesized direction.
Figure 1. Figure depicts mean z-scores of the nine variables. Error bars indicate 95% bootstrap confidence intervals. Note that couplings with
negative affect and deactivation have been multiplied by -1 to facilitate interpretation; high values on all estimates correspond to a strong coupling
in the hypothesized direction.
Figure 2. Figure depicts person-specific intra-individual couplings (see β2 in Equation (4)); error bars indicate +/- 1 standard error. Each symbol
represents one child. Black symbols indicate that person specific intra-individual regression coefficients are at least one standard error larger /
smaller than zero. Shaded grey areas depict 95% confidence intervals around the class mean. Note that couplings with negative affect and
deactivation have been multiplied by -1 to facilitate interpretation; high values on all estimates correspond to a strong coupling in the
hypothesized direction.
