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Recent studies have pointed out the effect of personality traits on athletes’ performance and success; however, fewer analyses have focused the relation among these features and specific athletic behaviors, skills, and strategies to enhance performance. To fill this void, the present paper provides evidence on what personality traits mostly affect athletes’ mental skills and, in turn, their effect on the performance of a sample of elite swimmers. The main findings were obtained by exploiting a component-based structural equation modeling which allows to analyze the relationships among some psychological constructs, measuring personality traits and mental skills, and a construct measuring sports performance. The partial least squares path modeling was employed, as it is the most recognized method among the component-based approaches. The introduced method simultaneously encompasses latent and emergent variables. Rather than focusing only on objective behaviors or game/race outcomes, such an approach evaluates variables not directly observable related to sport performance, such as cognition and affect, considering measurement error and measurement invariance, as well as the validity and reliability of the obtained latent constructs. The obtained results could be an asset to design strategies and interventions both for coaches and swimmers establishing an innovative use of statistical methods for maximizing athletes’ performance and well-being.
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AStA Advances in Statistical Analysis
1 3
Component‑based structural equation modeling
fortheassessment ofpsycho‑social aspects
andperformance ofathletes
Measurement and evaluation of swimmers
RosaFabbricatore1· MariaIannario2 · RosariaRomano3·
Received: 11 December 2020 / Accepted: 20 July 2021
© The Author(s) 2021
Recent studies have pointed out the effect of personality traits on athletes’ perfor-
mance and success; however, fewer analyses have focused the relation among these
features and specific athletic behaviors, skills, and strategies to enhance perfor-
mance. To fill this void, the present paper provides evidence on what personality
traits mostly affect athletes’ mental skills and, in turn, their effect on the performance
of a sample of elite swimmers. The main findings were obtained by exploiting a
component-based structural equation modeling which allows to analyze the relation-
ships among some psychological constructs, measuring personality traits and mental
skills, and a construct measuring sports performance. The partial least squares path
modeling was employed, as it is the most recognized method among the component-
based approaches. The introduced method simultaneously encompasses latent and
emergent variables. Rather than focusing only on objective behaviors or game/race
outcomes, such an approach evaluates variables not directly observable related to
sport performance, such as cognition and affect, considering measurement error and
measurement invariance, as well as the validity and reliability of the obtained latent
constructs. The obtained results could be an asset to design strategies and interven-
tions both for coaches and swimmers establishing an innovative use of statistical
methods for maximizing athletes’ performance and well-being.
Keywords Athletes’ performance· Latent and emergent variables· PLS-PM·
Component-based structural equation models
* Maria Iannario
Extended author information available on the last page of the article
R.Fabbricatore et al.
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1 Introduction
Throughout the past decade, the use of statistical modeling in the analysis of
sport performance has gained a rapidly increasing interest. In the approximate
20 years, there has been a remarkable change in both the collection of sports data
and the opportunities to address sports questions using statistical models. Meth-
ods for measurement and evaluation of player performance have become a rele-
vant issue as such as the prediction of game outcomes or the study of experimen-
tal sports science data involving non-standard data structures collected through
the use of recent technologies (Albert et al. 2016). Motion-tracking or remote
sensor technologies, for instance, have made it possible to accumulate detailed
information on player-level dynamics and athletes’ characteristics (Liebermann
etal. 2002), and large data archives for sports have become easily accessible even
to non-experts. Computational advances have also determined a growing number
of applications using sports data for measuring players’ and teams’ abilities, and
decision-making within a game (see Albert et al. 2016, and reference therein).
Apart from the value of the performance indicators, used to categorize athletes’
and teams’ performance, recent contributions focused on why and how some
behaviors emerge in performance contexts (McGarry 2009) and in the ways in
which performance interacts with personality traits (Laborde etal. 2020). There-
fore, recent studies investigated which types of personality have more success in
sport (Allen etal. 2013), widening the classical perspective focused on the meas-
urement of athletes’ abilities through tracking data. This led to the development
of a branch of psychology—sports psychology—geared to study and explain
performance and well-being of athletes in terms of their psychological traits.
Researchers tried to define the personality of the successful athlete, comparing
the personality test scores of lower performance athletes with those of higher per-
formance ones, or exploring differences between professional and amateur ath-
letes (Aidman 2007; Allen etal. 2011). Several studies investigated the associa-
tion between personality and participation in organized sports, also accounting
for gender differences (Allen etal. 2013; Malinauskas etal. 2014; Mckelvie etal.
2003; Paunonen 2003). Further analyses focused on athletes attending different
sport types, showing differences in personality traits between team sport and indi-
vidual sport athletes (Allen et al. 2011; Eagleton et al. 2007; Nia and Besharat
2010; Steca etal. 2018). Some contributions focused on interpersonal relation-
ships in athlete–athlete and coach–athlete dyads and team functioning (Bell 2007;
Jowett and Nezlek 2012; Rhind and Jowett 2011). These studies explored the role
of dissimilarity in personality traits and the contribution of personality to team
performance. Further approaches moved toward a deepening study of athletes’
mental strategies and skills (Olmedilla etal. 2018), often based on the study of
one of the main theoretical framework for analyzing personality in sport, that is
the five-factor model (McCrae and Costa 2008). Although the huge number of
mentioned researches, based on different statistical contents, fewer studies have
focused on the relationships among personality traits, specific athletic skills and
strategies to enhance performance. The present paper is framed in this line of
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Component-based structural equation modeling forthe…
research and aims to identify personality traits which can be successfully used
to assess the performance of athletes engaged in individual sports. In the study,
the performance is measured by means of an overall observable variable which
allows overcoming the drawbacks of the measurements obtained with game sta-
tistics solely (Piedmont etal. 1999). Furthermore, the identification of psycho-
social athletes’ profile may update skill and training to improve the performance
during competitions. The paper proposes a component-based structural equation
modeling (component-based SEM) to analyze the relationships between some
psychological constructs, measuring personality traits and mental skills, and a
combination of indicators (composite), measuring sports performance. The main
focus is on identifying personality traits and mental skills having the largest
impact on sports performance. Rather than focusing only on objective behaviors,
such an approach evaluates also variables not directly observable related to sport
performance, such as cognition and affect, considering measurement error and
measurement invariance, as well as the validity and reliability of the latent con-
structs. In the present paper, we consider data collected in 2019 for the STATSPO
project (Statistical modeling and Data Analytics for Sports. Psychosocial aspects
to assess the performance: the case of swimmers). The project was supported by
University of Naples Federico II and Italian Swimming Federation ISF (Campa-
nia Regional Committee). Data consist of a small number of observations, due
to the representative sample selected by ISF, along with a high number of both
latent and corresponding manifest variables. This structure supports the choice
of the component-based SEM as reference model for the proposed research as
remarked in the next section. Specifically, the work is organized as follows. Sec-
tion 2 presents methods for data collection and implementation in personality
trait analysis. Section3 provides a detailed description of the survey, the data
and the constructs considered in the research. Section4 presents the component-
based SEM, the reference methodology for analyzing the collected data. Results,
separately for the measurement and the structural model, along with the evalua-
tion of the model reliability, are reported in Sect.5. Finally, a discussion on the
main results and the conclusions with some further research developments to be
explored are included in Sects. 6 and 7, respectively.
2 Methodologies forpersonality traits analysis
To collect data relevant to the quantitative measurement of constructs like atti-
tudes and personality traits, multi-item scales are among the most popular meas-
ures used in questionnaires. More in detail, constructs are theoretical concepts not
directly observable that can be inferred from a series of observable indicators (Mac-
Corquodale and Meehl 1948). An example in our analysis is the athletes’ personal-
ity, inferred by responses given to questions on behaviors and choices (Schweizer
et al. 2020; Steca et al. 2018). According to the classical theory of measurement
(Spearman 1904; Thurston 1947), the measurement of latent constructs almost
always relies on the detection of a multivariate set of indicators of the construct
itself. Since no single indicator can capture the overall theoretical meaning, classical
R.Fabbricatore et al.
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theory exploits multiple measurements of the same latent concept. Many aptitude
and personality tests, for instance, use questionnaires with a certain number of items
which are combined to give a total score relative to some dimension of attitude or
personality. When the phenomenon to be analyzed has a complex nature, as for the
analysis of athletes’ personality, several multi-item scales are jointly used to meas-
ure the different aspects of the phenomenon. In some cases, causal connections are
also hypothesized among the different scales either making reference to underlying
theories or setting some research hypotheses (Simon 1954).
Regarding the statistical methods in sport psychology research, the most popu-
lar included regression analysis, mediation and moderation analysis, analysis of
variance, cluster analysis, and SEM (Biddle et al. 2001); in recent applications,
also more complex methods such as latent class analysis, latent profile analysis, and
growth mixture modeling are being to be used (Myers etal. 2018). Among them,
SEM is the reference methodology to deal with latent constructs interconnected by a
network of causal relationships.
SEM is a class of models aiming to analyze the relationships between a set of
latent variables (LVs), measured through multiple manifest variables (MVs) (Bol-
len 1989). SEM combines the principles of factorial analysis (Spearman 1904)
with those of path analysis (Wright 1918). In particular, factorial analysis relates
the observed variables (items) to the respective constructs. This part of the model
is named measurement or outer model. Instead, path analysis captures the structural
connections relating constructs to each other. Structural or inner model is the name
used to refer to this part of the model. Two main approaches have been proposed
in the SEM literature. They are distinguished by the different estimation procedure
(Henseler et al. 2009; Tenenhaus et al. 2005): covariance-based SEM (Jöreskog
1978) and component-based SEM (Wold 1982). Covariance-based SEM estimates
the model parameters by minimizing the discrepancy between the empirical covari-
ance matrix and the theoretical covariance matrix implied by the model. Instead,
component-based SEM estimates the parameters after determining the construct
scores as linear combinations of the corresponding observed variables while maxi-
mizing proximity to the connected constructs. Covariance-based SEM commonly
exploits maximum likelihood estimation (Bollen 1989), whereas partial least squares
path modeling (PLS–PM) is the usual choice for component-based SEM (Tenenhaus
etal. 2005; Wold 1982).
In the last two decades, there has been a heated debate among supporters of the
two approaches (Henseler etal. 2014; Rönkkö and Evermann 2013; Rönkkö etal.
2016). Very briefly, advocates of component-based SEM have outlined some par-
ticular advantages in terms of greater flexibility. Covariance-based SEM poses
indeed distributional assumptions (continuous and normal data), and special require-
ments about the number of indicators per construct (generally three or more) and
the sample size (generally several hundred, Iacobucci 2010). Recently, the debate
focused on the type of constructs considered in the model. On the one side, the
traditional constructs, typical of behavioral sciences, that assume a latent variable
underlying the set of indicators; on the other side, the artificial constructs (emergent
variables), typical of business and social sciences, that emerge from the indicators
(Henseler 2017). Personality traits are an example of constructs of the first type,
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Component-based structural equation modeling forthe…
business process performance of the second type. The two types of constructs give
rise to different models. In the first case, the hypothesis is that the manifest variables
are explained by a common factor, that is the latent variable, and a unique random
error. For this reason, indicators have to be strongly correlated since they are expres-
sion of the same underlying LV. In the case of emergent constructs, a linear combi-
nation of indicators provides the constructs. Therefore, the indicators of emerging
variables are not required to be correlated with each other. Latent variables are also
called reflective constructs, while emergent variables are also called formative con-
structs if they are intended to be formed and not caused by their indicators (Hense-
ler 2020). The nature of the constructs, latent vs emergent, establishes the choice
between covariance-based SEM and component-based SEM, the former being pre-
ferred when the model includes only latent variables, the latter when both latent and
emergent variables are considered (Benitez etal. 2020; Henseler 2017).
As discussed above, component-based SEM is the proper choice to test models
that simultaneously encompass latent and emergent variables as in the presented
3 Data
The presented survey aimed to investigate the relationships among sports perfor-
mance, personality and athletes’ mental skills. It involved a sample of young athletes
enrolled in Italian Swimming Federation (Campania Regional Committee). A sam-
ple of 161 elite swimmers (from now on simply swimmers) was examined. Leading
details on the sample are reported in Table1.
Personality was assessed by using a list of 25 adjectives representative of the Big
Five (B5) dimensions in the Italian lexical context (Barbaranelli etal. 2007; Caprara
and Perugini 1994). The list consists of 5 adjectives for each of the five person-
ality dimensions, namely Extraversion, Emotional stability, Openness, Agreeable-
ness, and Conscientiousness. Participants were required to fill out the questionnaire
indicating how appropriate each adjective is for describing themselves on a 5-point
scale (not at all, slightly, moderately, quite a lot, at all). A previous study in sport
Table 1 Summary statistics concerning the characteristics of the 161 respondents of the survey
Female (39.18%)—Male (60.82)%
Primary school diploma (77.14%), High school diploma (20.82%)
Bachelors degree or higher (2.04%)
Dolphin crawl (11.84%), Freestyle stroke (40.82%)
Backstroke (8.98%), Breaststroke (15.92%), None (22.44%)
Min (12)—Max (30)—Mean (15.42)—Standard deviation (3.20)
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psychology conducted by Steca etal. (2018) also used this self-report measure to
assess athletes’ personality traits. Mental skills were evaluated using the sport per-
formance psychological inventory (IPPS-48), made up of 48 items in which respond-
ents state how often (from 1 = never to 6 = always) they describe their sporting
experience (Robazza etal. 2009). IPPS-48 factors assess both cognitive and emo-
tional aspects relevant to athletes’ performance. This scale measures the following
eight dimensions: Self-talk, Goal setting, Self-confidence, Emotional arousal con-
trol, Cognitive anxiety, Concentration disruption, Mental practice, and Race prepa-
ration. Finally, in this contribution, the observable variable related to performance
(P) takes into account win on competed races on a scale with five anchored options:
1 refers to no success in any competitions, 5 refers to success in all participated
competitions. A detailed description of the scales and the analyzed traits/constructs
is reported in Table2, while Figs.1 and 2 depict the divergent stacked bar charts
for the B5 and the IPPS-48 dimensions, respectively. Each panel of the two figures
refers to a given dimension, the corresponding items being on the vertical axis while
the stacked bins represent the response rates associated with the different response
modes. The bars in each panel are located with reference to the neutral point scale
(moderately for the Big Five scale and 3.5 for the IPPS-48 scale). Therefore, in case
the bar for a given item tends to lie in the right part of the plot, this denotes a per-
centage of respondents with points in the upper part of the correspondent scale.
Inversely, in case the major part of the bar is located in the left part of the plot.
Course, if respondents with low points balance respondents with high points, the
Table 2 Description of the scales and related constructs used in the analysis
Big Five assessment (B5)
It is composed by polytomous items equally divided among:
Extraversion (item 8, item 13, item 15, item 16, item 20)
Agreeableness (item 4, item 10, item 18, item 21, item 23)
Conscientiousness (item 7, item 12, item 19, item 17, item 22)
Emotional stability (item 1, item 3, item 5, item 9, item 25)
Openness (item 2, item 6, item 11, item 14, item 24)
Sport performance psychological inventory (IPPS-48)
It is composed by polytomous items divided by:
Self-talk (item 2, item 10, item 18, item 26, item 34, item 42)
Goal setting (item 5, item 13, item 21, item 29, item 37, item 45)
Self-confidence (item 4, item 12, item 20, item 28, item 36, item 44)
Emotional arousal control (item 8, item 16, item 24, item 32, item 40, item 48)
Cognitive anxiety (item 3, item 11, item 19, item 27, item 35, item 43)
Concentration disruption (item 7, item 15, item 23, item 31, item 39, item 47)
Mental practice (item 6, item 14, item 22, item 30, item 38, item 46)
Race preparation (item 1, item 9, item 17, item 25, item 33, item 41)
Performance (P)
It is obtained by mixing two items related to competed races (win and participated in).
It is analyzed in an increasing value pointing at 5 for the best performance.
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Component-based structural equation modeling forthe…
bar is centered around the neutral point scale, depicted by the solid vertical line in
each panel. In addition, the bins composing a single bar (greyscale/different colors)
express the rate of respondents for the given response mode. Segments of the same
level in greyscale/same color are comparable across items and panels. Inspection of
Fig.1 shows that the majority of indicators has a negative asymmetric distribution,
highlighting a marked agreement for all. With reference to each dimension of the
B5 scale, this underlines the consistency of the items with respect to the construct
they intend to measure. On the other hand, Fig.2 points out discordant dimensions
Fig. 1 Divergent stacked bar chart for the five dimensions of the B5 scale
Fig. 2 Divergent stacked bar chart for the eight dimensions of the IPPS-48 scale
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of the IPPS-48 scale. In fact, the dimensions representing Cognitive anxiety and
Concentration disruption present positive asymmetric items, i.e., a disagreement of
respondents on them. The same type of graph is used in Fig.3 to report the observ-
able variable related to performance. In this case, the chart presents a rather uniform
distribution of athletes in terms of performance.
4 Method
SEM consists of two submodels, as already stated in Sect.2 namely a measurement
(outer) model, which describes the relationships between each construct and the cor-
responding indicators, and a structural (inner) model, which describes the relation-
ships between the different constructs. In turn, the structural model is composed of
as many structural equations as there are the dependent constructs in the model. A
construct that assumes the role of dependent variable in at least one of the structural
equations is defined endogenous, while a construct that assumes only the role of
predictor is defined exogenous. In SEM framework, a graphical representation called
path diagram is commonly used to represent in a visual way the variables and the
relationships in the models: ellipses are used to represent latent variables, hexagons
for emergent variables, squares for indicators, and arrows for relationships. The lat-
ter originate in the independent variables and point to the dependent variable and are
used to depict both the relationships between variables and constructs (measurement
model) and between the various constructs (structural model). The directionality of
the arrows is defined by the theory that explains the analyzed phenomenon or by
new research hypotheses. Note that most common SEMs are those in which relation-
ships do not create cycles, i.e., feedback effects, but all flow in one direction. These
models are called recursive, and we will refer to them throughout this work. Figure4
depicts the path diagram proposed in this paper, limited to the inner model; indica-
tors (measurement model) are not included for reasons of readability. From now on,
we will refer to this model as the STATSPO model. As evident from the path dia-
gram, the model proposed for the assessment of athletes’ personality involves a high
number of constructs, unlike what is typical in social and economic fields. This pro-
duces a dense network of relationships. The model assumes that both the exogenous
constructs of the B5 scale and the endogenous ones of the IPPS-48 scale impact on
the endogenous construct performance. Moreover, dependence relationships are also
39% 40%22%
100 50 050
1 (worst) 2345 (best)
Fig. 3 Divergent stacked bar chart for the observable variable related to performance
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Component-based structural equation modeling forthe…
assumed between the two scales B5 and IPPS-48, with the latter assuming the role
of mediator in the relationship between the B5 constructs and the P construct.
4.1 The model
The set of involved constructs can be formally represented by the vector
where, without loss of generality, the exogenous constructs are placed at the first
n positions, and the endogenous ones are positioned at the remaining m positions.
The indicators, observed on the N statistical units and corresponding to the j-th con-
struct, are denoted by
, where
h=1, ,pj
, with
denoting the number of indi-
cators in the construct j. Below we use the index i to refer to units (
i=1, ,N
Following the conventional notation, the structural model can be formulated as:
denotes the so-called path coefficients,
the error term, and where each
endogenous construct
can depend on one or more exogenous constructs
or on some preceding endogenous construct. This is because the present work
focuses exclusively on recursive models. In addition, we assume the prediction spec-
ification hypothesis, that is
(Wold 1982).
According to the recent literature, different types of measurement model can
be distinguished (Bollen and Bauldry 2011; Henseler 2017), and the selected can-
didate depends on the type of construct considered. In sciences, the constructs
𝛽jkYk+𝜁j,j=n+1, ,n+m
Fig. 4 Path diagram limited to the structural model for the assessment of athletes’ personality (STATSPO
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hypothesize the existence of a latent variable, and the reference model is the
reflective measurement model:
where each indicator is assumed to be a manifestation of a common factor
with an
error term
. The parameter
denotes the loading associated with the h-th mani-
fest variable in the j-th construct. Also, in this model the prediction specification
hypothesis is required, i.e.,
. Alternatively, when the construct
does not assume any latent variable but corresponds to a mixture of elements with-
out any kind of causal relationship, then the composite measurement model is the
Here, the
construct is composed as a linear combination of the
indicators with
The STATSPO model represented in Fig.4 includes both latent and emergent
variables. The B5 and IPPS-48 scales measure the personality and mental char-
acteristics of athletes and are therefore operationalized by reflective measurement
model (3). In contrast, the performance is composed by a single item measuring
win on competed races, and the composite measurement model (4) is employed.
4.2 The algorithm
Component-based SEM commonly exploits the PLS–PM algorithm as estimation
method (Wold 1975, 1982). From hereinafter, the indicators are assumed to be
centered. The algorithm starts with an initial phase where the weights for the
scores of the constructs are obtained through an iterative procedure. The algo-
rithm estimates then the parameters of the structural model (path coefficients) and
of the measurement model (weights and loadings) (Lohomöller 1989). The main
idea of PLS–PM is to obtain two alternative estimates of scores associated with
each construct. One takes into account the measurement model (outer), and one
takes into account the structural relationships (inner). In the first step, each con-
struct is calculated as a linear combination of its own centered indicators using a
set of arbitrary weights
summing to 1:
The first outer estimate of the construct scores is obtained. Then, the first inner esti-
mate of each construct is obtained as a normalized linear combination of the outer
estimations of the connected constructs:
Xjh =𝜆jhYj+𝜀jh ,j=1, ,n+m,
𝜋jhXjh ,j=1, ,n+m
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Component-based structural equation modeling forthe…
where the weights
can be defined according to different weighting scheme (see
Lohomöller 1989 for more details). At this point, the algorithm updates the weights
on the basis of two different modes, defined mode A and mode B:
mode A The weights are obtained through the simple regression of each indicator
on the inner estimate of the corresponding construct.
mode B The weights correspond instead to the multiple regression coefficients of
the inner estimate of the construct on the corresponding set of indicators.
The choice of the mode is strictly related to the nature of the measurement model:
Mode A is more appropriate for a reflective model, i.e., for latent variables (Eq.3),
Mode B for a composite model, i.e., for emergent variables (Eq. 4). Once the
weights have been updated, the algorithm iterates through the previous steps until
the convergence criterion is satisfied:
is an appropriately chosen positive convergence tolerance value. After con-
vergence, the final weights
are used to estimate the construct scores as a linear
combination of the indicators:
The final scores are used to obtain the least squares estimate of the structural coef-
ficients (
) according to Eq.2, and those of the measurement model (
according to Eqs.3 and 4.
Note that in principle PLS-PM estimates composites and not common factors, so
the scores obtained for the latent variables contain measurement errors. To over-
come this issue, a variant called consistent PLS-PM (PLSc) (Dijkstra and Henseler
2015b) has been proposed to estimate reflective measurement model. However, the
new approach could lead to not admissible solutions. This concerns the so-called
Heywood cases (Krijnen etal. 1998), which occur when one or more variances
implied by the model are negative. The small sample size is one of the causes related
to the occurrence of Heywood cases. The STATSPO model, as previously described,
has a very complex structure, with many constructs and a small sample size. The use
of the PLSc is therefore not possible as some not admissible solutions are obtained.
Therefore, we will consider Mode A to estimate the B5 and the IPPS-48 constructs.
Although Mode A does not consistently estimate reflective measurement model, it
provides weights that are proportional to the true correlations between the indicators
and their common factor (Dijkstra and Henseler 2015a).
𝜏jk ̂
ih w(s1)
̂yji =
jh xjhi
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4.3 Model assessment
The PLS–PM is generally validated separately for the measurement and the struc-
tural model using a sequential approach: once the assessment of the measurement
model is satisfactory, it is possible to move on to the structural one. The assess-
ment phase follows different tracks for reflective models and composite models. The
reflective measurement model assumes a latent variable responsible for the correla-
tion structure among the indicators, and several are the aspects to be verified; among
Composite reliability: it checks the amount of random error contained in the
construct scores, which is expected to be limited. The indicator
(Dijkstra and
Henseler 2015b) is a valid measure for PLS–PM. A reasonable threshold is the
value of 0.707, which indicates that more than
of the variance in the con-
struct scores is explained by the corresponding latent variable.
Convergent validity: it represents the amount of the indicators’ variance
explained by the latent variable. It is measured by the average variance extracted
(AVE) index. A value greater than 0.5 is considered acceptable because it would
mean that more than half of this variability is explained by the latent variable
(Bagozzi and Yi 1988).
Indicators reliability: it measures the amount of variance presented in latent
variable in terms of the contribution of each indicator. The loadings are good
candidates to measure this issue (Hair etal. 2010). Since loadings in PLS–PM
are standardized, a value higher than 0.707 indicates that more than
of the
indicator variance is explained by the corresponding latent variable. It should be
mentioned that slightly lower values are not a concern as long as the construct
validity and reliability are assured.
Discriminant validity: it allows differentiation between the different aspects
measured by latent variables. It can be measured through the heterotrait–
monotrait ratio of correlations (HTMT) criterion (Henseler etal. 2015). A value
lower than 0.85 indicates a good discriminant validity.
With respect to the composite measurement model, there are no stringent constraints
on the correlations between indicators. The only aspects to be evaluated are the sign,
size, and significance of the weights. It is also necessary to check for a possible
multicollinearity among the indicators. In a composite model, weights are crucial
as they determine the construct’s scores, just like a weighted sum of their indicators
(see Eq.4). Furthermore, since they are obtained through a multiple regression with
the construct scores as the dependent variable and the indicators as the independent
variables, multicollinearity must be checked. High levels of collinearity could pro-
duce unexpected signs of the coefficients or large confidence intervals. Furthermore,
to determine if the indicators really contribute to compose the construct, it is neces-
sary to test that they are significantly different from zero.
With respect to the structural model, the assessment is similar to that of any
regression model. Therefore the sign, size, and significance of the coefficients must
be evaluated and tested. In case of mediator variables, indirect and total effects have
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Component-based structural equation modeling forthe…
to be considered. The total effects correspond to the sum of the indirect and direct
effects, where the latter are expressed by the path coefficients. Furthermore, the
index allows to evaluate the amount of variability of each endogenous construct
explained by its predictor constructs. The
index (Chin 2010; Hair etal. 2016) is a
further measure of the predictive relevance of the model. It measures how accurately
the model predicts the omitted data points of indicators in reflective measurement
models of endogenous constructs and single-item endogenous constructs (the proce-
dure does not apply for composite models). Values of
greater than zero indicate
highly predictive model for a specific construct, whereas values less than zero repre-
sent a lack of predictive relevance. Finally, for the significant effects, it may be use-
ful to measure their effect size f2=R
. Values of
greater than 0.35, 0.15, and
0.02 indicate strong, moderate and weak effects, respectively (Cohen 1988).
It is worth noting that all statistical inference in PLS–PM is based on bootstrap
techniques, and in particular on percentile bootstrap confidence intervals (Aguirre-
Urreta and Ronkko 2018). Recent developments propose a bootstrap-based test for
the overall model fit (Dijkstra and Henseler 2015b; Henseler 2020; Henseler and
Schuberth 2020). The null hypothesis is that the model fits perfectly, i.e., the vari-
ance–covariance matrix
implied by the SEM does not differ from the observed
variables’ population variance–covariance matrix
. Since the latter is typically not
available, the empirical variance–covariance matrix
of the observed variables is
The discrepancy between the two matrices is measured using the squared Euclid-
ean distance:
An alternative measure exploits the geodesic discrepancy:
is the kth eigenvalue of
and P is the total number of indicators in the
model. A discrepancy value larger than the
) quantile of the correspond-
ing reference distribution HI95 (or HI99) leads to rejection of the null hypothesis.
The evaluation of the overall model fit of a saturated model, i.e., a model in which
all constructs are allowed to be freely correlated, is used to assess the measurement
and composite models’ validity. Moreover, the standardized root mean squared
residual (SRMR) is the reference measure of approximate model fit. A SRMR value
smaller than 0.080 indicates an acceptable model fit (Henseler etal. 2015).
5 Results forSTATSPO data
The following subsections report the PLS–PM results, first for the measurement
model, and then for the structural model. In particular, the measures of validity of
the latent constructs for the measurement model are reported in Sect.5.1, while for
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1 3
the structural model tests for the hypothesized relationship among constructs are
provided in Sect.5.2.
Statistical analysis was carried out using R version 4.0.2 (R Core Team 2020),
the semPLS (Monecke and Leisch 2012) and the cSEM (Rademaker and Schuberth
2020) packages. Additional custom R routines were used for creating specific graphs
to display the different outputs.
5.1 Measurement model results
The assessment of the measurement model starts with the evaluation of the overall
fit of the model with the saturated structural model. Table3 reports three discrep-
ancy measures and both the
quantiles of their corresponding reference
distributions. Only the
discrepancy measure is below the
quantile of the ref-
erence distribution (HI95), thus providing empirical evidence for the latent variables
and the emergent variable inside the model. Moreover, the SRMR is below the sug-
gested threshold of 0.080 (Henseler etal. (2014), indicating acceptable model fit.
The quality of the reflective measurement model is then assessed through several
measures aimed to evaluate reliability, convergent validity, and discriminant valid-
ity. Table4 shows the average variance extracted (AVE) and the Dijkstra–Henseler’s
rho (
). The constructs and the corresponding numbers of items are reported on
Table 3 Evaluation of the
overall fit of the saturated model Value HI95 HI99
SRMR 0.076 0.064 0.067
15.857 11.316 12.294
6.004 8.697 10.066
Table 4 Reliability analysis Constructs Items AVE
Extraversion 5 0.538 0.825
Agreeableness 5 0.526 0.826
Conscientiousness 5 0.517 0.841
Emotional stability 5 0.529 0.795
Openness 5 0.498 0.760
Self-talk 6 0.773 0.947
Goal setting 6 0.711 0.922
Self-confidence 6 0.705 0.921
Emotional arousal control 6 0.529 0.827
Cognitive anxiety 6 0.651 0.927
Concentration disruption 6 0.492 0.846
Mental practice 6 0.532 0.833
Race preparation 6 0.634 0.898
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Component-based structural equation modeling forthe…
the first two columns of the table. The value of
is greater than 0.70 for all latent
variables, pointing at good internal reliability. The reflective measurement model
also meets convergent validity, as indicated by the values of AVE. For all latent vari-
ables, indeed, AVE value is greater or close to 0.50.
Indicator reliability can be assessed through Fig.5 that depicts the results for the
loadings: each panel corresponds to a block of the measurement model, the indi-
cators are reported on the vertical axis, the values of the loadings on the horizon-
tal axis. In each panel, the indicators are sorted in decreasing order according to
Table 5 Discriminant validity (HTMT)
Construct Extr Agre Cosc Emot Open Self-T Goal Self-C Arou Cogn Conc Ment
Agre 0.455
Cosc 0.503 0.662
Emot 0.533 0.359 0.399
Open 0.744 0.548 0.396 0.410
Self-T 0.330 0.356 0.144 0.220 0.378
Goal 0.603 0.278 0.274 0.319 0.403 0.493
Self-C 0.716 0.298 0.207 0.593 0.461 0.469 0.738
Arou 0.525 0.226 0.210 0.701 0.486 0.307 0.520 0.778
Cogn 0.000 0.121 0.025 0.484 0.155 0.209 0.081 0.270 0.386
Conc 0.344 0.134 0.308 0.329 0.014 0.067 0.308 0.407 0.186 0.327
Ment 0.372 0.263 0.364 0.339 0.359 0.463 0.656 0.421 0.331 0.080 0.070
Race 0.470 0.181 0.201 0.193 0.363 0.516 0.753 0.600 0.499 0.015 0.150 0.653
0.00 0.25 0.50 0.75
0.000.25 0.50 0.75
0.00 0.25 0.50 0.75
0.00 0.25 0.50 0.75
Emotional stability
0.00 0.25 0.50 0.75
0.00 0.25 0.50 0.75
Self talk
0.00 0.25 0.50 0.75
Goal setting
0.00 0.250.50 0.75
Self confidence
0.00 0.25 0.50 0.75
Emotional arousal control
0.00 0.25 0.50 0.75
Cognitive anxiety
0.00 0.250.50 0.75
Concentration disruption
0.00 0.25 0.50 0.75
Mental practice
0.00 0.25 0.50 0.75
Race preparation
Fig. 5 Loadings (points) for the several constructs (panels) of the reflective measurement model. The
indicators are reported on the vertical axis. In each panel, the indicators are sorted in decreasing order
according to their values. Segments depict the 95% bootstrap confidence intervals. A vertical line is
located at 0, and a shaded area highlights the zone in which loadings are greater than 0.70
R.Fabbricatore et al.
1 3
their values. The points represent the estimates of the loadings, the segments the
95% bootstrap confidence intervals. The vertical line placed at 0 in each panel high-
lights the significance of all the loadings. Finally, a shaded area is used to mark val-
ues greater than 0.70. Figure5 shows that all indicators are statistically significant.
Moreover, all but B5_I12 report values greater than 0.50 (minimum threshold still
considered acceptable, Hair etal. 2010).
Finally, we assess discriminant validity through the HTMT ratio. As shown in
Table5, all HTMT values are less than 0.85, and then we can conclude that discri-
minant validity is satisfied for all constructs in the model.
In sum, results provide evidence for the reliability and validity of all the latent
variables we considered.
As regards the assessment of the composite model, the multicollinearity, the
weights, the loadings and their significance should be evaluated. However, the only
emergent variable of the STATSPO model is the P construct, which is a single-indi-
cator measurement (Diamantopoulos etal. 2012). In this case, the construct scores
are identical to the standardized indicator values and the model assessment is then
not required.
5.2 Structural model results
The evaluation of the structural model starts from the analysis of the overall fit of
the estimated model, shown in Table6. The
discrepancy value is below its cor-
responding HI95 value, indicating that the estimated model is not rejected at a
significance level.
The results for the path coefficient estimates, their significance, and the coefficient
of determination (
) are summarized in Fig.6. The figure follows the same style
of the previous representation of the loadings: each panel refers to an endogenous
construct, and the predictor constructs are on the vertical axis, sorted in decreasing
order according with their values. The points depict the path coefficients, and the
segments the correspondent 95% bootstrap confidence intervals (CIs). Lighter seg-
ments/points, crossing the vertical lines at 0 are not statistically significant, darker
segments correspond to significant coefficients. The values of
are reported in the
subtitle of each panel.
As we expected, personality traits are related to athletes’ mental skills. In particu-
lar, the Extraversion dimension affects Goal setting (
CI = 0.22–0.56),
Self-confidence (
CI = 0.35–0.65), and Race preparation (
CI = 0.06–0.46) in a positive way and the Concentration disruption (
CI =
) in a negative way. On the other hand, Emotional stability
Table 6 Evaluation of the
overall fit of the estimated
Value HI95 HI99
SRMR 0.117 0.072 0.074
38.200 14.191 15.318
6.553 8.728 10.099
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Component-based structural equation modeling forthe…
has a significant positive effect on Self-confidence (
CI = 0.20–0.43)
and Emotional arousal control (
CI = 0.33–0.60), and a negative
impact on Cognitive anxiety (
CI =
) and Con-
centration disruption (
CI =
). Openness affects
more mental skills: Self-talk (
CI = 0.02–0.40), Cognitive anxiety
CI = 0.01–0.39), and Concentration disruption (
= 0.05–0.42). Finally, Conscientiousness and Agreeableness have a less widespread
effect: the former is only related to Mental practice (
CI = 0.08–0.38),
whereas the latter to Self-talk (
CI = 0.03–0.41). The values of
the IPPS-48 dimensions are reported in the subtitles of each panel of Fig.6. They
turn out to be good, ranging from 0.158 to 0.478, especially for Self-confidence
), Emotional aurousal control (
), Goal setting (
), and
Cognitive anxiety (
Regarding the relationship between mental skills and personality traits
on performance, Self-talk, Emotional arousal control, and Cognitive anxiety
affect swimmer’s performance, accounting for
of the variance (
In particular, Self-talk and Emotional arousal control have a positive effect
on the performance (
CI = 0.03–0.44, and
CI =
0.07–0.54, respectively), whereas a negative effect is found for Cognitive anxiety
CI =
). Contrary to our hypotheses, personality
traits do not significantly affect performance directly (see results related to path
coefficient). However, indirect effects (mediated by mental skills) and the total
ones (direct and indirect) can be evaluated. This decomposition of the effects is
depicted in Fig.7: the dimensions are reported on the vertical axis in decreasing
Emotional stability
−0.40.0 0.4
Self talk
Emotional stability
−0.4 0.0 0.4
Goal setting
Emotional stability
−0.4 0.0 0.4
Self confidence
Emotional stability
−0.40.0 0.4
Emotional arousal control
Emotional stability
−0.4 0.0 0.4
Cognitive anxiety
Emotional stability
−0.4 0.0 0.4
Concentration disruption
Emotional stability
−0.40.0 0.4
Mental practice
Emotional stability
−0.40.0 0.4
Race preparation
Cognitive anxiety
Self confidence
Race preparation
Concentration disruption
Goal setting
Mental practice
Emotional stability
Self talk
Emotional arousal control
−0.4 0.0 0.4
Fig. 6 Path coefficients (points) for the several endogenous constructs (panels) of the structural model.
Segments depict the 95% bootstrap confidence intervals. The vertical lines located at 0 in each panel
allow to visually catch the significance of the path coefficients: lighter segments correspond to nonsig-
nificant path, darker segments to significant paths. The values of
are reported in the subtitle of each
R.Fabbricatore et al.
1 3
order according to the total effects (top bars for each dimension), the middle bars
and the bottom bars represent the direct and indirect effect, respectively. Results
in Fig.7 show a relevant indirect effect for the Emotional stability trait (indirect
effect = 0.25, CI = 0.12–0.41). In addition, the effect size of the significant path
coefficients ranges from 0.02 (Openess
Self-talk) to 0.31 (Emotional stability
Cognitive anxiety), and thus, it is small-to-medium, according to the Cohen’s
category (
index). Detailed information on the
values for all constructs is
given in the supplementary material. The significance of the indirect effect high-
lights the role of mediator of mental skills in the relationship between Emotional
stability and Performance. It is a full mediation (Henseler and Schuberth 2020;
Nitzl etal. 2016) since the direct effect of Emotional stability is not significant
(as evidenced by the confidence interval in Fig.6), while the indirect one is. This
means that mental skills absorb the direct relationship to change its direction, as
evidenced by the positive sign of the total effect. The results in Table7 report the
decomposition of the total effect into direct and indirect effects and the decompo-
sition of the indirect effect into the various components (partial indirect effects)
relating to each of the mental skills. It is worth noting that the indirect effect
through Emotional arousal control and Cognitive anxiety is substantial, implying
that they totally mediate the effect of Emotional stability on Performance.
index was calculated to measure the model’s predictive relevance for the
indicators of the reflective measurement models of the endogenous constructs. The
values are all greater than zero (Cognitive anxiety = 0.127, Concentration disrup-
tion = 0.048, Emotional arousal control = 0.152, Goal setting = 0.144, Mental prac-
tice = 0.047, Race preparation = 0.055, Self-confidence = 0.299, Self-talk = 0.056),
thus highlighting a predictive relevance for all the reflective constructs examined.
Fig. 7 Decomposition of the effects on Performance for the personality traits dimensions. The top bars
associated with each dimension (vertical axis) depict the total effects, the direct and indirect effects are
represented using the middle bars and bottom bars, respectively. The dimensions are sorted in decreasing
order according to their total effects on performance
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Component-based structural equation modeling forthe…
6 Discussion
The study examined by component-based SEM methodology how the personality
traits mostly affect swimmers’ mental skills and, in turn, the effect of mental skills
on their performance.
Our results show that Self-confidence and Emotional arousal control are the skills
strongly related to Big Five personality traits. As reported in Bellou etal. (2018),
the lack of Emotional stability (also defined as neuroticism) generally causes low
self-confidence levels. In our specific context, this means that the tendency to be
emotionally reactive and insecure lead swimmers to feel not being up to gain exper-
tise, achieve goals, and express their potential. On the other hand, experiencing posi-
tive emotions (being extravert) positively affects the swimmers’ confidence in their
skills. Emotional arousal control is greatly influenced only by the Emotional stabil-
ity personality trait. Therefore, swimmers who are able to manage stress and emo-
tions also succeed in controlling competition stress and anxiety and channeling the
concentration and energy on the performance. This finding is in agreement with the
results in Petito etal. (2016). Regarding the other two mental skills related to emo-
tional aspects, namely Cognitive anxiety and Concentration disruption, we found
that both are related to the personality traits of Emotional stability and Openness. In
particular, openness to experience can be defined as the tendency to seek new expe-
riences: swimmers who enjoy new and exciting tasks tend to report a higher cogni-
tive anxiety level and concentration disruption. As far as we know, these relation-
ships have not been clearly explored in the literature. We can speculate that being
fascinated by many different stimuli could not allow athletes to focus their attention
on sporting goals, generating more anxiety for their performance and concentration
problems. Conversely, swimmers with a low score on Emotional stability, and with
a high level of apprehensiveness and predisposition to anxiety, tend to experience
Table 7 Effect estimates of Emotional stability on Performance
Effect Estimate
Emotional stability > Performance (a) − 0.137
Emotional stability > Self-talk > Performance (b1) 0.014
Emotional stability > Goal setting> Performance (b2) 0.002
Emotional stability > Self-confidence > Performance (b3) − 0.039
Emotional stability > Emotional arousal control > Performance (b4) 0.137
Emotional stability > Cognitive anxiety > Performance (b5) 0.126
Emotional stability > Concentration disruption > Performance (b6) 0.004
Emotional stability > Mental practice > Performance (b7) 0.005
Emotional stability > Race preparation > Performance (b8) 0.003
Emotional stability > Performance (
) 0.252
Emotional stability > Performance
R.Fabbricatore et al.
1 3
more cognitive anxiety and worry before and during competitions, and a more
impaired concentration. These results are in line with those reported in Allen etal.
(2013) and Petito etal. (2016). Concentration disruption is also influenced by Extra-
version. This appears to be in contrast with the other evidence in sport psychology
research (Allen etal. 2020). Indeed, in our sample, extraverted swimmers present a
higher level of concentration. However, a study conducted by Kaiseler etal. (2019)
showed that extraversion negatively predicts the use of distraction-oriented coping
in sport. In other words, this means that when extraverted athletes cope with stress-
ful situations (i.e., what we mean by coping strategy), they are less likely to shift
their attention on non-sport-related aspects causing mental distraction.
Compared to emotional aspects, mental skills involving cognitive aspects are less
influenced by personality traits. The frequency of inner dialogue recourse to instruct
and motivate oneself, namely Self-talk (Van Raalte etal. 2016), is related to the
personality traits of Agreeableness and Openness. In particular, swimmers with a
more trusting and helpful way of thinking (Agreeableness) and an imaginative, crea-
tive, and flexible personality (Openness) are more prone to use self-talk to enhance
their performance. These results are consistent with what was reported in Brintha-
upt (2019) and Depape etal. (2006). In addition, Extraversion affects two cognitive
aspects related to swimmer’s mental skills: Goal setting and Race preparation. Being
determined, resolute, dominant, and energetic increases the swimmer’s ability to
define adequate action plans and strategies to reach athletes’ goals, practicing them
during their training. Finally, swimmers who are more organized, hardworking, and
responsible (i.e., Conscientious) tend to simulate reality: they mentally reproduce
their movements (Mental practice) to improve and refine their abilities. Other works
exploring the relationships between personality and mental skills for other sports
report similar results (Budnik-Przybylska etal. 2019; Judge and Ilies 2002). Fur-
thermore, results highlight the role of mediator of mental skills in the relationship
between Emotional stability and Performance.
As regards the latter, swimmers involved in this study are heterogeneous: 39%
did not participate in many competitions and did not often win, about 22% reported
a moderate success, whereas 40% participated in many competitions and had good
performances. Our study suggests that three of the considered mental skills are
particularly important to have successful performances in swimmer competitions.
Two skills involve emotional aspects (Self-confidence and Cognitive anxiety) and
one cognitive practice (Self-talk). Firstly, self-talking allows swimmers to focus on
the present moment, avoid distractions, acquire new skills, modify incorrect auto-
matic movements, and consequently improve their performance. Secondly, negative
expectations about performance and concern about the possibility of failure nega-
tively impact the performance, lowering swimmers’ possibility of success. Thirdly,
swimmers able to manage stress and emotions channeling their energy on the per-
formance reach also better results in very stressful competitions.
Finally, only indirect and positive effect of Emotional stability on Performance
has been detected when mental skills were used as mediators between person-
ality traits and performance. In such a case, no direct effect of personality on
performance emerges from the research. The total effects suggest a high impact
of Self-talk, Emotional arousal control, Cognitive anxiety, and Extraversion on
1 3
Component-based structural equation modeling forthe…
swimmers’ performance. We also highlighted the specific mental skills particu-
larly related to participation and success in swimmer competitions. From a prac-
tical point of view, we retain that these findings could be really useful to design
strategies and interventions both for coaches and swimmers to maximize the per-
formance and well-being.
7 Conclusion
The interest in the role of personality in sport has been increasing in recent years.
Several studies have pointed out the effect of personality traits on athletes’ per-
formance and success (see Allen et al. 2013; Allen and Laborde 2014; Steca
etal. 2018 among the others). In contrast, fewer studies have focused the rela-
tion among personality traits and specific athletic behaviors, skills, and strategies
to enhance performance. To fill this gap, our work provides evidence on what
personality traits mostly affect swimmers’ mental skills and, in turn, the effect
of mental skills on their performance. The current study advances an important
line of inquiry studying the interdependence of psycho-social aspects and per-
formance of athletes and providing evidence for a very specific athlete’s popula-
tion (elite swimmers). Our sample’s homogeneity, very uncommon in research on
organized sports (Steca etal. (2018), allows us to provide findings on an athlete’s
category that has received little attention in the literature. Although this study
addressed some relevant questions, it has its limitations. One limitation is that the
data are about a sample of young swimmers; therefore, claims may arise on some
specific questions concerning the personal sphere. It remains unclear whether the
results are cyclically related and together are caused by such factors as individ-
ual difference characteristics and sociocultural variables, as well as other factors.
Longitudinal and experimental research on different clusters could uncover these
potential multi-layered variables. Another extension is about the possibility to
consider further objective measures to evaluate the performance also with respect
to the swimming style that may be considered in future studies. With reference to
the last point, it would be interesting to investigate the role of coach and his/her
contribution in objective and subjective performance-related outcomes and ath-
letes’ skills or well-being (e.g., win-loss record, personal bests, technique acqui-
sition, competence, conflict). Finally, future research should extend the main find-
ings in both other sports and contexts.
Supplementary Information The online version contains supplementary material available at https:// doi.
org/ 10. 1007/ s10182- 021- 00417-5.
Acknowledgements This research was carried out in the context of the project “Statistical Modelling
and Data Analytics for Sports. Psychosocial aspects to assess the performance: the case of swimmers”
(University of Naples Federico II- Italian Swimming Federation, Campania) and partially supported by
Osservatorio Regionale delle Politiche Giovanili 2- POR CAMPANIA FSE 2014-2020-Cup Project:
R.Fabbricatore et al.
1 3
Funding Open access funding provided by Università degli Studi di Napoli Federico II within the CRUI-
CARE Agreement.
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Authors and Aliations
RosaFabbricatore1· MariaIannario2 · RosariaRomano3·
Rosa Fabbricatore
Rosaria Romano
Domenico Vistocco
1 Department ofSocial Sciences, University ofNaples Federico II, Vico Monte della Pietà, 1,
Naples80138, Italy
2 Department ofPolitical Sciences, University ofNaples Federico II, Via L. Rodinó, 22,
Naples80138, Italy
3 Department ofEconomics andStatistics, University ofNaples Federico II, Via Cintia, 21,
Naples80126, Italy
... The usefulness of the novel method is demonstrated using historical NFL data. Fabbricatore et al. (2022) propose a component-based structural equation modeling approach for the assessment of psycho-social aspects and performance of athletes. Performance in elite sports also depends on the personality traits of the athletes. ...
... Today, the collected data are often highly complex and may involve network structures like passing networks, and timecontinuous movement processes recorded by high-frequency camera systems, etc. This broad range of novel data problems motivates a wide range of novel statistical procedures, which is reflected in this special issue covering statistical tools such as machine learning algorithms (Dick and Brefeld 2022;Fadel 2022), Cox frailty models (Zumeta-Olaskoaga 2022), hidden Markov models Mews and Ötting 2022), Bayesian hierarchical models (Hanck and Arnold 2022;Ievoli et al. 2022), structural equation modeling (Fabbricatore et al. 2022), random process theory and functional data analysis (Pataky et al. 2022), bivariate Poisson regression (van der Wurp and Groll 2022; Benz and Lopez 2022), and latent Gaussian processes (Ekstrom and Jensen 2022). While all these works address specific statistical problems in sports, this editorial aims to stimulate statistical research with an application to sports in general, and to help non-statisticians understand why and how statistics can be a very valuable tool in this context. ...
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Triggered by advances in data gathering technologies, the use of statistical analyzes, predictions and modeling techniques in sports has gained a rapidly growing interest over the last decades. Today, professional sports teams have access to precise player positioning data and sports scientists design experiments involving non-standard data structures like movement-trajectories. This special issue on statistics in sports is dedicated to further foster the development of statistics and its applications in sports. The contributed articles address a wide range of statistical problems such as statistical methods for prediction of game outcomes, for prevention of sports injuries, for analyzing sports science data from movement laboratories, for measurement and evaluation of player performance, etc. Finally, also SARS-CoV-2 pandemic-related impacts on the sport’s framework are investigated.
... The R package cSEM was chosen as the tool to perform these Monte Carlo simulations because it was introduced by researchers in the field of composite-based SEM and is open to other researchers' contributions, making the latest developments related to composite-based SEM publicly available. Moreover, cSEM is now widely applied in research and is gaining increasing attention in academia(Chuah et al., 2021;Fabbricatore et al., 2021;Klesel et al., forthcoming). This chapter illustrates the guidelines by means of an illustrative Monte Carlo simulation that investigates PLS-PM's and PLSc's finite sample behavior, particularly regarding the consequences of sample correlations among measurement errors on statistical inference. ...
This thesis is about composite-based structural equation modeling (SEM). In traditional factor-based SEM, these theoretical concepts are modeled as common factors, i.e., as latent variables which explain the covariance structure of their observed variables. In contrast, in composite-based SEM, the theoretical concepts can be modeled both as common factors and as composites, i.e., as linear combinations of observed variables that convey all the information between their observed variables and all other variables in the model. This thesis presents methodological advancements in the field of composite-based SEM. In specific, Chapter 1 provides an overview of the underlying model, as well as a definition of the term composite-based SEM. Chapter 2 provides guidelines on how to perform Monte Carlo simulations in the statistic software R using the package “cSEM” with various estimators in the context of composite based SEM. The third Chapter presents estimators of composite-based SEM, which are adaptions of partial least squares path modeling (PLS-PM) and consistent partial least squares (PLSc), which are robust in responding to outlier distortion. These adjustments can avoid distortion that could arise from random outliers in samples. Chapter 4 presents an approach to performing out-of-sample predictions based on models estimated with ordinal partial least squares and ordinal consistent partial least squares. Here, the observed variables lie on an ordinal categorical scale which is explicitly taken into account in both estimation and prediction. Chapter 5 introduces confirmatory composite analysis (CCA) for research in “Human Development”. This chapter uses the Henseler-Ogasawara specification for composite models, allowing, for example, the maximum likelihood method to be used for parameter estimation. As an alternative, Chapter 6 presents another specification of the composite model by means of which composite models can be estimated with the maximum likelihood method. The last chapter, Chapter 7, gives an overview of the development and different strands of composite-based structural equation modeling. Additionally, here I examine the contribution the previous chapters make to the wider distribution of composite-based structural equation modeling.
... Recently, an increasing interest has been devoted to understanding the psychological behaviour of some athletes and how personality traits influence their performance [see (Aidman & Schofield, 2004;Laborde et al., 2020), among others], also by means of complex statistical models (Fabbricatore et al., 2021;Fabbricatore & Iannario, 2022). This data analysis work would be helpful for professional analytics, allowing effective behavior-based decision-making during games, improving the effects of teams' training and performance in competitions (Janetzko et al., 2014;Legg et al., 2012Legg et al., , 2013Rusu et al., 2010). ...
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Analyzing sports data has become a challenging issue as it involves not standard data structures coming from several sources and with different formats, being often high dimensional and complex. This paper deals with a dyadic structure (athletes/coaches), characterized by a large number of manifest and latent variables. Data were collected in a survey administered within a joint project of University of Naples Federico II and Italian Swimmer Federation. The survey gathers information about psychosocial aspects influencing swimmers’ performance. The paper introduces a data processing method for dyadic data by presenting an alternative approach with respect to the current used models and provides an analysis of psychological factors affecting the actor/partner interdependence by means of a quantile regression. The obtained results could be an asset to design strategies and actions both for coaches and swimmers establishing an original use of statistical methods for analysing athletes psychological behaviour.
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Structural equation modeling (SEM) has been used and developed for decades across various domains and research fields such as, among others, psychology, sociology, and business research. Although no unique definition exists, SEM is best understood as the entirety of a set of related theories, mathematical models, methods, algorithms, and terminologies related to analyzing the relationships between theoretical entities -- so-called concepts --, their statistical representations -- referred to as constructs --, and observables -- usually called indicators, items or manifest variables. This thesis is concerned with aspects of a particular strain of research within SEM -- namely, composite-based SEM. Composite-based SEM is defined as SEM involving linear compounds, i.e., linear combinations of observables when estimating parameters of interest. The content of the thesis is based on a working paper (Chapter 2), a published refereed journal article (Chapter 3), a working paper that is, at the time of submission of this thesis, under review for publication (Chapter 4), and a steadily growing documentation that I am writing for the R package cSEM (Chapter 5). The cSEM package -- written by myself and my former colleague at the University of Wuerzburg, Florian Schuberth -- provides functions to estimate, analyze, assess, and test nonlinear, hierarchical and multigroup structural equation models using composite-based approaches and procedures. In Chapter 1, I briefly discuss some of the key SEM terminology. Chapter 2 is based on a working paper to be submitted to the Journal of Business Research titled “Assessing overall model fit of composite models in structural equation modeling”. The article is concerned with the topic of overall model fit assessment of the composite model. Three main contributions to the literature are made. First, we discuss the concept of model fit in SEM in general and composite-based SEM in particular. Second, we review common fit indices and explain if and how they can be applied to assess composite models. Third, we show that, if used for overall model fit assessment, the root mean square outer residual covariance (RMS_theta) is identical to another well-known index called the standardized root mean square residual (SRMR). Chapter 3 is based on a journal article published in Internet Research called “Measurement error correlation within blocks of indicators in consistent partial least squares: Issues and remedies”. The article enhances consistent partial least squares (PLSc) to yield consistent parameter estimates for population models whose indicator blocks contain a subset of correlated measurement errors. This is achieved by modifying the correction for attenuation as originally applied by PLSc to include a priori assumptions on the structure of the measurement error correlations within blocks of indicators. To assess the efficacy of the modification, a Monte Carlo simulation is conducted. The paper is joint work with Florian Schuberth and Theo Dijkstra. Chapter 4 is based on a journal article under review for publication in Industrial Management & Data Systems called “Estimating and testing second-order constructs using PLS-PM: the case of composites of composites”. The purpose of this article is threefold: (i) evaluate and compare common approaches to estimate models containing second-order constructs modeled as composites of composites, (ii) provide and statistically assess a two-step testing procedure to test the overall model fit of such models, and (iii) formulate recommendation for practitioners based on our findings. Moreover, a Monte Carlo simulation to compare the approaches in terms of Fisher consistency, estimated bias, and RMSE is conducted. The paper is joint work with Florian Schuberth and Jörg Henseler.
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Confirmatory composite analysis (CCA) was invented by Jörg Henseler and Theo K. Dijkstra in 2014 and elaborated by Schuberth et al. (2018b) as an innovative set of procedures for specifying and assessing composite models. Composite models consist of two or more interrelated constructs, all of which emerge as linear combinations of extant variables, hence the term ‘emergent variables’. In a recent JBR paper, Hair et al. (2020) mistook CCA for the measurement model evaluation step of partial least squares structural equation modeling. In order to clear up potential confusion among JBR readers, the paper at hand explains CCA as it was originally developed, including its key steps: model specification, identification, estimation, and assessment. Moreover, it illustrates the use of CCA by means of an empirical study on business value of information technology. A final discussion aims to help analysts in business research to decide which type of covariance structure analysis to use.
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Dancing is mainly regarded as a form of art, which has been linked to the expression of emotions. Imagery is a well-known technique for enhancing performance. Additionally, specific personality traits are likely to facilitate performance. In the dancer’s performance, regarding the body as a tool is crucial. The following study examines personality and perceived body esteem as predictors of imagery ability in professional dancers. We analyzed two experimental groups, namely ballet dancers and professional dancers of other styles, and a control group. A sample of 249 people took part in the study: 155 women and 94 men aged 18–56 years. Participants filled in The Imagination in Sport Questionnaire and Polish adaptations of the Big Five Inventory—Short and the Body Esteem Scale. Results indicated that while each experimental group differed significantly from the control group in terms of their imagery ability, there were no differences between the two experimental groups. Findings revealed that personality traits, mainly higher openness to experience, and body esteem, mainly related to physical condition, were significant predictors of higher imagery ability in all groups.
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Partial least squares path modeling (PLS-PM) is an estimator that has found widespread application for causal information systems (IS) research. Recently, the method has been subject to many improvements, such as consistent PLS (PLSc) for latent variable models, a bootstrap-based test for overall model fit, and the heterotrait-to-monotrait ratio of correlations for assessing discriminant validity. Scholars who would like to rigorously apply PLS-PM need updated guidelines for its use. This paper explains how to perform and report empirical analyses using PLS-PM including the latest enhancements, and illustrates its application with a fictive example on business value of social media.
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Despite the popularity of research on intrapersonal communication across many disciplines, there has been little attention devoted to the factors that might account for individual differences in talking to oneself. In this paper, I explore two possible explanations for why people might differ in the frequency of their self-talk. According to the “social isolation” hypothesis, spending more time alone or having socially isolating experiences will be associated with increased self-talk. According to the “cognitive disruption” hypothesis, having self-related experiences that are cognitively disruptive will be associated with increased self-talk frequency. Several studies using the Self-Talk Scale are pertinent to these hypotheses. The results indicate good support for the social isolation hypothesis and strong support for the cognitive disruption hypothesis. I conclude the paper with a wide range of implications for future research on individual differences in self-talk and other kinds of intrapersonal communication.
This scoping review sought to identify every published study on extraversion in sport. A narrative synthesis was used to interpret findings across research themes. The evidence was graded with validated measures that use quantitative criteria to establish the quality of report writing and confidence in the findings reported. A comprehensive electronic and manual literature search identified 151 published articles (155 independent studies). The research was deductively coded into eight research themes within four causal hypotheses. Study quality varied according to publication date (r = –.52) and the evidence supporting major research questions was graded as ‘low’ or ‘very low’ in most instances. The most convincing evidence indicated that athletes are more extraverted than non-athletes (k = 58), team-sport athletes are more extraverted than individual-sport athletes (k = 18), female athletes are more extraverted than male athletes (k = 24), athletes scoring higher on extraversion use more adaptive coping strategies (k = 9), have stronger coach-athlete relationships (k = 6), and tend to be more successful (k = 33). Insufficient evidence was available to draw conclusions regarding playing position, group processes, or team success. Further research on coaches and officials, and using longitudinal and experimental research designs, are recommended.
Objectives: The present research addresses a neglected aspect within the current Zeitgeist of improving methodological standards in (sport)psychology: reliable measurement. We discuss and highlight the importance of reliable measurement from different perspectives and empirically assess reliability of three commonly used performance outcome measures in order to give guidelines to researchers on how to increase reliability of measurements of performance outcomes. Method: In three studies we estimate 5 different reliability coefficients for three performance outcome measures based on 14 golf putts (study 1; N=100), 14 dart throws (study 2; N=200; 100 sports students; 100 non-sports students) and 14 free throws in basketball (study 3; N=192; 100 non-basketball players; 92 basketball players). Results: The highest reliability was the odd-even reliability for darts for the whole sample (0.888), followed by golf putts (0.714 for distance from the hole, 0.614 for successful putts) and free throws (0.504 non-basketball players; 0.62 for basketball players; and 0.826 for whole sample). Conclusions: Based on theoretical considerations and our empirical findings we give practical guidelines to improve reliability for performance outcome measures in sport psychology.
This study aimed to develop a systematic map of all trait-based research in sport and exercise psychology journals and to provide a detailed research agenda for progressing personality science in the context of sport and exercise. Abstracts were located for all articles published in 10 international journals from the field of sport and exercise psychology and were screened for trait measures. Definitions were obtained for each trait and thematic analysis was used to search for repeated patterns of meaning. We also mapped each trait to the 30 facets of the Big Five trait dimensions. Of the 5152 abstracts screened, 64 discrete traits were identified that met inclusion criteria. These traits could be categorised into 15 higher-order themes based on trait definitions. The most popular traits assessed in sport and exercise psychology research were trait anxiety, self-efficacy, perfectionism, social physique anxiety, and depression. The most popular higher-order themes were traits related to negative affect, self-confidence, perfectionism, competitiveness, and self-consciousness. Most traits could be mapped to facets of the Big Five, but some did not map well to any one particular facet. Few traits mapped to facets of agreeableness and openness. Eleven directions for future research are discussed including implications for systematic research synthesis.
Soccer (or association football) is themost popular sport in theworld, with an estimated 3.5 billion fans and 250 million players worldwide (Sporty Desk, 2015). Betting on outcomes in soccer matches is also very popular, unsurprisingly, and the value of the soccer betting market in 2012 is estimated to be between £500 billion and £700 billion (Keogh and Rose, 2013). Consequently, statistical modelling of outcomes in soccer matches is popular among researchers, both in academia and industry, not only for the potential for financial returns but also for the challenges that suchmodelling presents. This is not to say that betting drives all research in statistical modelling in soccer andmany interesting problems relating to tactical questions (e.g. Wright and Hirotsu, 2003; Hirotsu and Wright, 2006; Brillinger, 2007; Tenga et al., 2010; Titman et al., 2015); team, player and manager rating (e.g. Knorr-Held, 2000; Bruinshoofd and Weel, 2003; Schryver and Eisinga, 2011; Baker and McHale, 2015); competitive balance and outcome uncertainty (e.g. Koning, 2000; Buraimo and Simmons, 2015); match importance (e.g. Scarf and Shi, 2009; Goossens et al., 2012); tournament outcome prediction (e.g. Koning et al., 2002; Groll et al., 2015) and tournament design and scheduling (e.g. Scarf et al., 2009; Goossens and Spieksma, 2012; Scarf and Yusof, 2011; Lenten et al., 2013) have been studied. Nonetheless, modelling results and scores, and other in-match outcomes, both straightforward (e.g. first player to score) and unusual (e.g. number of player cautions), motivated by the search for betting market inefficiency, have been a major motivational factor in the development of the state of the art. In this chapter, our aim is to describe the state of the art in the statistical modelling of match results and scores in particular.