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Article

Assessment of Psychological Zone of Optimal Performance among Professional Athletes: EGA and Item Response Theory Analysis

1
Virtual Laboratory of Sports and Health, Southwest University, Chongqing 402460, China
2
Sports Psychology and Education Research Center, Southwest University, Chongqing 402460, China
3
Education Sciences and Professional Programs, University of Missouri-St. Louis, St. Louis, MO 63121, USA
4
Faculty of Psychology, Southwest University, Chongqing 402460, China
*
Author to whom correspondence should be addressed.
Sustainability 2023, 15(10), 7904; https://doi.org/10.3390/su15107904
Submission received: 2 March 2023 / Revised: 29 April 2023 / Accepted: 3 May 2023 / Published: 11 May 2023
(This article belongs to the Special Issue Sports Psychology and Performance)

Abstract

:
Sport psychology researchers have been investigating athletes’ ideal performance levels for a long time. Key areas of investigation in this field involve determining if there is an optimal performance zone and how to evaluate it. To advance this line of research, the current research aimed to create a short but reliable tool for assessing the psychological state of professional athletes during their peak performance, known as the “optimal performance zone”. After developing an initial item pool, the final 10-item scale was retained and validated using factor analytical models and item response theory analysis based on 357 Chinese professional athletes in 12 different sports types. The average age of the participants was 19.4 years (SD = 3.67), and 54% were male. Experience in the sport ranged from 2 to 15 years, with a mean of 5.82 years (SD = 3.65). The brief scale was found to form a one-factor solution, with factor loading ranging from 0.55 to 0.77. The IRT-based marginal reliability of this scale is 0.90, and the scale showed predictive validity in predicting an athlete’s professional ranking (χ2(3) = 8.34, p = 0.039). The brief scale can quickly screen for a psychological zone of optimal performance among professional athletes, and implications are discussed.

1. Introduction

The quest to understand the factors contributing to an athlete’s optimal psychological state for achieving peak performance has been a prominent topic in sport psychology since Ravizza’s groundbreaking research in 1977 [1]. Achieving peak performance is a crucial goal for all athletes, especially in competitive settings, and it refers to a state in which they can achieve optimal physical and psychological functioning, resulting in superior performance [2,3]. The inquiry into whether rigorous training leads to specific psychological states among athletes, such as anxiety, anger, hostility, fatigue–inertia, and low self-confidence, has been the subject of extensive research for a considerable period (e.g., [4,5,6,7]). Additional inquiries persist regarding the definition of an ideal performance state that consistently facilitates superior athletic performance during competitions [8,9]. As Anderson, Hanrahan, and Mallett [10] indicated, understanding the psychological behaviors contributing to superior performance is essential in guiding professional athletes’ recruitment, training, and interventions.
In this regard, a persistent question in sport psychology has been whether a set of psychological behaviors exists for optimal performance. A survey of existing research suggests that peak performance is linked to several factors, including having self-confidence and high expectations for success, being both energized and relaxed, feeling in control, maintaining a high level of concentration, staying intently focused on the task, and being determined and committed [9]. However, several critical issues have been debated in the literature. For example, the definitions of peak performance are closely related to the concept of flow, and there is an overlap between these two ideas [11]. Toner and Moran [12] suggest that automated performance processes, such as effortlessness and a lack of awareness, should accompany controlled processes. Automated and controlled processes can work together to achieve optimal performance. This view is consistent with dual-process theories, which state that both automatic and controlled processes control human behaviors [13]. In fact, studies have suggested that the brain’s cognitive control and supervisory attentional systems are entirely engaged during flow [11,14]. Swann et al. [11] indicated that no single ideal or optimal performance state exists, and athletes should be aware of the psychological states necessary to control and maintain each condition rather than apply them to all performance circumstances.
Previous studies suggest optimal performance is associated with various cognitive, emotional, and psychological states [5,9,15,16,17]. For example, the individual zones of optimal functioning (IZOF) model [18] has been used to study emotion–performance relationships to identify a high likelihood of successful performance [3,15]. According to the IZOF model, emotion is a significant part of the biopsychosocial state. In the description of performance anxiety, five core dimensions—form, content, intensity, time, and context—were identified as essential [19]. When the intensity of emotions falls within the optimal zone, high performance is more likely to occur [20]. Ruiz, Raglin, and Hanin [21] suggest that future directions should focus on methodological aspects such as assessing performance-related emotions.
Along this line of research on assessment, a recent assessment tool is the psychobiosocial states (PBS-S) scale [22] to assess the personalized and multifaceted examination of athletes’ emotional and non-emotional experiences that are linked to their performance from the IZOF model perspective. Previous assessment tools include scales developed from similar but somewhat different perspectives, such as flow state scale-2 (FSS-2) [23], the profile of mood states (POMS) [24], positive and negative affect schedule (PANAS) [25], State-Trait Anger Expression Inventory-2 (STAXI-2) [26], Affect Grid [27], and competitive state anxiety inventory-2 (CSAI-2) [28]. Our literature review on the emotion–performance relationship and its assessment suggests two key themes. The first theme is that various psychological variables have been identified, with a focus on emotion and cognition, such as anxiety, emotional and cognitive regulation, self-efficacy, and arousal level [3,5,16,17,29,30]. In addition, athletes with particular personalities and emotional profiles are also thought to have optimal performance [31]. For example, a study conducted on British gymnasts has revealed that personality traits impact their training effectiveness [32]. Specifically, this study found that conscientiousness was linked to higher quality preparation, extraversion was associated with distractibility, and emotional stability was connected to the ability to handle challenges. However, it is worth noting that there are differing empirical findings on this topic. Similarly, Casolino et al. [5] found that athletes’ psychological state was similar to the iceberg profile as assessed by the Profile of Mood States (POMS) [24]. This profile consisted of a high degree of vigor and activity at the positive end, accompanied by low level of five negative states: depression, tension, anger, fatigue, and confusion. However, POMS did not make any distinction or differentiation among elite athletes in their study.
The second theme is that optimal performance is associated with automatic and controlled processes [3,10,11,12,33]. Anderson et al. [10] proposed a model that outlines the ideal psychological state for achieving outstanding performance. In this model, some components of the emotion–performance relationship are relaxation, focus, concentration, enjoyment, automatic execution, control, and a clear goal. For instance, in their study of Australian elite athletes, outstanding performance is marked by a mixture of automatic execution of tasks and self-regulation or control.
These two themes suggest that although there may not be one optimal psychological state for excellent performance, a common “zone-like” state may exist, as suggested by Ferrell et al. [33]. We characterize it as a zone of zero gravity because it embodies the idea of being free from anxiety, worries, and all other distracting factors, allowing athletes to experience automatic and controlled performance processes to the best of their ability. It describes the lower boundary of optimal performance.
Thus, in this study, we attempted to assess this zero-gravity zone phenomenon from the perspective Ferrell et al. [33] and Anderson et al. [10] suggested. Specifically, this study aimed to design a short assessment tool that can be used to quickly screen levels of psychological zero for optimal performance among professional athletes. This short instrument is intended for ongoing assessment for regular monitoring athletes’ emotional state during training and competition. As Barlow, Ellard, Boisseau, Allen, and Ehrenreich-May [34] stated, three fundamental parts make up emotion. The first is a subjective “feeling” state produced physiologically, and the second is cognitive, a plethora of thoughts and images accompanying particular emotions. The third part is a behavioral action propensity, which echoes the athlete’s learned behavioral reactions to the aforementioned emotional experience. Therefore, emotion can be considered a multifaceted process that includes experiencing and expressing a specific emotional state. Athletes must understand how their emotions and cognition engage in the performance process for any training to be effective. The first thing that athletes acquire is the ability to internalize their responses to performance on specific tasks and exhibit corresponding emotional reactions. Thus, an effective beginning involves establishing a starting point for emotional responses that may either facilitate or impede athletes’ performance and emotional well-being. As a monitoring tool, the brief assessment tool can also increase self-awareness about athletes’ psychophysiological evaluation skills. It enables athletes to analyze the factors that contribute to their success and the areas where they might face challenges during their performance. Thus, we aimed to develop a brief scale to ensure that the measurement is highly accessible to both coaches and athletes for regular monitoring with a minimized burden on them.
In order to achieve the objective stated above, we first used a two-step design to develop an initial item pool: (1) create items based on a critical realism ontological viewpoint [35]; and (2) validate the item using a focus group. Second, we used the item response theory (IRT) model to systematically explore the characteristics of the items regarding item discrimination and information. Third, we examined the scale’s predictive power in classifying professional athletes into different achievement groups.

2. Method

A Qualitative Approach to Initial Item Generation

In this study, we developed a set of initial items using a two-step design. First, we attempted to discover a link between psychological state and optimal performance, grounded in a critical realist position [35]. Specifically, the critical realism ontological viewpoint [35] seeks to identify causal explanations and asserts that causal mechanisms, processes, and contextual factors, such as optimal performance, impact particular events and circumstances. From this perspective, we sought a set of psychological elements (e.g., excitement or calmness) that may bear a causal explanation for excellent performance in sports. An in-depth examination of a relatively small sample of athletes may benefit the explanation of a complicated phenomenon. Accordingly, a qualitative technique is viable for critical realism, which has been considered a better methodology for exploratory studies on psychological states [36]. Thus, our technique of item development adopted the critical realist procedures [37,38].
Specifically, using a maximum variation subgroup sampling approach [39], we recruited a group of 31 athletes (male = 20, female = 11) who had recently delivered outstanding performances at national competitions. Because of this purposeful sample for theoretical reasons [40], we might have a better chance of obtaining data linking their ideal psychological states to their descriptions of these states during a particular competition event. The recruited athletes were from various sports types (e.g., field sports and fencing) and standards (e.g., national elite and world-class elite) so that we could maximally uncover patterns of the psychological states encountered. Using a semistructured and open-ended approach, we conducted the event-focused interview, focusing on the participants’ descriptions of their performance and the psychological states experienced in chronological sequence. The participants were asked the following probing questions and were free to expand on and develop any perceived significance.
-
What are the most common problems that you encounter during competition?
-
What do you consider to be the most important factors for performing optimally?
-
Could you describe a typical psychological process using an example from your experience?
-
How would you deal with a stressful or high-pressure situation?
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What strategies do you use to handle challenges during competition?
-
What factors may debilitate you from delivering an optimal performance?
-
What would be the decision-making process during the competition? Could you outline the factors that would go into your decision?
Items were developed primarily based on an emergent cross-case analysis [41], where we iteratively searched for similarities and differences between athletes to identify patterns and consistencies in psychological processes experienced when describing performance. Then, we defined themes representing the athletes’ psychological states that led to their optimal or non-optimal performance. Items were written according to the key terms that emerged from the themes. As a result, a pool of 13 items was compiled. The Supplemental Table S1 shows these original 13 items.
In the second step, these 13 items were reviewed and evaluated by a group of judges comprising five high-performance athletes and six coaches. The evaluation process was conducted based on a method proposed by [42], in which judges rated the items on five criteria: (1) clarity (item clearly written), (2) relevancy (relevancy of this item in optimal performance situations), (3) frequency (how often this psychological state occurs during competition), (4) intensity (how strong athletes experience this emotion), and (5) predictability (does this item predict excellent performance). Ratings were provided on a scale of zero to five, with zero indicating “not a very good item” and five indicating “a very good item.” We retained the items with a rating of three or above on all five criteria. This analytical process resulted in ten items. On average, these ten items were deemed good (M > 3.00) for their clarity, relevancy, frequency, intensity, and predictability.

3. Psychometric Study

The ten items were used for the further psychometric study, which included (1) factor analysis of dimensionality, (2) item response theory (IRT) analysis of item and scale characteristics, and (3) predictive validity of the scale. We detail each of these analyses below.

3.1. Participants

Participants in the psychometric study included 357 Chinese professional athletes (54% male, 46% female) from 12 different sports types, mainly from individual competition types, such as boxing or fencing. The average age of the participants was 19.4 years (SD = 3.67). Experience in the sport ranged from 2 to 15 years, with a mean of 5.82 years (SD = 3.65). The weight category level ranged from 40 kg to 96 kg. Among the participants, 8 were world-class elite athletes, 87 were national elites, 119 were first-tier, and 143 were second-tier. In deciding the sample size required for the psychometric study, we targeted more than 300 participants based on the studies by de Winter, Dodou, and Wieringa [43] and Kyriazos [44].

3.2. Procedure

Participants were recruited via the athletic college research participation network using online media about research opportunities. The informed consent form was obtained from those willing to participate, and they completed the questionnaire using a link to the questionnaire website. Athletes had the option to participate in this study voluntarily and had the right to withdraw from it at any time. This study was approved by the university’s research ethics committee (Protocol ID 2020314).

3.3. Measures

Psychological Zone of Optimal Performance (PZOP) scale. The ten items developed from the initial stage were used for IRT analysis. We expected these ten items to form one general factor to assess the latent construct of the psychological zone of optimal performance. They were rated on a four-point scale ranging from one (disagree) to four (completely agree). A high score indicates a high level in the psychological zone of optimal performance.
Demographic questionnaire. The participants were asked to fill out a demographic questionnaire, which gathered information about their age, gender, educational background, and level of achievement in their performance. Athletes’ performance success was assessed based on their performance rankings. We considered participants’ standing or performance success on a continuum scale corresponding to their ranking, with four indicating the most elite or more performance success and one indicating less performance success.

3.4. Data Analysis

Factor analysis. We used two types of factor analyses to examine the factor structure of the 10-item PZOP scale. The first type was exploratory graph analysis (EGA) [45], a new method within the framework of network psychometrics to estimate the number of latent factors. It provided a network plot to indicate the number of dimensions to retain, item clusters, and their association level. Other advantages include: (1) it can verify the stability of the dimensions and items in those dimensions; (2) the model fit was assessed using the entropy index, with the lower the value, the better the model; and (3) it can also identify redundant items in the data. The second was the confirmatory factor analysis to check the validity of the identified factor structure after the EGA analysis.
EGA model. EGA analysis, part of network psychometrics, was a novel addition to quantitative psychology aimed at examining psychological concepts [46]. Network psychometrics are based on the Gaussian graphical model (GGM) [47], which estimates the joint distribution of variables by modeling the inverse of the variance-covariance matrix. In EGA, nodes are variables or items connected by edges or links, which are partial correlation coefficients [48]. EGA combines the GGM model with a clustering algorithm for the weighted network [49] to assess the factor structure of the items. The use of network modeling to assess factor structure is justified because network modeling and factor modeling are closely related, as Golino et al. [45] indicated. For orthogonal factors, the resulting GGM consists of unconnected clusters (called communities), while for oblique factors, the resulting GGM consists of weighted clusters connecting each item. A community detection algorithm for weighted networks can transform a network model into a factor structure (dimensionality) assessment method. Golino et al. [45] proposed a new EGA algorithm for unidimensional and multidimensional factor structures using a graphical lasso or Triangulated Maximally Filtered Graph (TMFG). EGA is found to be superior to traditional dimension assessment methods (e.g., minimum average partial) and robust [50].
In addition, we used the bootstrap method to examine the stability of the dimensions and items in those dimensions. The fit of the factor structure from EGA was assessed using the entropy fit index. We also conducted Unique Variable Analysis (UVA) [51] to identify redundant items.
Confirmatory factor analysis. After exploratory analysis, we verified the factor structure using confirmatory factor analysis. Model fit was assessed by commonly used model fit indices, with acceptable fit achieved when RMSEA ≤ 0.08, CFI ≥ 0.90, TLI ≥ 0.90, and SRMR ≤ 0.08, whereas excellent fit is indicated by RMSEA ≤ 0.05, CFI ≥ 0.95, TLI ≥ 0.95, and SRMR ≤ 0.05 [52].
IRT model. After factor analysis, we conducted an item response theory (IRT) analysis to examine the characteristics of each item. There are two goals. The first goal was to examine how well the PZOP scale functions through two specific questions. (a) How do the items differ regarding discrimination and the information provided? In other words, the question is how much each item is associated with the underlying attribute and whether it can differentiate between individuals who vary regarding the trait. (b) How do the items differ regarding difficulty? That is, what is the range of trait levels each item assesses?
The second goal was to examine differential item functioning (DIF). We examined whether items of PZOP perform differently for various ranks of athletes (i.e., elite status vs. not).
Graded response model. Since the items were on the ordered rating scale, we used the graded response model (GRM) [53,54]. GRM is an item response theory model for polytomous items. The GRM models the probability of a response of m equal to or greater than a response category, c, for a given location along the latent trait, θ:
p ( m     c | θ i ) = e a j ( θ i - b j c ) 1 + e a j ( θ i - b j c )
where i is the person; aj is the item discrimination (i.e., slope parameter); and bj is the item threshold locations of each category (i.e., item difficulty parameters). In other words, Equation (1) indicates the likelihood of an individual answering with a score of 2 or higher on a 1 to 4 scale, assuming they possess a specific value of θ on the latent trait scale. The IRT model typically measures the latent variable or trait on a scale with a 0 average value and a standard deviation of 1.0. For example, if an item has a response scale of 1 to 4 and the threshold value for category 1 is −1.24, this means that, according to the model’s prediction, an individual needs to be more than one and a quarter standard deviations below the mean in order to have a 50% chance of being rated in category 1. Another important feature of IRT models is item and test information. It is possible to convert the slope parameter estimates into a curve of item information [55]. An item with larger slope parameters provides relatively more information, maximized around the threshold parameters. Item fit was assessed using generalized S-X2 statistics [56].
DIF analysis. Due to limitations in sample size among athletes with different elite statuses, a comparison of athletes with and without elite status was conducted. The item with a p-value less than 0.01 was considered a DIF item.
Predictive validity. In this study, we examined the predictive power of the PZOP scale in predicting the ranks of athletes (world-class elite, national elite, tier 1, and tier 2) using multinomial logistic regression.
In the current study, the analyses were performed using EGAnet [57], lavaan [58], mirt [59], Lordif [60], and nnet [61] packages in the R environment [62].

4. Results

4.1. Factor Analysis

Based on the EGA model, the result in Figure 1 shows one dimension of the 10-item PZOP scale, reflecting the construct’s unidimensional nature. To determine the stability of the unidimensional and its items, we ran a bootstrap analysis with 500 samples. The results indicated one dimension across all sample runs, with all ten items belonging to the dimension (or community). The results suggested the stability of one-dimensional PZOP and its items. The entropy fit index was zero, suggesting a perfect fit. The results of the UVA analysis showed that no redundant items were identified.
As further evidence of the scale’s unidimensional nature, the CFA results indicated a good model fit: CFA = 0.94, TLI = 0.92, RMSEA = 0.082, SRMR = 0.045. Figure 2 shows the parallel analysis results; the first-to-second eigenvalue ratio was 27. All the results confirmed the expected unidimensionality of the PZOP scale. Table 1 shows the items’ factor loading on the unidimensional structure.

4.2. IRT Model

Table 2 shows the item slope estimates and threshold parameters for the ten items and their corresponding item fit statistics. All items have a good item-level fit, as indicated by the S-X2 statistic, its corresponding root mean squares error of approximation (RMSEA), and p-value. The size of the item slope parameters, αi, ranges from 1.43 to 2.68, with the median being 1.93. This suggests that these items tend to be able to differentiate among athletes and have a strong relationship with the psychological zone of optimal performance level. Because αi is related to the item information (a larger αi implies more information), items 3, 7, 8, 9, and 10 tend to provide a bit more information than the rest. To clarify this concept, let us examine the item information curves for the three items, as shown in Figure 3. The x-axis displays the estimated standard score units for the latent trait values. The average of the latent trait (estimated θ = 0) suggests the mean of this specific athlete population. As can be seen in Figure 3, Item 7 provided much more information than Item 5.
An item is considered good if its difficulty parameters cover the widest range of θ values. In the current case, the item difficulty parameters and, thus, the item information were symmetrical around estimated θ, with the median being −1.52 at the low end, −0.02 at the middle, and 1.24 at the high end (see Table 2). Thus, the items on the PZOP scale assessed a wide range of trait levels. Although the amount of information provided varied depending on the value of θ, the differences were not large.
Figure 4 shows the distribution of information on the total scale. The scale provided the most information for estimated θ values between θ = −2 and θ = 2, with a maximum between −1 and 0. That is, the information was maximal for values of θ that were slightly located to the left of the center of the scale, reflecting that the scores’ distribution is a bit skewed to the left. This result suggests that the scale discriminated best between athletes with average to somewhat low PZOP scores. IRT-based marginal reliability is 0.90.

4.3. DIF Analysis

We tested for DIF in PZOP items between low- and high-elite-status athletes, and the results of the DIF analysis did not identify any items with significant DIF. Table 3 shows the p values associated with χ2 tests for each threshold of an item, and Figure 5 shows the item probability function curves across these two groups for each response option. As shown in Figure 5, the item probability function curves between these two groups of athletes were identical across all items.

4.4. Predictive Validity

In order to assess how the PZOP performance zone scale is predictive of athletes’ elite status, we conducted a multinomial logistic regression analysis with the PZOP scale as an independent variable and tier 2 athlete status (i.e., the lowest level in the sample) as a reference group. As shown in Table 4, the results indicated that the PZOP scale significantly predicted athletes’ elite status (χ2(3) = 8.34, p = 0.039). Specifically, with one unit increase in the PZOP score, the odds of elite status from tier 2 to national elite increased by 73%, and from tier 2 to world-class elite increased by 221%. There was no significant difference in odds between tier 2 and tier 1 status. Table 3 shows the results of the multinomial regression analysis.

5. Discussion

The primary purpose of the current study was to develop a brief measure that coaches and athletes can use as a monitoring tool to quickly screen athletes’ psychological zone for optimal performance. The item generation process was based on the critical realism ontological framework [35], since we seek mechanisms, processes, and contextual factors that may bear a causal explanation for excellent performance in sports. To this end, we adopted the critical realist procedures [37,38] for item development, using an emergent cross-case analysis [41]. As a result, a pool of ten items was compiled and subjected to further psychometric study.
The EGA and confirmatory factor analysis results supported the unidimensional structure of the 10-item psychological zone for optimal performance (PZOP) scale. The factor loading of all items on the dimension was high, and this result was further supported by the IRT analysis, where the slope parameter showed a strong association between the items and the underlying construct. The items of the PZOP scale assessed a wide range of psychological zone levels, with the most discriminant ability between average and somewhat low levels (i.e., 0.3 to −1.0 range). The DIF analysis did not find any items with differential performance. The predictive analysis of the PZOP scale showed that the scale could predict the athletes’ elite status, with a higher score being more likely to be at the elite level.
Our conceptualization of the psychological zone for optimal performance is based on the ideas discussed by Ferrell et al. [33] and the conceptual model suggested by Anderson et al. [10]. Our literature review regarding the assessment of optimal performance showed that many studies approach the assessment based on emotional and non-emotional experiences. Most assessment tools are multidimensional, such as Flow State Scale [36] or assessments based on the IZOF model perspective. In contrast, the PZOP represents an assessment strategy that can be used as a frequent monitoring tool before, during, and after training or competition. Creating a unidimensional and brief measure of a broadly defined psychological zone for optimal performance can reduce the burden of multidimensional measures (e.g., the Flow State Scale) that possess intricate factor structures, scoring rules, and excessive length, which may hinder their practical utility.
Further, we intentionally chose a small set of items representing various psychological features. Because some coaches and researchers are interested in obtaining a quick snapshot of an athlete’s performance-related psychological state but have minimal time, we attempted to create an instrument by selecting items most informative across the latent trait levels. This work’s overarching theme is that coaches or athletes do not necessarily use complex instruments to obtain a high-quality assessment of a psychological zone for optimal performance.
Understanding how psychological states are experienced and the processes that lead to them is a complex issue. Swann et al. [11] indicated that different psychological states could occur in specific contexts via distinct processes, and different psychological skills can be used to maintain each state. They found that two psychological states are responsible for optimal performance: flow and clutch. Although these two states differed [11], they shared common core elements for achieving the outcomes. Given the dynamic account of the psychology of optimal performance, it is very challenging to have an instrument that captures all these different psychological states under various conditions or contexts. What we attempted to achieve by developing a brief psychological zone for excellent performance was to capture the essential elements of the basic psychological needs of optimal performance instead of a comprehensive account of psychological states for excellent performance. For example, we found that the PZOP scale could account for 35% to 47% of the variance across the subscales of the flow state scale developed by Jackson and Eklund [23]. While we acknowledge that placing too much weight on one measure of the psychological zone for excellent performance would not be appropriate, it provided a practical monitoring tool for assessing athletes’ psychological zones that could function across different psychological states and performance conditions in training and competitions. For example, the coaches could regularly assess athletes’ emotional states during training and establish a baseline profile of these emotional states. The strengths and weaknesses of each athlete’s profile can be evaluated and linked to performance and its improvements. The emotional profiles can be dynamically tuned for optimal emotional states during training. In competition, the profile of these emotional states can be used as a reference point so that the athletes can intentionally calibrate their emotional levels accordingly.
Several limitations should be considered and addressed in future studies. First, the retrospective self-report nature of the measure of the psychological zone for optimal performance allows for potential recall bias that may affect findings. However, we aimed to use it as a momentary ecological assessment of a psychological zone for optimal performance. Second, a limitation of our sample was that it was a sample of professional athletes from China. Future research needs to examine the performance of the items on diverse athlete samples from various regions worldwide to increase the instrument’s generalizability and utilities. Third, since the short scale is intended to be regularly used, there is the risk of providing socially desirable responses, making the scale less sensitive to emotional change. Thus, the timing of the assessment should be empirically established to minimize the risk. Fourth, as we conceptualized it, the psychological zone of optimal performance could be similar across individual and team sports. However, differences may exist regarding the psychological zone involved in different sports competitions, such as individual versus team competitions. Future studies can examine this issue using this short scale, which should be interesting.
Despite these limitations, this study contributes a short measure of a psychological zone for optimal performance composed of items representing some critical aspects of optimal performance-related psychological state. We expect that the concise nature of this measure, coupled with its solid psychometric foundation, will likely enhance its usage in both practical settings and future investigations.

Supplementary Materials

The following supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/su15107904/s1. Table S1: Original 13 Items Developed Based on Qualitative Study.

Author Contributions

Conceptualization, B.L. and C.D.; Methodology, B.L., C.D. and H.S.; Resources, H.S., F.F. and L.G.; Data curation, H.S., F.F. and L.G.; Writing—original draft, B.L.; Writing—review & editing, C.D. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Institutional Review Board Statement

The research ethics committee of the university approved the this study (Protocol ID 2020314), and the procedures adhered to the principles of the Declaration of Helsinki. Informed consent was obtained from all participants involved in this study.

Informed Consent Statement

Informed consent was obtained from all subjects involved in the study.

Data Availability Statement

The datasets produced and evaluated during this study are accessible from the first author upon a reasonable request.

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 1. EGA plot of the ten-item PZOP scale. Each circle with a number inside represents a PZOP item, and the circle with label 1 indicates that the graph represents 1 factor.
Figure 1. EGA plot of the ten-item PZOP scale. Each circle with a number inside represents a PZOP item, and the circle with label 1 indicates that the graph represents 1 factor.
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Figure 2. Parallel analysis of items in the psychological zone of the optimal performance scale.
Figure 2. Parallel analysis of items in the psychological zone of the optimal performance scale.
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Figure 3. Distribution of item information function for Items 5, 7, and 9.
Figure 3. Distribution of item information function for Items 5, 7, and 9.
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Figure 4. Distributions of total scale information.
Figure 4. Distributions of total scale information.
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Figure 5. Item probability function curves between low- and high-elite-status athletes for each response option. cat:1 = low-elite status. cat:2 = high-elite status. The items are sorted in descending order. The response curves are identical across the two groups; thus, there appears to be only one set of response curves.
Figure 5. Item probability function curves between low- and high-elite-status athletes for each response option. cat:1 = low-elite status. cat:2 = high-elite status. The items are sorted in descending order. The response curves are identical across the two groups; thus, there appears to be only one set of response curves.
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Table 1. Factor loading of 10 items of the psychological zone of the optimal performance scale.
Table 1. Factor loading of 10 items of the psychological zone of the optimal performance scale.
Factor Loading
1I feel my performance is effortlessly smooth.0.61
2I feel calm when I perform.0.65
3I feel confident, regardless of the outcomes.0.71
4I have a clear focus during the performance.0.61
5I am very competitive during the performance.0.55
6I can become excited before the competition.0.56
7I feel my karma during the competition.0.77
8I have clear strategies during the competition.0.73
9I enjoy the competition process.0.68
10I can capture the details that benefit me during the competition.0.70
Table 2. Slope, threshold parameter estimates, and item fit indices for the graded response model.
Table 2. Slope, threshold parameter estimates, and item fit indices for the graded response model.
Slope and Threshold ParameterItem Fit
ItemSlopeThreshold 1Threshold 2Threshold 3S-X2RMSEAp
11.65 −1.270.441.9640.970.020.19
21.78 −1.050.391.6623.230.000.89
32.13 −1.010.171.1841.570.030.17
41.69−2.29−0.800.7132.940.010.42
51.43−2.68−0.680.8655.170.050.01
61.44−2.55−0.850.7734.560.000.63
72.68−0.860.351.3624.620.000.59
82.33−1.370.031.2951.940.040.01
92.08−1.97−0.560.4343.160.030.07
102.09−1.67−0.061.3530.590.010.44
Note. α level is adjusted to be 0.001.
Table 3. p-value associated with χ2 tests for each item.
Table 3. p-value associated with χ2 tests for each item.
ItemThreshold 1Threshold 2Threshold 3
10.6340.8770.848
20.4330.1280.061
30.5410.8140.844
40.8550.7930.512
50.9130.8680.602
60.4570.1830.092
70.4900.7830.907
80.7760.9320.807
90.0830.1920.589
100.0100.0340.636
Note: p-value < 0.01 is considered statistically significant.
Table 4. The coefficients of the multinomial regression analysis.
Table 4. The coefficients of the multinomial regression analysis.
β0βOdds Ratio
Tier 2---
Tier 1−0.350.0211.23 (0.83, 1.82)
National Elite−1.74 **0.55 *1.73 (1.11, 2.69)
World-class Elite−5.89 **1.17 *3.21 (1.01, 10.17)
Note: The status of Tier 2 is set as the reference group. * p < 0.05. ** p < 0.01. The number in the parentheses indicates the 95% confidence interval.
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Li, B.; Ding, C.; Shi, H.; Fan, F.; Guo, L. Assessment of Psychological Zone of Optimal Performance among Professional Athletes: EGA and Item Response Theory Analysis. Sustainability 2023, 15, 7904. https://doi.org/10.3390/su15107904

AMA Style

Li B, Ding C, Shi H, Fan F, Guo L. Assessment of Psychological Zone of Optimal Performance among Professional Athletes: EGA and Item Response Theory Analysis. Sustainability. 2023; 15(10):7904. https://doi.org/10.3390/su15107904

Chicago/Turabian Style

Li, Bing, Cody Ding, Huiying Shi, Fenghui Fan, and Liya Guo. 2023. "Assessment of Psychological Zone of Optimal Performance among Professional Athletes: EGA and Item Response Theory Analysis" Sustainability 15, no. 10: 7904. https://doi.org/10.3390/su15107904

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