1 Introduction

The psychology of language learning has traditionally emphasized psychopathology and dysfunction. However, the emergence of positive psychology in the field has redirected attention towards positive aspects of second or foreign language (L2) learning and teaching. The burgeoning expansion of positive psychology (PP) as an interdisciplinary domain (Seligman & Csikszentmihalyi, 2000) has prompted researchers to conceptualize the essential constituents of positive personal experience across various fields, such as psycholinguistics (Dewaele et al., 2023; Elahi Shirvan & Taherian, 2020; Kruk et al., 2022; Li et al., 2023). The notion that the subjective well-being of L2 learners extends beyond the mere absence of negative emotions is crucial in this transition (Dewaele & Li, 2020; Pawlak et al., 2020). Simply put, acquiring the skill to regulate negative situations in a manner that reduces distress does not guarantee that learners will encounter happy feelings that improve their overall state of wellbeing.

Savoring refers to “the capacity to attend to, appreciate, and enhance the positive experiences in one’s life” (Bryant & Veroff, 2007, p. xi). It involves actively generating, intensifying, and prolonging one’s positive emotions and experiences. Within the realm of language learning, it is essential to emphasize that simply having positive emotions does not necessarily ensure that a learner feels capable of fully savoring them. In contrast, effectively regulating positive feelings requires not only the capacity to experience positivity but also the ability to identify, handle, and maintain it (Bryant, 2021).

Bryant’s (2003) study had a substantial influence on the growing body of research on savoring in multiple disciplines (e.g., Borelli et al., 2020; Smith & Bryant, 2019). The outcome was the creation of the 24-item Savouring Views Inventory (SBI), a self-assessment instrument designed to measure one’s capacity to identify and appreciate positive emotions and events. However, because of the context-dependent nature of psychological concepts, it is necessary to create a scale of savoring that is specific to the language domain.

Up to now, other PP constructs have been introduced into this domain, such as foreign language enjoyment (FLE; Dewaele & MacIntyre, 2014), foreign language boredom (FLB; Pawlak et al., 2020), and foreign language playfulness (FLP; Kruk et al., 2023). There is an increasing recognition of how negative feelings, such as boredom, can be substituted with good emotions, such as enjoyment, throughout the process of learning a language (e.g., Dewaele et al., 2023; Elahi Shirvan & Taherian, 2020; Kruk et al., 2022; Li et al., 2023). Nevertheless, there is still a need to develop a specialized construct and a dedicated scale within the L2 domain to better understand and enhance the appreciation, maintenance, and intensification of positive emotions. The purpose of this research is to explore the psychometric properties of the L2 Savouring Beliefs Inventory via the utilization of ESEM. ESEM integrates the advantages of both exploratory factor analysis (EFA) and confirmatory factor analysis (CFA) within a cohesive measuring framework (Alamer & Marsh, 2022).

2 Conceptualization of Savoring and Previous Research

Bryant and Veroff (2007) contend that savoring involves the intentional application of individuals’ beliefs and behaviors to enhance the intensity, length, and recognition of positive experiences and emotions. It governs individuals’ positive emotions using techniques and strategies that focus on emotions related to positive events in our past, present, and future. Savoring pertains to the beliefs concerning an individual’s abilities or capacity in order to explain and capitalize on positive experiences in previous, current, and forthcoming events using different strategies. Savoring strategies refer to specific actions and mental processes, such as enhancing memory and self-praise, that are used to cultivate positive attitudes and, hence, enhance positive emotions.

Research conducted by positive psychologists has demonstrated a positive correlation between a heightened level of savoring and increased levels of optimism (Biskas et al., 2018), happiness (Salces-Cubero et al., 2019), and life satisfaction (Smith & Bryant, 2019). In addition, empirical studies have indicated that a decreased level of savoring is related to sadness (McMakin et al., 2011), hopelessness (Chen & Zhou, 2017), and anxiety (Pereira et al., 2021). Research in the field of education has shown that savoring has several benefits. In addition to preventing emotional exhaustion among teachers (Picado, 2012), it increases creativity among learners (Lee et al., 2016), it improves engagement and learning results (Chang et al., 2021), and it decreases the detrimental influence of perfectionism on distress (Klibert et al., 2014). Pitts (2019) has expanded the notion of savoring to include the use of speech and language in social interactions.

A milestone in empirical research into savoring was the development of the Savoring Beliefs Inventory (SBI; Bryant, 2003) as a self-evaluation instrument that investigates individuals’ inherent beliefs regarding their capacity to appreciate positive events in three distinct time periods: (1) looking for the future, (2) savoring the here and now, and (3) contemplating the past. Bryant (2003) provided evidence that supports the validity and reliability of the SBI, including its structural, discriminant, convergent, and predictive validity, along with its internal consistency and longitudinal reliability. Researchers have examined the accuracy of the SBI and its measurement properties in several locations, including France (Golay et al., 2018), China (Lin et al., 2011), Japan (Kawakubo et al., 2019), Korea (Kim & Bryant, 2017), Iran (Aghaie et al., 2017), and Turkey (Metin-Orta, 2018).

2.1 Savoring in SLA

While studies on savoring have been increasing in various fields, there is a limited amount of research specifically focusing on this idea in the field of applied linguistics. Gregersen et al. (2016) employed a PP qualitative intervention design, which involved savoring tasks. They observed how a language learner and a teacher utilized savoring strategies to integrate self-awareness into classroom activities and to embrace everyday experiences as part of language learning and teaching. The findings revealed that both the learner and the teacher perceived the savoring strategy as a highly successful method for managing their emotions. It is important to mention that the activity of savoring was specifically focused on one part of savoring, which is reminiscing about savoring. In the tasks, learners focused on recalling enjoyable experiences and consciously sought to maintain a positive mindset. Jin et al.’s (2021) empirical study indicated that the practice of savoring can effectively reduce anxiety and alleviate some of its adverse effects. According to Gregersen (2022), reflecting on past achievements in foreign language learning and the growth of proficiency over time has an impact on various aspects of EMPATHICS (Oxford, 2016). This is because savoring strategies can elicit positive emotions, enhance awareness of learners’ strengths, and foster positive self-perception.

2.2 The Current Study

Differences in the capacity to savor positive emotions from enjoyable events can lead to differences in overall happiness. Anticipating positive outcomes might be difficult if there is uncertainty about whether a learner will actually feel positive about them. Likewise, the notion that enjoyment is fleeting might impede present joy, particularly if one is anxious about being unable to experience that joy again in future circumstances. Hence, identification of individual differences in savoring beliefs could aid researchers in clarifying disparities in positive functioning (Bryant, 2021). It is possible to envisage two language learners, each displaying modest levels of positive emotions in terms of frequency, intensity, and duration while learning a new language. Suppose one learner feels that despite their utmost efforts, they are unable to experience positive emotions from learning an L2. In contrast, the other learner believes they can enjoy such experiences but currently prioritizes other more intriguing activities. Existing tools employed to measure emotional states would categorize both learners as having low levels of positive emotions. However, the first learner seems to lack certain skills essential for effective learning, while the second does not. Therefore, there is a need for an instrument that is both conceptually sound and psychometrically robust to effectively assess savoring beliefs in the context of L2 learning.

The current study sought to validate the L2SBI, which is a modified version of the domain-general SBI (Bryant, 2003), based on the belief that specialized tools should be created to accurately measure the unique aspects of L2 learning. The aim was to explore the psychometric characteristics of the L2SBI in a group of Iranian individuals who are learning the English language as a foreign language. Specifically, we examined the instrument’s internal consistency, construct validity, dimensionality, and measurement invariance across gender and proficiency level. To obtain the most concise model for the L2SBI, we compared CFA solutions with ESEM solutions, the latter of which combine the advantages of EFA and CFA.

ESEM provides several advantages compared to traditional CFA and EFA. According to the research by Morin et al. (2020) and Marsh et al. (2014), ESEM is considered to be a more robust, strict, and adaptable statistical method compared to others. This is because: (1) it has the ability to compute both CFA and EFA solutions at the same time; (2) it can estimate measurement solutions that are less restrictive and allow for cross-loadings, resulting in fit metrics and parameter estimates that are less biased; (3) it often provides a substantially superior fit to the data in comparison to CFA and EFA solutions; and (4) the latent factor correlations generated by ESEM solutions are less biased.

Alamer and Marsh (2022) provide a set of guidelines for effectively utilizing ESEM and bifactor ESEM to establish the construct validity of measuring tools in the field of SLA. ESEM has been employed in recent empirical studies to evaluate the construct validity of various scales, including the Basic Psychological Needs in Second Language scale (Alamer, 2022a), the self-determined motivation scale (Alamer, 2021a), the Boredom in Learning English Outside of School questionnaire (Pawlak et al., 2023), and the Boredom in Practical English Classes-Revised (Kruk, Pawlak et al., 2023). Based on these studies, it was found that both ESEM and bifactor ESEM were highly effective and performed better than their CFA counterparts. Accordingly, the following research question was addressed:

What is the factor structure of the L2SBI, and what are its psychometric properties?

3 Method

3.1 Participants

Participants comprised 327 non-English university students from five Iranian universities. They completed an online survey utilizing the Google Form online survey tool. The results of the Oxford Placement Test revealed that participants’ language proficiency ranged from elementary to upper-intermediate. Table 1 shows demographic properties of participants.

Table 1 Demographical properties of participants (N = 327)
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3.2 Instrumentation

The data were collected by means of the L2 Savoring Belief Inventory (L2SBI), which was adapted from the SBI (Bryant, 2003). The tool employs 24 items with the same 7-point Likert scale as the SBI, with answers varying from ‘strongly disagree’ (1) to ‘strongly agree’ (7) (see Appendix). Higher L2SBI scores indicate a stronger perceived capacity to savor L2 learning experiences and make progress. In order to ensure that the adopted language-domain-specific SBI includes items about L2 learning, the majority of the items were adjusted accordingly (e.g., “feel uncomfortable when anticipating” was modified to “I feel uncomfortable when anticipating my progress in learning English”).

It was anticipated that the L2SBI would have a componential structure similar to the SBI: a general factor of L2SBI and three subfactors, including anticipating progress in learning English, savoring the moment while learning English, and reminiscing about experiences in learning English. For the sake of simplification, we call them anticipating, savoring the moment, and reminiscing.

We translated all the statements into Persian, and two translation experts back-translated the Persian version into English. After comparing the back-translated items to those from the original scale, we created the final Persian version of the L2SBI. Finally, a pilot study with a limited number (N = 18) of university students showed that all the items were suitable in terms of content and were understandable. This resulted in a final scale of 24 statements, that is, anticipating (8 items), savoring the moment (8 items), and reminiscing (8 items). Participants in the pilot research were excluded from the main phase of data collection.

3.3 Data Analysis

3.3.1 Measurement Models

Data analyses were conducted by Mplus v8.6. (Muthén & Muthén, 2017). It should be noted that when performing a confirmatory factor analysis (CFA) on the structural model of a questionnaire, researchers commonly opt for the maximum likelihood (ML) estimation when dealing with continuous data. However, recent research by Brauer et al. (2023) has indicated that Likert-type scales utilized in psychology represent a type of data that is not continuous or normally distributed. As a result, it is recommended to utilize the Weighted Least Squares Mean and Variance Adjusted (WLSMV) method for analysis purposes (Brauer et al., 2023). Consequently, the WLSMV estimator was employed in order to address the ordinal characteristics of the response data produced by Likert-type rating scales.

To evaluate the construct validity of the L2SBI, Mplus was used to employ a competitive measurement modeling technique that included CFA and ESEM (Asparouhov & Muthén, 2009; Alamer, 2022b; Alamer & Marsh, 2022; Van Zyl & Ten Klooster, 2022). Within the framework of CFA solutions, all elements were strictly limited to loading exclusively into their intended factors, whereas the cross-loadings were fixed to zero, but the error terms were permitted to associate (Wang & Wang, 2020). Three CFA solutions were created and calculated:

  • Model 1: the unidimensional CFA solution of general L2SBI.

  • Model 2: the first-order CFA solution is comprised of three factors.

  • Model 3: the bifactor CFA solution of general L2SBI (see Fig. 1).

Fig. 1
figure 1

The bifactor CFA model of L2SBI

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Subsequently, two ESEM models were also evaluated. The ESEM solutions were based on the same theoretical principles as the CFA solutions, the only difference being that cross-loadings were permitted. However, these cross-loadings needed to be minimized as much as possible. The following ESEM solutions were taken into account:

  • Model 4: the ESEM solution (see Fig. 2).

  • Model 5: the bifactor ESEM solution of general L2SBI (see Fig. 3).

Fig. 2
figure 2

The ESEM model of L2SBI

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Fig. 3
figure 3

The bifactor ESEM model of L2SBI

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The sufficiency of these models was assessed using the following metrics: \({\chi ^2}\)/df < 3, CFI > 0.90, TLI > 0.90, RMSEA < 0.08, and SRMR < 0.08 (Hu & Bentler, 1999). Following the identification of suitable fitting solutions, a thorough assessment of the measurement quality of the solutions with appropriate model fit was carried out (Morin, 2023). When evaluating quality measurements, we considered the following criteria: (1) standardized factor loadings, which should have significant loadings with λ > 0.35; (2) item uniqueness, which should have residual error variances (δ) > 0.10 but < 0.90; (3) cross-loadings, which should have λ < 0.30; and (4) subscales’ correlations, where the solution with lower factorial intercorrelations between the subscales is potentially the best solution (Morin et al., 2020).

3.4 Descriptive Statistics and Factor and Item Level Parameters and Reliability

Descriptive statistics consisted of the following measures: item means (M); skewness; kurtosis; and corrected item total correlations (CITC). The CITC scores indicate the distinct association between each item and the general factor that is assigned to it (Zijlmans et al., 2019). The skewness and kurtosis values (+ 2; -2) were employed to assess the normal distribution of the data (Collier, 2020). In addition, the criterion for representing related factor items was the use of CITC scores greater than 0.30 (George & Mallery, 2019).

Initially, we computed Cronbach’s alpha coefficients to evaluate the internal consistency of each subfactor and the general L2SBI. Based on this estimate of reliability, which is derived from item variances and covariances, all items are assumed to have equal loadings on the underlying factors. Therefore, the value of the measurement is affected by the average intercorrelation among items and the quantity of items. Simply put, if the number of items and their intercorrelation values are increased, Cronbach’s alpha will increase as well (Rodriguez et al., 2016). Cronbach’s alpha is affected by both shared and unique item variability when dealing with multidimensional data. This can result in either an overestimation or an underestimation of the scale’s reliability (Al Nima et al., 2020). Considering the restrictions of Cronbach’s alpha, we calculated Omega reliability coefficients that demonstrate robust generalizability and can help researchers overcome the constraints of Cronbach’s alpha. Omega coefficients are derived from factor loadings and do not require that the loadings be equal. They can determine the multi-dimensional instrument’s reliability by distinguishing variation caused by general factors from that of specific components (Reise et al., 2018). Four omega coefficients were computed in this study.

  1. (1)

    General Omega Composite (ωC), which is a reliability estimate quantifying the proportion of shared variability among items in a solution that can be attributed to a reliable variance in both the general factor and specific subfactor. A score above 0.70 indicates satisfactory internal consistency and reliability (Hayes & Coutts, 2020).

  2. (2)

    The Omega composite subscale (ωCS), which is a reliability estimate offering information about the portion of reliable variance in a specific solution that is attributed only to the reliable variance of the general component (Al Nima et al., 2020).

  3. (3)

    The general omega hierarchical (ωH), which is a reliability estimate offering information about the amount of variance in all items within a solution that is solely due to reliable variance for the general component (Al Nima et al., 2020). A score exceeding 0.50 indicates strong evidence in favor of a wide-ranging general latent component, as stated by Reise et al. (2018).

  4. (4)

    The Omega hierarchical subscale (ωHS) is being referred to as a measure of reliability that indicates the proportion of reliable variance specific to a particular subfactor while accounting for the reliable variance related to the general component.

Subsequently, we calculated the explained common variance (ECV). The ECV is a metric that precisely quantifies the proportion of shared variation that can be explained by the general component. Studies on ECV estimations applying multiple data suggest that data with ECV values lower than 0.80 demonstrate multidimensionality and should be divided into multiple variables. On the other hand, data that has ECV values greater than 0.80 are considered to be unidimensional, according to Quinn (2014). Furthermore, the computation of the item-explained common variance (I-ECV) was performed. The I-ECV is a measure that calculates the amount of shared variability at the individual item level that can be associated with the general factor (Stucky & Edelen, 2014). I-ECVs greater than 0.85 indicate that the general component is unidimensional (Stucky & Edelen, 2014). Hence, IECVs that are below 0.85 are selected to provide evidence for the multidimensionality of the general component.

We additionally examined the added values of the three subscales (i.e., anticipating, savoring the moment, and reminiscing) to ascertain if the scores of these individual components contributed to a greater extent to the general score variation. The added values were derived from the hierarchical Omega or ECV values of individual factors, as advised by Dueber and Toland (2023), conditional upon the composite Omega of specific components. According to Dueber and Toland (2023), when specific components have poor reliability (Omega = 0.60), a hierarchical Omega of 0.25 or an ECV of 0.45 is considered sufficient. This suggests that the specific elements are likely to provide additional value beyond the general score. When the reliability is modest (Omega = 0.80), a value of hierarchical Omega = 0.20 or ECV = 0.30 is sufficient. However, the importance of hierarchical Omega, or ECV, decreases as Omega increases beyond this point (Dueber & Toland, 2023).

4 Results

4.1 Measurement Models

Table 2 shows the goodness-of-fit data for the different possible CFA and ESEM measurement solutions. The unidimensional CFA solution and the first-order CFA model could not effectively fit the data (\({\chi ^2}\)/df > 3, CFI, and TLI < 0.90). Adequate model fit was seen in the bifactor CFA, ESEM, and bifactor ESEM solutions (\({\chi ^2}\)/df < 3, CFI & TLI > 0.90, RMSEA & SRMR < 0.08).

Table 2 Fit indices for the six measurement models
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In evaluating the measurement models, Table 2 indicates that the bifactor CFA model provided a satisfactory match for the data. The bifactor ESEM solution demonstrated a relatively better fit compared to the ESEM solution (CFI = 0.99 vs. 0.98; TLI = 0.97 vs. 0.96; RMSEA = 0.02 vs. 0.03). In order to choose the most suitable model, we additionally evaluated the measurement quality of the bifactor CFA, ESEM, and bifactor ESEM solutions.

4.2 Measurement Quality

Table 3 displays the measurement quality for ESEM, bifactor CFA, and bifactor ESEM solutions. Since we found that two out of the seven factor loadings for anticipating in the ESEM solution were lower that 0.30, we were unable to establish a clearly defined model for the ESEM solution. Furthermore, in this model, certain items had medium cross-loadings and they did not meet the required level of item uniqueness (δ > 90). We looked at the bifactor CFA and the ESEM solution since moderate to high cross-loadings in the ESEM could suggest a higher factor existed (Morin et al., 2020).

The measurement quality of the bifactor CFA was confirmed by the presence of the well-defined factors in the bifactor CFA solution. The level of item uniqueness was adequate (δ > 0.10 but < 0.90). Therefore, the bifactor CFA models were retained for subsequent analysis. Regarding the bifactor ESEM solution, we found that the model is well-defined based on the fact that the factor loadings for both the specific and general factors were mostly medium to large (λ > 0.30), and the cross-loadings were minor (λ < 0.35). The item’s uniqueness was adequately high (δ > 0.10 but < 0.90). Consequently, both bifactor CFA and bifactor ESEM models were retained for additional examination. It is important to mention that since the bifactor solution fits the data more appropriately, it was not possible to calculate inter-factor correlations because they were restricted to zero.

Table 3 Standardized parameter estimates from the CFA and ESEM models
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Prior to selecting bifactor CFA or bifactor ESEM solutions as the best model, we should thoroughly assess the reliability and validity of parameter estimations (such as ωs, ECV, and IECV) (Morin et al., 2023). Therefore, we conducted an additional evaluation of these parameters before making the final decision.

4.3 Factor and Item Level Parameters and Reliability

Cronbach’s alpha values greater than 0.80 indicate that the general factor and specific factors were adequately addressed by both the bifactor CFA and bifactor ESEM solutions (Nunnally & Bernstein, 1994). However, as shown earlier, the high level of Cronbach’s alpha coefficient might be due to the influence of several factors, including general and specific factors. To overcome the restrictions of Cronbach’s alpha, we further calculated Omega reliability coefficients. The results, presented in Table 4, provide a comparison of the hierarchical and composite omega values for specific and general factors. Additionally, the ECV and I-ECV (see Table 5) values for two competing models, namely the bifactor CFA solution and the bifactor ESEM solution, are also included.

Table 4 Item level and factor level reliability indicators of bifactor CFA model and bifactor ESEM model
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Table 5 Descriptive statistics for the bifactor ESEM solution
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The bifactor ESEM and bifactor CFA solutions were compared. The findings indicated that the bifactor ESEM model produced higher composite omega values for the general factor (ωc = 0.97 vs. 0.93) and for the three individual factors: anticipating (ωc = 0.91vs. 0.90), savoring the moment (ωc = 0.92 vs. 0.91), and reminiscing (ωc = 0.95 vs. 0.91). Furthermore, the bifactor ESEM model produced a greater hierarchical omega value for the general factor (ωh = 0.84 vs. 0.53) but not for the three specific factors of anticipating (ωh = 0.30 vs. 0.56), savoring the moment (ωh = 0.26 vs. 0.64), and reminiscing (ωh = 0.29 vs. 0.68). In addition, the ECV score for the general component in the bifactor ESEM model exhibited a higher value (ECV = 0.68) compared to the alternative value (ECV = 0.31). However, the bifactor CFA solution showed somewhat higher ECV scores for the three specific components that measure anticipating (ECV = 0.34 vs. 0.63), savoring the moment (ECV = 0.29 vs. 0.71), and reminiscing (ECV = 0.31 vs. 0.72). A lower ECV is not inherently notable as long as the total score demonstrates sufficient psychometric features, such as an ωh value greater than 0.80 (Dueber & Toland, 2023).

On the basis of the following considerations, we reached the conclusion that the bifactor ESEM solution of L2SBI was the most suitable model: (1) Tables 2 and 3 show that the bifactor ESEM model outperformed the CFA and ESEM solutions in terms of data-model fit and measurement quality; (2) the latent variables calculated within the bifactor ESEM solution are well-defined, with high loadings as indicated in Table 3; (3) the bifactor ESEM model displayed a lower level of cross-loadings (see Table 3); (4) as seen in Table 4, the bifactor ESEM solution produced higher values for both the composite omega and the hierarchical omega; and finally, the bifactor ESEM solution produced higher value for general ECV.

Table 5 displays item-level descriptive statistics, CITC, and I-ECV for the optimal model, which is the bifactor ESEM solution. According to the findings, the items were distributed normally, with skewness and kurtosis values falling within the + 2 to -2 range (Collier, 2020). Additionally, each item was found to have a strong correlation with its own subfactor, with a CITC value greater than 0.30 (Zijlmans et al., 2019). Ultimately, the I-ECV values for all the items were below 0.85, which supports the notion that the general factor is multidimensional (Stucky & Edelen, 2014).

The study also evaluated the measurement invariance of the L2SBI across gender and language proficiency level using the bifactor ESEM solution. The supplementary materials present the findings of the measurement invariance analysis of the L2SBI for gender. The results indicate that there is metric, scalar, and configural invariance across gender and language proficiency levels.

5 Discussion

The goal of the present research was to explore and validate the psychometric properties of the L2SBI among L2 learners, using an ESEM approach. This approach was chosen for its ability to provide more accurate conceptual boundaries between the general and specific components of L2SBI, effectively addressing the limitations associated with the CFA method (Alamer & Marsh, 2022; Morin et al., 2020). The study identified a bifactor ESEM solution as the most effective model, indicating that the L2SBI is optimally represented by a general factor of L2 savoring beliefs, distinct from the three specific subfactors: anticipating progress in learning English, savoring the moment while learning English, and reminiscing about experiences in learning English.

General L2 savoring beliefs encompass self-perception beliefs concerning individuals’ capability to appreciate and intensify positive outcomes in language learning, representing perceived self-regulation of positive L2 affect that is mainly distinct from beliefs about coping or perceived self-regulation of negative L2 affect (Bryant, 2021). The L2SBI also provides separate subscale scores for the three specific subfactors. Language savoring beliefs in the form of anticipating progress in learning English involve the ability to appreciate incoming positive experiences related to L2 learning. In this regard, an L2 learner with a high level of these beliefs may frequently look forward to impending positive outcomes in a manner that motivates him/her to persist in L2 learning. On the other hand, an L2 learner with low anticipating beliefs may experience challenges in predicting positive outcomes in learning a new language, potentially dreading rather than savoring upcoming positive experiences. L2 savoring beliefs in the form of savoring the moment while learning English indicate the ability to appreciate current positive experiences in L2 learning. A learner with high levels of such beliefs may relish moment-by-moment enjoyment when learning an L2, while a learner with low levels of savoring the moment beliefs may find it difficult to enjoy such moments when they actually happen. Lastly, language savoring beliefs in the form of reminiscing about experiences in learning English entail the capacity to seize previous positive experiences in L2 learning. An L2 learner with high levels of reminiscing beliefs may find it easy to reflect on pleasant experiences related to language learning and be able to continue enjoying them. In contrast, a learner with low levels of such beliefs may feel distant from his/her pleasant experiences and achievements because he/she is unable to build upon positive experiences in an effort to feel joy while learning an L2.

We discuss the psychometric properties of the L2SBI with respect to the general factor level, specific factor level and item levels. At the general-factor level, the findings indicated that the general omega composite (ω) of L2SBI was 0.97, implying that the general factor, along with the three subfactors (anticipating, savoring the moment, and reminiscing) collectively accounts for 97% of the general variability observed across all 24 items in the bifactor ESEM solution. This suggests that the bifactor ESEM solution accounted for 97% of the variance, with only 3% potentially attributable to random error. In addition, the omega hierarchical (ωh) for the general component was 0.84, suggesting that L2SBI could explain 84% of the variance in total scores as a single overarching latent component. Thus, a single general factor, L2SBI, accounted for 86% (0.84/0.97) of the shared variance in total scores according to the Omega hierarchical analysis, with 11% (0.97 − 0.87) of the variance in total scores attributed to specific factors, including anticipating, savoring the moment, and reminiscing.

At the specific-factor level, the Omega hierarchical subscales for anticipation (0.34), savoring the moment (0.29), and reminiscing (0.31) indicate that these specific factors correlate more strongly with the general factor of L2SBI than with their intended components. In addition, the scores of Omega for specific factors and the factor loadings on their target factors (ranging from 0.23 to 0.61 for anticipating, 0.29 to 0.52 for savoring the moment, and 0.37 to 0.57 for reminiscing) show that the items of these specific factors tend to influence the general factor more than the specific factors themselves.

Regarding the dimensionality of L2SBI, the findings indicate that 68% of the shared reliable variance (i.e., variance that can be due to a single general factor) was mostly determined by the initial single general factor of L2SBI. Specifically, 32% of the shared variance among all 24 items in the bifactor ESEM solution was allocated to distinct components, namely anticipating, savoring the moment, and reminiscing. This supports the existence of a multidimensional framework of L2SBI (ECV < 0.80), which encompasses a singular general factor as well as three distinct subfactors. The reliabilities of these specific components were found to be moderate to large (Omega > 0.80), indicating that the scores of these variables accounted for a significant amount of variance in the general L2SBI score (Dueber & Toland, 2023). This suggests that specific factors add value beyond the total score (Dueber & Toland, 2023).

At the item level, although anticipating, savoring the moment, and reminiscing subscales are more strongly associated with the general factor, two items related to anticipating (items 11 and 20) and two related to savoring the moment (items 9 and 12) have I-ECV values of approximately 0.50. This indicates that these items are equally influenced by both the general factor and their respective specific variables.

Overall, it was found that the less restricting L2SBI solution, which accommodates small cross-loadings across items, outperformed the more limited CFA models in terms of model fit and measurement quality indices. This outcome highlights the necessity of relying on a methodological approach capable of accurately distinguishing learners’ general levels of L2SBI (i.e., learners’ general beliefs of focusing on the positive) from the specific beliefs that characterize each type of L2 savoring belief. Failure to use this model may result in premature removal of key dimensions of L2SBI and the possibility of an inaccurate conclusion in the related literature.

6 Conclusion

The present study can hopefully trigger necessary improvements in the development of PP measurement tools in the field of SLA by exploring the psychometric features of the L2SBI. The L2SBI could be employed by researchers and practitioners to establish levels of L2 savoring beliefs in relation to both the general factor of L2SBI and the three specific subfactors of (i.e., anticipating progress in learning English, savoring the moment while learning English, and reminiscing about experiences in learning English) with the purpose of evaluating beliefs concerning L2 learners’ ability to savor L2 learning positive experiences, moments and emotions. The L2SBI can also be employed by L2 researchers to explore the association between L2 savoring beliefs and a number of language-related outcomes (e.g., language achievement, L2 willingness to communicate, motivation, engagement) as well as positive and negative L2 emotions (e.g., enjoyment, boredom).

Regarding limitations, the study failed to include evaluation for other types of validity besides construct validity, such as convergent, discriminant, and predictive validity. Further studies can investigate the L2SBI’s convergent validity with other relevant scales (e.g., enjoyment; Dewaele & MacIntyre, 2014). Future research can additionally establish the SBI’s discriminant validity in learners who also respond to other self-assessed scales of conceptually unrelated variables. Furthermore, the predictive validity of the L2SBI may be established in learners who also complete self-assessed scales of variables believed to be influenced by L2SBI, such as in-class FLB (Li et al., 2023; Pawlak et al., 2020), after-class FLB (Kruk, Pawlak et al., 2023), FLP (Kruk et al., 2023), FLA (Horwitz et al., 1986), and L2 grit (Alamer, 2021b; Elahi Shirvan et al., 2022; Teimouri et al., 2022). Another limitation is related to the nature of data collection. This study is a cross-sectional evaluation of the construct validity of L2SBI. However, Elahi Shirvan et al. (2022) highlighted the need to carry out longitudinal CFA of L2 constructs to explore the multivariate analysis of the associations among different subfactors over time and to see if items contribute to specific factors in a comparable way across time points. Thus, rigorous longitudinal examinations would be required to ensure more definitive conclusions with respect to the factorial structure of L2SBI.