Factorial Structure of the Emotional Beliefs Questionnaire: Testing Measurement Invariance and Competitive Models

The role of metacognitive beliefs towards positive and negative emotions has been stressed by several theoretical models. The Emotion Belief Questionnaire (EBQ) has been developed to assess these metacognitive beliefs. We administrated the Italian version of the EBQ, the Difficulties in Emotion Regulation Scale (DERS), the DERS-Positive and the short form of the Depression Anxiety Stress Scale (DASS-21) to a sample of Italian adults. (N = 516). Structural Equation Modelling testing the factorial structure of EBQ evidenced a good fit in the four-factor model compared to the three-factor model and model with two second order variables. The EBQ showed invariance across sex, and significant associations with validating variables. These results demonstrate the goodness of the four-factor structure for the EBQ and support its use for assessment of metacognition beliefs towards emotions.


Introduction
Emotional experience represents one of the most crucial aspects in the life of the human being (Goleman, 2012). The different shades of emotions accompany the human being from the first day of life, allowing from the pre-verbal stage onwards to communicate with others and adapt to the external environment (Thompson, 1991;Ackerman et al., 1998;. Underlining its importance, the study of emotions and their regulation is central in empirical research (Garofalo et al., , 2021Velotti et al., 2021). The construct of emotion regulation refers to the set of processes underlying the modification of emotional experiences aimed to adapt to environmental demands (Thompson, 1994). Conversely, emotion dysregulation refers to difficulties in awareness, understanding, and acceptance of emotional Combining the awareness of both these results and the centrality of emotion regulation, recent research focused on the study of beliefs in the context of emotional processes. Tamir and colleagues (2007) showed that beliefs regarding emotions (incremental vs. entitarian) influence the perception of self-efficacy and controllability of emotions. Specifically, individuals with an entitarian approach to emotions, compared to their counterparts, showed lower emotion regulation performance, and experienced a higher proportion of negative emotions. In contrast, those with an incremental approach to emotions experienced greater emotional controllability, self-regulation, longer enjoyment of positive emotion and higher social benefits (Tamir et al., 2007).
In sum, to believe in the malleability of emotions leads to higher emotional regulation capacity, that in turn predicts better well-being, interpersonal functioning, and mental health (Gross, 2015;Kneeland et al., 2016;Ortner & Pennekamp, 2020). Ford and Gross's (2018) theorize the connection between emotion beliefs and emotional outcomes can be found in the notion of "emotion regulation", which refers to the individual's ability to monitor, evaluate and adjust emotional responses (Thompson, 1994). Complementarily, Gratz and Roemer (2004) define "emotion dysregulation" as the difficulties in regulating one's emotional states in the different domains. Beliefs on the emotions may influence regulation abilities in all the phases involved (identification, selection, implementation, and monitoring), defining their effectiveness (Gross, 2015). Maladaptive beliefs about emotions, such as believing that emotions are not controllable or functional, have important implications on emotional regulation strategies (Veilleux et al., 2021). Specifically, beliefs about goodness are involved more frequently in the implementation stage: individuals that perceived the emotion as good, are more prone to seek activities that maintain and/ or increase that emotion. Beliefs on controllability mostly impact the selection phase (Ford & Gross, 2018). Studies highlighted that dysfunctional beliefs were associated with maladaptive regulatory strategies, such as avoidance, withdrawal and reduction in the use of cognitive reappraisal: if the emotions are unmanageable, by definition, any attempt in regulating them is worthless (Tamir et al., 2007;De Castella et al., 2013;Castella et al., 2018). Based on these premises, the role of beliefs on emotions appears promising to understand the relationship between difficulties in emotion regulation and psychopathological conditions (Kneeland et al., 2016). Most research focuses on the relationship between emotional dysregulation and beliefs on controllability of emotions, however other beliefs are also associated with an increased risk of psychopathology (Veilleux et al., 2021). For instance, believing emotions are useless, or being convinced that one's subjective experiences are radically different from those of others, has been associated with anxiety and depression (Manser et al., 2012;Veilleux et al., 2015Veilleux et al., , 2019. Considering recent developments in the field of emotion regulation stressing the role of positive emotions in mental health (Weiss et al., 2015;Gloria & Steinhardt, 2016), beliefs toward positive emotions are likely to be involved in clinical manifestations such as depression (Schick et al., 2019). In sum, within the framework of emotion regulation, beliefs on emotions appear to be essential to understand psychological functioning.

Emotion Beliefs and Emotion Regulation
According to Ford and Gross (2019), some subordinate beliefs may be more influential than others, meaning the value of a specific emotion might playing a more crucial role in the organization of beliefs compared to other. Subordinate beliefs can combine with each other, giving birth to various and complex beliefs on emotions.

Ford and Gross's Model and Emotion Beliefs Questionnaire
Within the framework of emotions, Gross (2018, 2019) systematized the network of beliefs on emotions, identifying two main categories: on their goodness (perceived as good or bad), and their controllability (perceived as uncontrollable or controllable). The authors (2018, 2019) recognized that beliefs on emotions are several, but the division into two categories (goodness and controllability) turns out to be essential for understanding the wide range of attitudes, expectations, and opinions the individual have toward emotions. These beliefs are orthogonal to each other, and their specific dysfunctions lead to distinct clinical impairments, including emotion dysregulation (Ford & Gross, 2019). Specifically, beliefs on goodness include several associated dimensions of the perceived emotion -such as desirability vs. undesirability, or usefulness vs. uselessness -that do not necessarily correspond to the pleasantness of the emotion itself; not all individuals may perceive negative emotions as unpleasant or vice versa (Tamir & Ford, 2012). Controllability beliefs refer to individuals' certainty that they may or may not have control over their emotions (Ford & Gross, 2019).
Despite such beliefs are considered superordinate, referring to broader beliefs about emotions, a range of subordinate, more specific, beliefs are identified. They relate to (a) specific emotions, (b) the intensity of emotions, (c) specific channels of emotion expression, (d) specific contexts of emotions onset, (e) specific time courses of emotions, and (f) specific targets. Considering the implications of metacognitive beliefs of emotions, and their role in emotion regulation, a validation of instrument capable of assessing this construct appears necessary. According to Gross' theory (2018, 2019), Becerra and colleagues (2020) filled this gap, developing the Emotion Beliefs Questionnaire (EBQ), a self-report tool aimed at evaluating beliefs on positive and negative emotions. The tool was designed aiming at three goals: (a) to measure the two domains that characterize the emotional beliefs -usefulness and controllability-independently, in line with the theorization of Gross andFord (2018, 2019); (b) to evaluate the superordinate level of beliefs in order to adequately assess the extent of the construct; (c) to provide information on the subordinate level of beliefs, in order to obtain an insight on the valence of positive and negative emotions. Due to its effectiveness in grasping the complexity of said beliefs, the EBQ differs from other similar psychometric tools such as Implicit Theories of Emotions Scale (Tamir et al., 2007), Beliefs about Emotions Scale (Rimes & Chalder, 2010) or the Attitudes Toward Emotions Scale (Harmon-Jones et al., 2011).
In a preliminary phase of their study, based on the theory of Gross (2018, 2019), Becerra and colleagues (2020) created a pool of 30 items evaluating negative and positive beliefs. They then submitted the items to a team of two psychiatrists, two clinical psychologists and three high school teachers, for their review regarding the items' readability. Based on the feedbacks, Becerra and colleagues (2020) adjusted the items, and then administered them to a sample of 161 adults. The battery included other self-report tools, such as the Implicit Theories of Emotions Scale (Tamir et al., 2007), the Emotion and Regulation Beliefs Scale (Veilleux et al., 2015), the Beliefs about Emotions Scale (Rimes & Chalder, 2010), the Perth Emotion Regulation Competency Inventory (Preece et al., 2018) and the and the Depression Anxiety Stress Scales-21 (Lovibond & Lovibond, 1995). Of the 30 initial items, the 16 most representative were selected, and equally divided into four subscales (Negative-Positive Controllability and Negative-Positive Usefulness) to reach content validity, and two composite scales (Controllability and Usefulness).

Factorial Structure of the Emotional Beliefs Questionnaire
In their study, with the aim of identifying the underlying factors of the emotion belief questionnaire, Becerra et al., (2020) tested several factorial models. The authors (2020) examined a total of seven models: six models with firstorder factors, and one model -built on the best fitting model with first-order factors -which added a second-order variable, i.e., a general and comprehensive level of maladaptive emotion beliefs. The first model tested a one-factor structure. The second and third models tested two versions of a two-factorial structure: one grouping items based on the emotions' positivity and negativity, and the other based on the emotions' controllability and usefulness. In the fourth model, items loaded on three factors being Negative Controllability, Positive Controllability and Usefulness. Specularly, the fifth model tested the existence of three factors, namely Controllability, Negative Usefulness and Positive Usefulness. The sixth model counted four factors, i.e. Negative Controllability, Positive Controllability, Negative Usefulness and Positive Usefulness. The authors (2020) then compared the models' fit indices, and found in the threefactor solution (fifth model) the best fitting one. The second-order model was built on this selected model, adding a single general factor resulting from the convergence of the three first-order factor. Despite showing good level of fit, it was lower than the original model.
Related to the factorial structure of the EBQ, a theoretical issue that still deserves attention is potential multidimensional nature of the metacognitive emotional beliefs' construct. Specifically, it is still unclear if negative metacognitive beliefs should be considered a unitary construct and, if not, which dimensions should be identified.
A first distinction between dimensions is directly suggested in the theory of Ford and Gross (2019), who state that beliefs about uncontrollability and unusefulness are two independent types of metacognitive beliefs. An argument for this distinction has been provided by theoretical contributions evidencing the different nature of failures in the emotion regulation process determined by these two dimensions of negative emotional metacognitive beliefs (Berglund et al., 2023). For instance, one may consider that emotions are controllable but are not useful leading to suppressive or avoidant approach to emotions. Others may believe that emotions are useful but not controllable, leading to poor attempt in increasing their frequency, intensity, or duration (Berglund et al., 2023). This issue appears relevant, as inter-individual differences in these two types of metacognitive beliefs may account for differences in maladaptive emotion regulation profiles, which, in turn, may explain different vulnerability to specific mental disorders. Regarding the EBQ, the conclusions drawn by Becerra et al. (2020) converge towards the idea that uncontrollability and unusefulness are two distinct variables. Indeed, in the selected factorial structure, these two factors were identified as orthogonal.
Another potential distinction regarding the construct of negative emotional metacognitive beliefs is related to the valence of emotions involved either positively or negatively. This issue has been debated in other fields of research. For instance, a recent study suggested that the proneness to act rashly in response to emotions (i.e. urgency) should not be differentiated according to the type of emotions . However, several arguments for the need to convergence of Positive/Negative Controllability and Positive/Negative Usefulness factors respectively. Another issue that needs investigation in relation to the EBQ is the measurement invariance across sexes: reaching measurement of invariance appears fundamental to allow comparisons between groups (i.e., sex) and ensure that significative differences are related to a real distinction and not from psychometric inequality of instrument. Only be reaching said invariance the construct can be deemed as having the same meaning across groups (Putnick & Bornstein, 2016). To the best of the authors' knowledge, this aspect of the EBQ has not been investigated so far, limiting the soundness of conclusions drawn by future studies using the tool.

Psychometric Properties of EBQ
In the original study conducted by Becerra et al., (2020), all EBQ subscales showed an adequate alpha, indicating good internal consistency. Regarding concurrent validity, analyses evidenced an association between the higher belief that emotions as uncontrollable, and greater difficulty in regulating emotions, as well as with higher levels of depression, anxiety, and stress (Becerra et al., 2020). Concerning criterion validity, analyses showed that EBQ scores significantly predicted emotion regulation ability and psychopathological symptoms (Becerra et al., 2020). According to the authors (2020), these results stress the strength of the EBQ that would measure a broader, more complex, and clinically significant variables, than the available tools assessing components of the emotion regulation nomological network. These preliminary data are promising, suggesting the soundness of EBQ among English speakers, as a theoretically grounded tool to evaluate the complexity of emotional beliefs. In particular, the questionnaire goes beyond the negative affective sphere, by focusing on the positive one which, in recent years, has been assuming a central role in studies on the regulation of emotions. However, these promising preliminary results on the instrument's construct validity still need to be tested with additional, widely used measures, assessing emotion dysregulation such as the Difficulties in Emotion Regulation Scale or the Difficulties in the Regulation of Positive Emotions Scale (Gratz & Roemer, 2004;Weiss et al., 2015).

The Current Study
In light of these considerations, further studies extending the results brought by Becerra et al. (2020) are required. The aim of the below-depicted study was to examine the factorial structure of the Italian version of the EBQ among a sample of adults. Specifically, we wanted to replicate the procedure of Becerra et al., (2020), testing all the first differentiate between positive and negative emotions come from the field of emotion regulation. First, several studies highlighted that albeit capacities in the regulation of positive emotions is associated with capacities in the regulation of negative emotions, these are discriminated constructs Weiss et al., 2015). Then, the ways regulation of positive emotions account for mental disorders is well distinct from the mechanisms linking poor regulation of negative emotions to psychopathology (Gruber et al., 2019;. In addition, according to the nature of emotional states, poor malleability beliefs have been shown to lead to different negative psychological outcomes (Harmon-Jones et al., 2011). Similarly, preliminary results evidenced that the valence of emotional states involved differentiates the consequences beliefs on uncontrollability and unusefulness have on emotion regulation process (Preece et al., 2022). As a whole, contrasting arguments exist regarding the need to differentiate negative emotional metacognitive beliefs according to the valence of emotions involved. Some answers to this question have been provided by the factorial tests performed by Becerra et al. (2020). Specifically, in the model selected, the distinction resulted to be pertinent only for the unusefulness factor, whereas for the uncontrollability one, the solution provided a unique factor, without distinction between positive and negative emotions.
Notably, assuming the construct of negative emotional metacognitive beliefs includes the four independent dimensions, the question is how these dimensions should be considered as related to each other still needs additional investigation. One hypothesis distinguishes the four dimensions, but assuming that these are not perfectly independent, and share a common basis. For instance, beliefs of uncontrollability regarding negative emotions, and beliefs of uncontrollability regarding positive emotions, might depends on a general belief of uncontrollability regarding emotional states. Similarly, the four types of negative metacognitive beliefs may be single manifestations of a general negative attitude towards emotions. In other words, it is not clear if these dimensions should be considered as separate dimensions of a same general psychological variable, or distinct constructs.
Despite these important results, some issues regarding the EBQ still needed to be addressed. For instance, no studies attempted to replicate the procedure followed by Becerra et al. (2020) and the factorial structure of the EBQ was never tested among Italian speakers. Also, despite the second-order model test by Becerra et al. (2020) made sense, since they identified the three-factor model as the optimal first-order solution, the theoretical framework underlying the development of the measure (Ford & Gross, 2018 suggest the existence of two second-order factors resulting from the Measures Demographic Information was collected. Participants were invited to provide information regarding age, sex, and education level. Italian Version of the Emotion Beliefs Questionnaire (EBQ; Becerra et al., 2020). In order to create the Italian version of the Emotion Beliefs Questionnaire, a back-translation procedure was applied, which is one of the most common techniques for translating questionnaires into another language. The translation was carried out from the original language to another language and, subsequently, the translation from the second language to the original was reproposed to evaluate its consistency (Brislin, 1980). The Emotion Beliefs Questionnaire (Becerra et al., 2020) is a 16-item self-report questionnaire, which measures beliefs towards positive and negative emotions. Answers are provided along a 7-point Likert scale ranging from 1 (totally disagree) to 7 (totally agree), with high scores indicating the subject's belief that emotions are uncontrollable and/or useless. The items also provide information about 4 specific subscales: Negative-Controllability (beliefs towards the malleability of negative emotions), Positive-Controllability (beliefs towards the malleability of positive emotions), Negative-Usefulness (beliefs towards the usefulness of negative emotions) and Positive-Usefulness (beliefs towards the usefulness of positive emotions). In addition to the subscales, the questionnaire also includes two composite scales: General Controllability (obtained from the sum of the Controllability Subscales) and General Usefulness obtained from the sum of the Usefulness Subscales). The original version of the EBQ showed good internal consistency with a Cronbach's alpha of 0.88 for the total EBQ score and an alpha range of 0.70-0.88 for the subscales (Becerra et al., 2020).

Difficulties in Emotion Regulation
Scale (DERS; Gratz & Roemer, 2004;Giromini et al., 2012): is a self-report questionnaire of 36 items that measures the difficulties in emotion regulation. Through a five-point Likert-type scale ranging from 1 (never) to 5 (always), participants were invited to indicate how often the described experience applies to them. The questionnaire provides a total score obtained from the sum of the subscales scores, and a score for each subscale: Non acceptance (non-acceptance of emotional responses), Goals (difficulties in engaging in goal-directed behaviors), Impulse (difficulties in the control of impulsive behaviors), Awareness (lack of emotional awareness), Strategies (limited access to emotional regulation strategies) and Clarity (lack of emotional clarity). Internal consistency of the DERS is excellent with a Cronbach's alpha of 0.93 for the total score and an alpha range of 0.80-0.89 for the subscales seven models, in addition to another model, composed by two second-order factors, in accordance with the theoretical framework of Gross (2018, 2019). The study also aimed to test the invariance of the EBQ across sexes. Another goal is to provide additional data documenting the construct validity of the instrument, replicating and extending the conclusion drawn by Becerra et al. (2020) using the DERS and DERS-P, which are widely validated instruments used in the literature to evaluate difficulties in positive and negative emotion regulation.

Procedure
The research procedure was approved by the Ethical Board of the University of Rome La Sapienza 0000689 (N. 02/05/2022) and complied with the ethical guidelines of the American Psychological Association.
The sample was recruited through a convenience sampling technique. Specifically, a digital survey was created on the Eusurvey platform and promoted through social media and during university courses. After an initial presentation of the study's aims and procedure, all participants provided informed consent for the treatment of their data. Then, participants were asked to fill a battery of self-report questionnaires.
were carried out with the lavaan package (Rosseel, 2012), running on the Rstudio software for Mac. Specifically, eight models, each corresponding to a different factorial structure of the EBQ, were created and tested. The first six models were identical to those tested in the original validation article (Becerra et al., 2020) and the scores obtained at the items of the EBQ as manifest variables (MVs) were used to create latent variables (LVs) corresponding to the hypothesized factors. The CFAs were conducted using the Robust Maximum Likelihood Method of Estimation (Ben-Tal et al., 2009) and their goodness of fit were examined throughout the inspection of the robust version of two fit indices namely the Root Mean Square Error of Approximation (RMSEA) and the Comparative Fit Index (CFI). Guidelines regarding the interpretation of these indices usually agree that significance of the chi-square value is not strongly indicative, and that an RMSEA below 0.08 and an CFI over 0.90 indicate an acceptable fit (Browne & Cudeck, 1992;Kline, 2005).
To select the best fitting model, comparisons were made on these indices of fit. In addition, the acceptability of the factorial structure selected was examined trough the inspection of factor loadings that were requested to be all positive and significant. Once the best fitting one-order model was identified, two additional CFAs were carried out to test two distinct two-order models introducing either a single second-order LVs (related with all the factors) or two separate second-order LVs related to the Controllability and Usefulness factors respectively. Again, fit indices were inspected and compared to select the best fitting model between these eight alternatives.
Once the best model was selected, the Average Variance Explained (Henseler et al., 2009) was computed for each factor of the EBQ using the bluegrafir function for Rstudio. In addition, the measurement invariance of this model was tested (Meredith, 1993;Vandenberg & Lance, 2003) starting from the test of configural invariance across sexes performing a multigroup CFA. Then, metric, scalar, and strict invariances were progressively tested, constraining the model to maintain equals, across groups, factor loadings, item intercepts and factors variances respectively. After the test of each of these measurement model, the reaching of measurement invariance was decided performing the chi square difference with a significant result indicating that measurement invariance was not met (Satorra & Bentler, 2001).
Lastly, to evaluate construct validity, r-Pearson partial correlations coefficients were computed estimating the associations between the EBQ subscales and the other continuous variables. To correct the alpha inflation for multiple testing, Bonferroni correction was applied for each of the three set of analyses involving the DERS, DERS-P and DASS-21 respectively. This last set of analyses was performed with the SPSS software for Mac v.23. (Gratz & Roemer, 2004). These psychometric properties were also found in the Italian version (Giromini et al., 2012) with a Cronbach's alpha of 0.93 for the entire tool and a range of 0.77-0.89 for the six subscales.

Difficulties in the Regulation of Positive Emotions
Scale (DERS-P; Weiss et al., 2015;: is the positive version of the DERS (Gratz & Roemer, 2004). It is a 13-item self-report questionnaire that measures the difficulties in the regulation of positive emotions through a five-point Likert-type scale ranging from 1 (almost never) to 5 (almost always). The DERS-P provides a total score obtained from the sum of the subscales scores, and a score for each subscale: Non acceptance (non acceptance of positive emotions), Goals (difficulties in engaging in goaldirected behaviors when experiencing positive emotions) and Impulse (difficulties in the control of impulsive behaviors when experiencing positive emotions). The psychometric properties of the original DERS-P were adequate with a Cronbach's alpha of 0.90 for the total score, and a range of 0.83-87 for the subscales (Weiss et al., 2015). The Italian version of the DERS-P confirmed good reliability with a Cronbach's alpha of 0.90 for the total score, and a range of 0.80-0.86 for the subscales.

The Depression Anxiety Stress Scale 21-items (DASS-21;
Lovibond & Lovibond, 1995;Bottesi et al., 2015) is the short version (21 items) of the original 42-item version (Lovibond & Lovibond, 1995), measuring the negative emotional states of depression, anxiety, and stress, that also are the subscales of the instrument. The DASS-21 measures through 21 items (7 for each dimension) rated on a fourpoint severity/frequency where 0 means "did not apply to me at all" and 3 means "applied to me very much or most of the time". The values of internal consistency reported were 0.93 for the whole scale, and a range of 0.84-90 for the subscales (Henry & Crawford, 2005). Cronbach's alpha values of the Italian version of DASS-21 (Bottesi et al., 2015) consist of 0.82 for the Depression Scale, 0.74 for the Anxiety Scale, 0.85 for the Stress Scale and 0.90 for Internal Consistency.

Statistical Analyses
First, the main characteristics of our variables were explored, computing frequencies, means, standard deviations as well as Cronbach values. These analyses were performed with the SPSS software for Mac v.23. The test of the psychometric proprieties of the Italian version of the EBQ included several steps being a series of Confirmatory Factorial Analyses (CFA) and measurement invariances tests. These operations

Confirmatory Factor Analysis
A series of CFAs was conducted to test the factorial structure of the EBQ. A summary of the models tested is available in Fig. 1.
Within the first six models tested (i.e., with only first order LVs), only the sixth obtained a good fit according to both the RMSEA and CFI indices (see Table 1). Therefore, models with second-order LVs were created on the basis of model six. Model seven obtained satisfactory fit indices that were however below those obtained by the more parsimonious Model six. Also, Model eight did not reach an acceptable fit according to the CFI index. Detailed results are available in Table 1.

Instrument Internal Consistency Reliability
Considering the instrument administered in the present study, all questionnaires reached the internal consistency reliability. In particular, for the EBQ, Cronbach's alphas range from 0.78 to 0.90 while an excellent internal consistency was found in the DERS (α = 0.90), with Cronbach's alphas of subscales ranging from.70 to 0.92. A good internal consistency was also found for DERS-P, with a Cronbach's alpha of 0.86 for the total score and an alpha range of 0.80-0.89 for the subscales. Lastly, Cronbach's alpha values of DASS-21 ranged of 0.83-0.90 for the subscales. good fit of the model. On this model, metric, scalar, and strict invariances were tested and evaluated trough the χ 2 difference test that, at each step, resulted to be non-statistically significant, indicating that full measurement invariance was reached. Indices of fit related to each of these steps of measurement invariance testing are displayed in Table 2 together with results of χ 2 difference tests.

Partial Correlations Between Variables
The partial correlations between the variables were analyzed using Pearson's coefficient, controlling for age and sex. As In addition, inspection of the model measurement of fourfactor model evidenced all positive and significant loadings of the MVs on the respective LVs. Lastly, Average Variance Extracted was calculated for each factors providing satisfactory results with values being between 0.42, 0.45, 0.45 and 0.47 for the Controllability Negative, Controllability Positive, Usefulness Negative and Usefulness Positive factors respectively. Considering the results obtained, model six was selected as the best fitting model. The reader can find details regarding coefficients obtained in Fig. 2.
Then, we tested the invariance of measurement model across sex through multigroup CFA. Results indicated a  Regarding the association between the EBQ and DERS-P scores, data evidenced that the Goals subscale of the DERS-P was not significantly associated with none of the EBQ subscales. In contrast, the Uncontrollability subscales showed positive and significant associations with all the other DERS-P dimensions. Results regarding the Unusefulness subscales were more nuanced with positive and significant associations of these subscales with the Acceptance factor of the DERS-P and a significant relationship between the Impulse subscale and the Unusefulness Positive -but not Negative-subscale.
Finally, we found that the relationship between EBQ and DASS-21 subscales were always significant and positive except the relationship between the DASS-21 Stress subscale and with the Positive Unusefulness factor. shown in Table 3, all subscales of the EBQ correlated positively and significantly with each other.
Then, partial correlations, controlling for age and sex, between the EBQ scores and the DERS, DERS-P and DASS-21 scores were performed (see Table 4). The two Uncontrollability factors were significantly and positively associated with all the subscales of the DERS except the Uncontrollability positive subscale that was not significantly related to the DERS Clarity scores. Regarding the Unusefulness subscales, whereas these were both significantly and positively correlated with both the Awareness and Acceptance dimension of the DERS, their associations with the other DERS subscales differed. Indeed, the Unusefulness negative subscale was significantly related to the Impulse subscale of the DERS whereas the Unusefulness positive was not. In turn, this last dimension showed an association with the Strategies and Clarity scores whereas the other did not. Also,the   regulation profiles, which in turn might result in different psychopathological outcomes. Beyond the recognition of different associates of these two types of metacognitive beliefs, our result also suggests that these may be related to different developmental trajectories. Since the development of negative emotional metacognitive beliefs is thought to be rooted in the interaction between child and caregiver (Halberstadt et al., 2013), our results suggests that these different beliefs may be associated with different childhood experiences and parenting styles. Therefore, our data may indicate that, considering the independent nature of the uncontrollability and unusefulness factors, specific hypotheses should be developed and tested regarding their psychological, psychopathological, and developmental associates. Another result that is likely to have theoretical implications consists in the identification of unconnected factors in relation to the valence of emotional states (i.e. positive or negative). This partially contrasts with the results of Becerra et al. (2020), who obtained separated factors only regarding the unusefulness metacognitions. Despite the preliminary result of Becerra et al. (2020), and some recent studies asserting the inutility to differentiate negative from positive triggers in the field of emotional impulsivity , our result is consistent with several expectations. Research showed that the nature of the emotional state accounts for the type of psychopathological consequences determined by emotion dysregulation, and that negative emotions dysregulation does not empirically totally overlap with dysregulation of positive emotion (Preece et al., 2022;Weiss et al., 2015). The reason we found separated factors in relation to the metacognitions regarding unusefulness, in contrast with Becerra et al. (2020), may consist in cultural differences impacting the variability across individuals concerning this psychological variable. We also observed that considering metacognitive beliefs, regarding positive and negative emotions, as different facets of the same general constructs (i.e. general uncontrollability and general unusefulness) did not add significant explanation on the data compared to the more parsimonious solution. Therefore, future studies may want to separately investigate the nomological network of each of these four types of emotional metacognitive beliefs. Furthermore, it could be assumed that the interaction between these metacognitive beliefs may account for specific emotion regulation profiles. From this perspective, our results encourage theorists to further develop the topic of the potential influence between different levels of these metacognitions and their consequences on both an emotion regulation and psychopathological level. Noteworthy, results regarding the AVE values slightly temper the soundness of the conclusion regarding the discriminant validity of the uncontrollability factors, related to positive and negative emotions respectively. Indeed, the square

Discussion
The importance of beliefs on emotions has only recently become the subject of analysis. Currently, both the international and the Italian panoramas lack of sufficient tools capable of grasping this construct (Becerra et al., 2020). The Emotion Beliefs Questionnaire responds to the growing interest in the topic, by providing a valid tool for investigating beliefs on emotions (Becerra et al., 2020). The main purpose of the present study was to replicate the psychometric structure of EBQ, and test the factorial structure of the Italian version of the tool.
The results confirmed the reliability of the instrument, in its Italian adaptation, in detecting the beliefs on the controllability and usefulness of positive and negative emotions. In line with the objectives of the study, the seven models proposed by Becerra et al., (2020) in their study were tested. Moreover, an eighth model was tested to evaluated if four first-order factors (Negative-Positive Controllability and Negative-Positive Usefulness) loaded on two secondorder factors (Controllability and Usefulness), as envisaged by Gross's theory (2018, 2019), and by the EBQ structure of four subscales and two composite scales.
Of all eight models tested, only the sixth and seventh models reached a good index fit. However, from the comparison between the four-factor model and the model with second-order variables, the significant superiority of the first solution was confirmed. AVE values showed that each factor explained between 42 and 47% of variance if its converging indicators. This data is discordant with the results obtained by Becerra (2020), in which the three-factor model (Positive-Controllability, Negative-Usefulness and Positive-Usefulness) was described as the best fitting, but is consistent with the theoretical model of Gross (2018, 2019), with two superordinate beliefs (Uncontrollability and Unusefulness) in turn related to two subordinate beliefs (Positive and Negative). The four-factor models could therefore add value to the EBQ, emphasizing the orthogonal relationship and central role of controllability and usefulness in the broader sphere of beliefs on emotions, as proposed in the theoretical framework of Gross (2018, 2019).
From a theoretical point of view there are several observations worth of attention. The gathered data suggests that the uncontrollability and unusefulness metacognitions should be differentiated. This result was also brought by Becerra et al. (2020), and it is in line with the distinction made by Ford and Gross (2019). Notably, Berglund et al. (2023) recently stressed the benefit to differentiate between these metacognitions in considering the impact of negative metacognitive beliefs on emotion regulation process. Specifically, these two variables seem to lead to specific maladaptive emotion access to adaptive regulatory strategies. Similarly, positive and significant correlations emerged between the most EBQ subscales and the difficulty in accepting positive emotions. Furthermore, stronger beliefs on the controllability of emotion were found to be related to greater difficulties in impulse control, mirroring what was discovered regarding dysregulation of negative emotions.
A correlation between the tendency to consider positive emotions as useless, and increased difficulty in controlling impulse when experiencing positive emotions, emerged. This relationship was not detected regarding beliefs on the usefulness of negative emotions. This data highlights importance to consider the nature of emotional state, underlining the need to specifically assess metacognition towards the utility of positive emotions in highly impulsive individuals under the influences on positive emotions, as such as binge drinkers and pathological gamblers (Weiss et al., 2018;Rogier et al., 2022).
Lastly, in line with the literature (Manser et al., 2012;Veilleux et al., 2015Veilleux et al., , 2019Veilleux et al., , 2021, results highlight an association between beliefs on maladaptive emotions and greater psychopathological risk. The dimensions of the EQB were found to be correlated, in a significant and positive way, with the Depression, Anxiety and Stress indexes; the only notable exception is the relationship between the belief in the Positive-Usefulness, and the dimension of Stress. This result could suggest that interventions aiming to reduce stress need to be focused on beliefs toward malleability of positive emotions, rather than restructuring beliefs on their utility. The analysis of the not-significant correlations showed that the difficulty in regulating positive emotions (DERS-P) is not associated with beliefs on the usefulness of negative emotions. This is likely to be due to the absence of a significant relationship between the usefulness of positive and negative emotions, and the difficulty in engaging in target-directed behaviors. This result is plausible, since the intensity and controllability of the experienced affective state influences the ability to engage in activities outside the emotional state, rather than the belief about the utility of the experienced emotion. Emotions -both positive and negative-characterized by high intensity (consequently more difficult to control and modulate) will decrease the individual's ability to orient focus on any activity external to the emotional experience, due to their all-encompassing character. The previously reported significant association between the controllability dimension of the EBQ, and the goal dimension of the DERS and DERS-P, confirms this hypothesis. correlation between uncontrollability negative and uncontrollability positive is slightly higher than the AVE of these factors, showing that discriminant validity between these two variables may deserve further empirical and theoretical investigation.
Regarding sex, Becerra et al., (2020) observed that, overall, males scored higher than female on EBQ total score, indicating that men had more maladaptive beliefs on emotion than women., Males, additionally, described positive emotions as more useless, while no significant differences were observed for general Controllability and Negative-Usefulness. Despite the insightful nature of these results, the soundness of their conclusion was somewhat limited by the lack of demonstrated invariance of the EBQ across sexes. In our study, the analysis of metric, scalar, and strict invariances indicated that the Italian version of the EBQ is invariant across sexes. These results additionally stress the value of the EBQ, highlighting that measurements provided by the tool do not appear to be influenced by sex, providing the possibility to compare scores obtained in different samples (Chiorri et al., 2019;Tamir et al., 2007). Therefore, our results regarding the invariance of the EBQ across sexes suggest that the differences observed by the authors may be due to real sex discrepancy. Of note, to confirm this result, the invariance of the English version of the EBQ should be demonstrated in future studies.
The idea, stated in literature, that metacognitions towards emotions are relevant in daily life is supported in our study, suggesting that individuals with strong beliefs about the unusefulness and poor controllability of emotions have greater difficulty in emotional regulation of negative and positive emotions, and a higher level of stress, anxiety, and depression. These results seem to confirm Dweck's (1999) theory, that an entitarian approach to emotions is associated with maladaptive functioning. In this perspective, recent studies confirm the contribution of beliefs about emotions in the maintenance or development of a psychopathological state (Kneeland et al., 2016;Goodman et al., 2018).
From the analysis of correlations, controlling for age and sex, different associations with the EBQ subscales emerged. Positive and significant correlations were found between the four EBQ subscales (Negative-Controllability, Positive-Controllability, Negative-Usefulness and Positive-Usefulness) and most of the DERS subscales (Non acceptance, Impulse, Awareness, Clarity, Strategies). These results suggest that stronger negative beliefs about emotions, both on their controllability (i.e. the ability to modify the emotional experience) and on their functionality (i.e. the extent to which emotions are perceived as good or bad, useful or useless), are linked to greater difficulties in acceptance of emotions, in the ability to control impulses, in the awareness and clarity of the emotions experienced and in the perceived reported in this study, lead to important implications on the behavioral, relational, and social functioning. The EBQ is therefore a useful tool for the clinician to investigate beliefs on emotions, to help improving the adaptive and behavioral efficacy level, and to address the every-day challenges involving the emotional sphere. The EBQ is an effective tool for deepening the understanding of beliefs on emotions, which only recently were given attention, and which are increasingly being studied. Funding This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. Open access funding provided by Università degli Studi di Roma La Sapienza within the CRUI-CARE Agreement.

Data Availability
The data that support the findings of this study are available from the corresponding author, Patrizia Velotti, upon reasonable request.

Declarations
Competing interest The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
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Limitations and Further Directions
Although the obtained results validate the Italian adaptation of the EBQ, this research comes with some limitations. The study was conducted in a nonclinical population. Although the sample is reliable for validation purposes, further research including a clinical sample is desirable. This seems necessary considering the link between maladaptive beliefs, emotion dysregulation, and psychopathological conditions (Kneeland et al., 2016;Veilleux et al., 2015Veilleux et al., , 2019. In addition, the self-report battery used in the evaluation of beliefs on emotions used by Becerra et al., (2020) was not administered in the study, and the concurrent validity was therefore not tested. To further verify the validity of the Italian version, further studies should include the original instrument, as used by Becerra et al., (2020). In the present study this was not possible for several reasons, primarily the absence of an Italian adaptation of some of these tools. A further limitation is related to the cross-sectional research design, which did not provide data on test-retest reliability, nor longitudinally tested the predictive capacity of the EBQ scores. Lastly, given the recent interest in the study of the positive emotions regulation, still partially unexplored, deepening their connection with the analyzed variables in our study would be interesting. Based on the results obtained, the clinical and research utility of the EBQ and the investigated construct appears useful. Taking into consideration the highlighted limitations, further studies are recommended to fill these gaps (Saggino et al., 2020), and offer an added contribution to the validation of the instrument, while considering the cultural influences on emotion beliefs, as highlighted by Ford and Gross (2019).

Conclusion
Emotions represent a dimension experienced by all humans from the very first moments of life (Goleman, 2012). Recent scientific evidence highlights how beliefs on emotions can influence the regulatory capacities of the emotions themselves. Individuals with strong beliefs on the uncontrollability of emotions tend to have greater psychopathological symptoms, and less effectiveness in emotional regulation strategies (Veilleux. et al., 2021). Considering the important link between emotions and beliefs, on a clinical, social, and relational level, the presence of tools to investigate these constructs represents an important resource.
Thanks to the ability to approach the complexity of the emotional dimension, both negative and positive, the EBQ (Becerra et al., 2020) is proposed as an effective tool, responding to widespread interest. The EBQ offers to the Italian public the opportunity, both in clinical and research fields, to detect implicit beliefs on emotions, which, as