Investigating the Multidimensionality and Psychometric Properties of the Children’s Anger Rumination Scale (CARS): A Bifactor Exploratory Structural Equation Modeling Framework

Abstract

Anger Rumination (AR) represents a maladaptive cognitive process that contributes negatively to psychosocial functioning. The purpose of the present study was to investigate the psychometric properties (e.g., factorial structure, measurement invariance, and reliability) of the Children’s Anger Rumination Scale (CARS). Factorial structure was tested by contrasting alternative model representations of the instrument (one- and four-factor independent cluster models–confirmatory factor analysis [ICM-CFA], exploratory structural equation modelling [ESEM], bifactor-CFA and bifactor-ESEM) in a convenience sample of 552 Greek students (M_age = 11.50 years; 53.6% girls). The hypothesized bifactor-ESEM solution, composed by a general anger rumination factor and four specific factors (Angry Afterthoughts, Thoughts of Revenge, Angry Memories, and Understanding of Causes) provided the best fit to the data and revealed the unitary dimensionality of the CARS. Measurement invariance across gender and age in level of the latent means indicated no significant differences in relation to AR tendency. The CARS showed internal consistency, one-month test–retest reliability as well as desirable patterns of convergent and discriminant validity. The predictive power of the instrument was also supported as participants’ AR propensity was found to explain both depressive symptoms and bullying behaviors. Overall, our findings indicate that the CARS is a developmentally appropriate and psychometrically sound instrument that conceptualizes AR as an unidimensional construct among children and preadolescents.

Keywords

anger rumination psychometric properties CFA bifactor ESEM models bullying

Rumination is a multifaceted, multidimensional construct that has been studied in relation to a variety of psychological and health outcomes (J. M. Smith & Alloy, 2009). According to the response styles theory (Nolen-Hoeksema et al., 2008) rumination represents a maladaptive form of self-reflection that involves repetitively and passively dwelling on the causes and the consequences of distress symptoms. Literature suggests that this inward-focus, perseverative, and harmful cognitive strategy not only fuels negative emotions (J. M. Smith & Alloy, 2009) but also amplifies a pessimistic and fatalistic way of thinking, thwarting individuals from goal attainment (Papageorgiou & Wells, 2004) and interpersonal problem solving (Watkins & Baracaia, 2002). High ruminators usually demonstrate an ineffectiveness to behave instrumentally as they tend to remain cognitively and emotionally fixated on a problem without taking actions to solve it actively (Nolen-Hoeksema et al., 2008). Rumination has been extensively identified as a transdiagnostic risk factor for several forms of psychopathology, including depression, anxiety, substance abuse, and eating disorders (Hankin et al., 2016; Lyubomirsky et al., 2015). However, the majority of studies in the relevant literature have conceptualized and measured rumination as a response tendency to sad mood and affect (Hilt & Pollak, 2013). Consequently, less is known about the role of other forms of rumination, such as anger rumination.

Anger rumination is regarded an unintentional and recurrent cognitive process that focuses one’s attention on the causes and consequences of frustrating previous experiences (Sukhodolsky et al., 2001). It represents a dysfunctional emotional regulation strategy that unfolds after an anger-inducing experience (Sukhodolsky et al., 2001). It differs from hostile attribution bias, in which ambiguous or benign behaviors are interpreted as having hostile intent (Nasby et al., 1980). Individuals engaging habitually in anger rumination, seem to be trapped into a vicious cycle of emotional cascades including perseverative thinking, sustained affective arousal and prolonged anger (Denson et al., 2012; Offredi et al., 2016; Selby et al., 2008). Furthermore, their reduced capacity to bridle the distressing thoughts has been found to contribute negatively to their overall functioning and subjective well-being (Selby et al., 2008; Takebe et al., 2016).

Evidence of a link between anger rumination and maladjustment outcomes is based primarily on studies conducted with adults (Besharat et al., 2013; Denson et al., 2011; Hennessy 2017; Martino et al., 2015; Suhr & Nesbit, 2013). However, maladaptive strategies in coping with angry affect are also common among youth (Rohlf & Krahé, 2015). The few recent studies that expanded anger rumination research to children and adolescents have confirmed the integral role of the aforementioned cognitive response style in psychological dysfunctions including aggression and depression (Gilbert et al., 2005; Harmon et al., 2019; Patel et al., 2017; Peled & Moretti, 2007; S. D. Smith et al., 2016; Vasquez et al., 2012).

Bullying represents a multifaceted and intentional form of aggression that is characterized by the repeated exposure of one person to the physical and/or emotional mistreatment of a more powerful individual or group (see Hong et al., 2019). Zsila et al. (2018) in a study conducted with 1,500 adolescents and young adults found that anger rumination was a risk factor for perpetration among male past cyberbullying victims. Additionally, Caprara et al. (2007) in a longitudinal 20-year study with school-aged children confirmed the predictive power of hostile rumination to aggression and violence. Similarly, Vasquez et al. (2012) found that anger rumination predicted significantly behaviors of displaced aggression (e.g., aggression toward innocent targets) which are prevalent in bullying (Archer et al., 2007) even after controlling for trait anger, trait hostility, and trait irritability. Finally, S. D. Smith et al. (2016) confirmed the link between children’s rumination toward anger and elevated levels of overt and relational aggression.

Alongside with aggression, depression represents one of the greatest and often devastating mental health problems that increases rapidly during the transition from childhood to adolescence (Hankin, 2015; McLaughlin & King, 2015). Adolescent depression portend a range of aversive consequences across the life-course, including poor psychosocial functioning, suicidality, physical, and mental health problems (Maughan et al., 2013). The depressogenic qualities of rumination are well supported by cognitive models of depression (Beck et al., 1979; Nolen-Hoeksema et al., 1993). More specifically, deficiencies in coping effectively with anger have been found to result detrimentally in the onset and persistence of depression (Katsumata, 2015; Sahu et al., 2014; Young et al., 2019). Harmon et al. (2019) in a cross-sectional study conducted with 254 children found that rumination toward anger uniquely predicted depressive symptoms over and above sadness rumination. Similarly, the role of anger-focused rumination in depression, feelings of shame, and entrapment thoughts was supported in a sample of 166 undergraduate students (Gilbert et al., 2005). Additionally, Patel et al. (2017) in a mixed sample of 24 ASD (autistic spectrum disorder) and no ASD adolescents, found that anger rumination was associated with depressive symptoms even after controlling for autism symptom severity.

Findings suggest that rumination is formed in childhood (Schweizer et al., 2018) by the dynamic interaction of the family context (e.g., overcontrolling parenting; Hilt et al., 2012) and personality traits (e.g., neuroticism; Broeren et al., 2011). Particularly, neuroticism defined as the temperamental disposition to experience negative emotions (e.g., sadness or anger) accompanied by heightened reactivity to stressors (Costa & McCrae, 1985; Widiger & Oltmanns, 2017) has been found to correlate positively with rumination toward anger (Mezulis et al., 2011; Sauer-Zavala et al., 2013). Mezulis et al. (2011) in a longitudinal study conducted with 301 youths found that mothers’ reports of their child’s negative emotionality at age 1 predicted their child’s self-reported rumination at age 13. Furthermore, undergraduate students’ retrospective childhood memories in regard to their tendency toward negative affect was associated with higher current levels of rumination toward anger (Sauer-Zavala et al., 2013).

It has been suggested that the rapid social, academic, and biological changes (Blakemore & Mills, 2014) as well the emotional turmoil (Bailen et al., 2018) demonstrated in adolescence result in the dramatic increase and greater stability of rumination (Hampel & Petermann, 2005; Hankin, 2008). Furthermore, these factors seem to mark the onset of age differences in this cognitive strategy, as girls are more likely to ruminate than boys (Jose & Brown, 2008; Rood et al., 2009). Given that rumination is a risk factor for the onset and maintenance of a range of mental and behavioral disorders in youths (e.g., McLaughlin et al., 2014; Sütterlin et al., 2012), the early identification of ruminative processes is of utmost importance to prevent the stabilization of this maladaptive response style in later life stages (Baiocco et al., 2017). Thus, both childhood and early adolescence represent a crucial developmental period to study rumination as a mechanism of change for treatment and preventing interventions of later mental health issues (Harmon et al., 2019).

The effective identification of ruminative response styles early in life requires developmentally appropriate and valid measures. Given the profound interest of the research community in children’s rumination toward sad mood (e.g., Bonifacci et al., 2020) there is a dearth of proposed age-appropriate assessment inventories (see Lo et al., 2017). However, rumination toward anger has only recently attracted the scientific interest as another worth of study cognitive vulnerability in youths. To our knowledge, the Children’s Anger Rumination Scale (CARS) is the only validated measure found in the literature for assessing children’s ruminative response style toward anger (S. D. Smith et al., 2016).

The CARS (S. D. Smith et al., 2016) is a valid and reliable self-report questionnaire that targets children’s tendency to engage in anger ruminative thoughts. It was adapted from the Anger Rumination Scale (ARS; Sukhodolsky et al., 2001) to be developmentally appropriate and psychometrically sound in children and early adolescents (S. D. Smith et al., 2016). The CARS consists of 9 items from the ARS that were remained exactly the same and 10 items that were linguistically modified to be comprehensible by younger respondents. In ARS, anger rumination represents a multidimensional construct conceptualized by the following dimensions: (a) Anger Afterthoughts (cognitive rehearsal of recent anger experiences), (b) Thoughts of Revenge (thoughts and ideas of retaliation), (c) Angry Memories (thoughts about past anger episodes), and (d) Understanding of Causes (thoughts about the causes of an anger experience). These dimensions are not considered conceptually independent. On the contrary they are construct relevant, representing a sequence of interactive, yet distinct stages in the anger rumination process. Thus, anger-provoking memories (Angry Memories) may trigger individuals’ reoccurring thoughts of anger episodes (Angry Afterthoughts) which in turn can amplify the intensity and duration of negative affect and lead to counterfactual thoughts associated with action tendencies toward resolution (Understanding of Causes) or retaliation (Thoughts of Revenge; Sukhodolsky et al., 2001). Counterfactual thinking (CFT) has been found to be a cross-cultural affective regulatory strategy (Gilovich et al., 2003) that emerges in early developmental stages (Nakamichi, 2019). More specifically, CFT refers to mental representations of hypothesized alternatives “what might have been” to occurred events, actions, or states (Epstude & Roese, 2008). In ARS/CARS, the “Understanding of Causes” dimension; interpreting in a meaningful way an angry episode; is supported to be a self-referent adaptive type of CFT that alleviates negative affectivity (Parikh et al., 2020) and facilitates behavioral change (Epstude & Roese, 2008). Conversely, the “Thoughts of Revenge” dimension represents an other-referent type of CFT because fantasies of retaliation imply blame that is deflected on others (Broomhall & Phillips, 2018). Vengeful thinking perpetuates feelings of hate and anger (Barber et al., 2005) and hinders subjective well-being (e.g., Gul & Rana, 2013) by acting as a barrier to forgiveness of others (Barber et al., 2005).

The dimensionality of the ARS has been examined in different cross-cultural settings: Iran (Besharat, 2011), Hong Kong, and Great Britain (Maxwell, 2004; Maxwell et al., 2005), Australia and Spain (Ramos-Cejudo et al., 2017), Colombia (Toro et al., 2020), France (Reynes et al., 2013), Turkey (Satici, 2014), Mexico (Ortega-Andrade et al., 2017), and Spain (Uceda et al., 2016). All but one studies (Maxwell, 2004) have confirmed the hypothesized four-factor structure of the inventory proposed by Sukhodolsky et al. (2001). Unexpectedly in case of CARS, literature findings are scarce and provide mixed results regarding the instrument’s dimensionality. More precisely, S. D. Smith et al. (2016) in two different studies conducted with children and juvenile male offenders, respectively, provided support for the four-factor structure of the CARS. Conversely, Repper (2006) investigating the construct of anger rumination in childhood and its relationship with aggression, pertained the one-factor solution of the CARS.

The studies on dimensionality of ARS/CARS mainly employed CFA (e.g., Ramos-Cejudo et al., 2017) and, to a minimum extent, exploratory factor analysis (EFA; e.g., Maxwell, 2004). In the traditional independent clusters modeling confirmatory factor analysis (ICM-CFA) models the construct-relevant multidimensionality of instruments such as ARS/CARS (e.g., S. D. Smith et al., 2016; Sukhodolsky et al., 2001) is not taken into account both conceptually and statistically. Construct-relevant multidimensionality pertains to the fact that items of a measurement usually tap into more than one construct or source of true score variance (Morin et al., 2016). Thus, cross-loadings between items and construct-relevant nontarget factors are considered theoretically justifiable (Asparouhov & Muthén, 2009). Consequently, the expected existence of cross-loadings challenges the overrestrictive ICM-CFA approach (cross-loadings are fixed to zero) leading often to unsatisfactory model fit, and biased parameter estimates (e.g., substantially increased factor correlations) that could undermine the discriminant validity of the measurement scale (Marsh et al., 2014; Morin et al., 2017). Indeed, the inflated factor correlations that were detected in studies using the ICM-CFA approach, both in adult (e.g., Uceda et al., 2016) and children versions of the anger rumination scale (S. D. Smith et al., 2016) raise concerns related to issues of discriminant validity, and multicollinearity in the context of regression-based models (T. A. Schmitt et al., 2018). Conversely, the unrestricted estimation of cross-loadings in EFA measurement models is considered a more flexible investigation of complex indicator-factor structures (e.g., Asparouhov & Muthén, 2009) that does not result in such biased parameter estimates (Asparouhov et al., 2015). However, optimized linear combinations of variables created in EFA models could result in overfitting data (see Osborne et al., 2008) as well to an oversensitive model solution to random sample variations (Morin et al., 2016). On the other hand, the recently integration of EFA with CFA into exploratory structural equation modelling (ESEM) allows researchers to incorporate the benefits from each technique into a single analytic framework (Asparouhov & Muthén, 2009). Nevertheless, the absence of hierarchically superior global factors in ESEM approach can possibly result in inflated estimates of cross-loadings (Morin et al., 2016). Literature suggests that theory-based multidimensional scales, such as CARS, often correspond to a bifactor measurement model with a general latent construct known as Global Factor—G Factor (e.g., anger rumination) alongside several conceptually related latent subdimensions knows as specificities—S-Factors (e.g., Angry Afterthoughts, Thoughts of Revenge) all used to explain the covariances among items (Myers et al., 2014). More specifically, the bifactor model tests whether the G-Factor exists as a unitary dimension underlying all items and coexists with S-Factors explaining the residual variance not accounted for by the G-Factor (Reise et al., 2010). However, the exclusion of cross-loadings between items and construct-relevant nontarget factors in a CFA bifactor model can result in inflated estimates of the items’ loadings on the G-Factor, and thus, in a mispecification regarding the true variance attributed to the G-Factor (Murray & Johnson, 2013). Finally, the recent incorporation of bifactor models with ESEM provides researchers with an opportunity to investigate two sources of “construct-relevant psychometric multidimensionality related to: (a) the hierarchical nature of the constructs being assessed and (b) the fallible nature of indicators which tend to include at least some degree of association with non-target constructs” (Morin et al., 2016, p. 134).

The Present Study

Anger-related problems (e.g., depression, bullying) are very common both in Greek youths (Giovazolias et al., 2017; Lazaratou et al., 2017; Papadaki & Giovazolias, 2015; Zacharopoulou et al., 2014) and in international samples (Hong et al., 2019; O’Neal et al., 2017; Özyurt et al., 2021). Thus, early and valid identification of possible cognitive risk factors is more than imperative for a successful treatment.

The purpose of the present study was to explore Anger Rumination in Greek children/preadolescents through the validation of the CARS instrument. More specifically, the specific objectives were as follows:

to thoroughly examine the factorial structure of the Greek version of the CARS in Greek children/preadolescents by contrasting alternative representations of the instrument: (a) one-factor ICM-CFA, four-factor ICM-CFA and ESEM models; and (c) bifactor-CFA (B-CFA) and bifactor ESEM (B-ESEM) models (Morin et al., 2016). Based on the original theoretical framework suggesting an interactive and temporally orientated relationship between the four cognitive mechanisms involved in the anger rumination process (Sukhodolsky et al., 2001), it was expected that the B-ESEM model would provide the most adequate representation of CARS item responses. Nevertheless, model selection was not based solely on model fit indices but included a careful examination of parameter estimates (e.g., factor loadings, cross-loadings, and interfactor correlations) and the underlying theory as well (Morin et al., 2016). Furthermore, given the high tendency of bifactor models to overfit even random data (Bonifay et al., 2016), several psychometrically informative bifactor-derived statistics were also considered (Rodriguez et al., 2016).

To examine the measurement invariance of the CARS in order to evaluate if the measured construct has the same meaning across gender and age subgroups samples, regardless of group membership. Based on previous research findings, no gender (e.g., Rood et al., 2009) and age differences (e.g., Hankin, 2008) were expected.

To determine the psychometric properties (test–retest reliability, convergent, discriminant, and predictive validity) of the CARS. Convergent and discriminant validity of the inventory in question were tested by assessing its relationship with the Big Five personality traits, namely Neuroticism (Emotional Instability), Energy/Extraversion, Intellect/Openess, Consciousness, and Agreeableness. Particularly, it was expected a positive correlation with Emotional Instability (Sukhodolsky et al., 2001) and a divergent minimal correlation with the other aforementioned personality traits (Oral & Arslan, 2017). The predictive validity of the CARS was assessed by examining the established predictive power of Anger Rumination to Bullying (Zsila et al., 2018) and Depression (Harmon et al., 2019).

Method

Participants

A sample of 552 native Greek students (80% participation rate), 10 to 13 years old (M_age = 11.50 years, SD = 1.11; 53.6% girls) participated in the present study. The sample was subdivided into children (n = 293, age range = 10-11 years) and preadolescents (n = 259, age range = 12-13 years). The convenience sample was collected from five primary and four secondary public schools, all located in Heraklion of Crete (Greece). Specifically, 24.5% of the students were fifth graders, 25.4% were sixth graders, 25.6% were seventh graders, and 24.5% were eighth graders. No differences were detected among schools (χ² = 5.14, degrees of freedom [df] = 8, p = .74) and school grades (χ² = 2.45, df = 3, p = .48) in terms of gender distribution. With regard to socioeconomic status, as defined by the parents’ educational status (Aarø et al., 2009) approximately 4.8% of mothers and 2.8% of fathers had completed primary studies, 40.7% of mothers and 8.5% of fathers had completed secondary studies, 25% of mothers and 18.5% of fathers had attended or completed college, whereas 29% of mothers and 16.9% of fathers had completed higher education.

Procedures

Permission by teachers and school principals as well as written parental consent and verbal child agreement were obtained prior to research. Data were collected in a group format, in which children were asked to complete a battery of self-report measures that assessed their thoughts and feelings. Participants were given detailed information regarding the anonymous, confidential, and voluntary nature of their participation and any doubts that arose were clearly explained. All participants (N = 552) completed CARS, whereas a convenience subsample of 300 participants (M_age = 10.63 years, SD = 0.63; 51% girls) completed Children’s Depression Inventory (CDI), Peer Experiences Questionnaire–Standard Version (PEQ-STDV), and Greek Big Five Questionnaire for Children–Short Form (GBFQ-C-SF), as described below. The two samples (initial vs. subsample) did not differ on gender (χ² = 1.82, df = 1, p = .18) and paternal educational status (χ² = 5.70, df = 3, p = .13), although mothers of subsample participants had achieved higher education (χ² = 11.41, df = 3, p < .05). After 1 month, which is the optimal recommended time for the analysis of test–retest reliability (Cea D’ Ancona, 1996 as cited in Gómez-Ortiz et al., 2016), the CARS was readministered to 19.7% (n = 59) of the subsample. All procedures were approved by the Institute of Educational Policy and the Greek Ministry of Education.

The CARS original items and instructions were translated to Greek by two independent experts, following Brislin (1970) recommendations. Τhe translators met to elaborate and agree on a consensus version of the adapted scale (i.e., linguistically, conceptually, and clarity). When in disagreement, an external specialist participated in the discussion to obtain consensus. This form was then back-translated into English by another two independent translators who agreed on a common back-translated version. The final translated Greek scale was administered to the sample of this study.

Measures

Children’s Anger Rumination Scale (S. D. Smith et al., 2016)

The CARS is a 19-item self-report questionnaire of children’s tendency to ruminate toward anger. As it has already been mentioned the instrument assesses four components of anger rumination: (a) Angry Afterthoughts (six items; e.g., “Memories of being angry pop up into my head before I fall asleep”); (b) Thoughts of Revenge (four items; e.g., “I have day dreams and fantasies that are violent”); (c) Angry Memories (five items; e.g., “I think a lot about other times when I was angry”); and (d) Understanding of Causes (four items; e.g., “I think about the reasons people treat me badly”; S. D. Smith et al., 2016). Participants are asked to rate the frequency of their ruminative response on a 4-point Likert-type scale (1 = almost never to 4 = almost always). Consistent with previous findings CARS yielded satisfactory test–retest reliability of .74 (standard error [SE] = .06, p < .001).

Children’s Depression Inventory (Giannakopoulos et al., 2009; Kovacs, 1992)

The CDI is a brief 27-item self-report questionnaire that assesses cognitive, affective, and behavioral signs of depression in children and adolescents 7 to 17 years of age. Participants are asked to endorse on a 3-point Likert-type scale (0 = absence of symptoms to 2 = definite symptoms) the statement that best describes their behavior or emotions with regard to a specific symptom of depression (e.g., “I’ feel like crying every day”). The 26th suicidal ideation item (“I want to kill myself”) was omitted at the request of the Institute of Educational Policy and the Greek Ministry of Education. The original five-factor structure (Negative Mood, Anhedonia, Ineffectiveness, Negative Self-esteem, and Interpersonal Difficulties) of the CDI (Kovacs, 1992) was not replicated in the subsample of 300 students. More specifically, even though the five-factor model yielded a reasonable fit to the data, WLSMVχ²₍₂₈₉₎ = 449.31, p < .001; comparative fit index (CFI) = 0.92; Tucker–Lewis index (TLI) = 0.92; root mean square error of approximation (RMSEA) [90% confidence interval (CI)] = 0.04 [0.04, 0.05], discriminant validity of the five corresponding constructs were not supported (r = 1.08-1.23, p < .001). Our findings were in line with previous studies (e.g., Garcia et al., 2008; Lee et al., 2012; Logan et al., 2013) supporting the one-factor structure of the instrument, WLSMVχ²₍₂₉₉₎ = 462.36, p < .001; CFI = 0.92; TLI = 0.92; RMSEA 90% CI = 0.04 [0.04, 0.05]; M_λ = 0.50). Internal consistency and reliability of the CDI has been well supported (e.g., Giannakopoulos et al., 2009). In the present study, internal consistency of the CDI was (ω = .82, SD = 0.02, 95% CI [0.78, 0.85].

Peer Experiences Questionnaire–Standard Version (Giovazolias et al., 2010; Vernberg et al., 1999)

The PEQ-STDV is an 18-item self-report questionnaire of children’s experiences in bullying behaviors. The PEQ-STDV consists of two subscales: The Victimization of Self (VS; nine items) subscale and the Victimization of Others (VO; nine items) subscale. Participants are asked to rate on a 5-point Likert-type scale (1 = never to 5 = a few times a week) how often in the past 3 months the item content applied to them. The two-factor structure of the instrument, WLSMVχ²₍₁₃₄₎ = 239.16, p < .001; CFI = 0.96, TLI = 0.95; RMSEA [90% CI] = 0.05 [0.04, 0.06]) as well as the discriminant validity of the two subscales (r = 0.73, p < .001) were confirmed in the subsample of 300 students. The VO subscale that targets aggressive behavior toward another children (e.g., “I chased a teen like I was really trying to hurt him or her”) was employed for the present research needs. The PEQ is a valid and reliable measure (e.g., Giovazolias et al., 2017). The internal consistency of the applied VO subscale was (ω = .84, SE = 0.04, 95% CI [0.76, 0.89]).

Greek Big Five Questionnaire for Children–Short Form (Barbaranelli et al., 2003; Markos & Kokkinos, 2017)

The GBFQ-C-SF is a valid and reliable 30-item self-report instrument that assesses the five basic factors of personality in children, as young as 8 years, and adolescents. Each factor consists of six items; Energy/Extraversion (e.g., “I easily make friends”); Agreeableness (e.g., “I treat my peers with affection”); Neuroticism (e.g., “I am in a bad mood”); Intellect/Openness (e.g., “I like to read a book”); Conscientiousness (e.g., “I respect the rules and the order”). Participants are asked to rate on 5-point Likert-type scale (1 = almost never to 5 = almost always) how often the item content describes them. In line with previous studies (e.g., Markos & Kokkinos, 2017), the five-factor structure of the instrument, WLSMVχ²₍₃₉₅₎ = 670.13, p < .001; CFI = 0.93, TLI = 0.92; RMSEA [90% CI] = 0.05 [0.04, 0.05], as well as the discriminant validity of the five subscales (r = 0.2-0.8, p < .001) were confirmed in the subsample of 300 students. In the present study, internal consistency coefficients of the GBFQ-C-SF subscales were as follows: Energy/Extraversion (ω = .70, SE = 0.05, 95% CI [0.55, 0.74]; Agreeableness (ω = .69, SE = 0.03, 95% CI [0.62, 0.74]; Emotional instability (ω = .75, SE = 0.03, 95% CI [0.68, 0.79]; Intellect/Openess (ω = .70, SE = 0.03, 95% CI [0.65, 0.74]; Conscientiousness (ω = .72, SE = 0.03, 95% CI [0.65, 0.77].

Data Analysis

Analyses were conducted using Mplus 8.1 (Muthén & Muthén, 2017) and SPSS version 25. In our data, assumptions of univariate skewness (0.30-2.14) and kurtosis (−0.10-3.80) were not met. Furthermore, Mardia’s coefficients (Mardia, 1970) for multivariate skewness (Mardia’s_skewness = 14.44, SD = 0.60, p < .001) and kurtosis (Mardia’s_kurtosis = 397.86, SD = 2.27, p < .001) indicated deviation from multivariate normality. Since items were measured on a 4-point Likert-type scale, they were treated as ordinal rather than continuous indicators of the latent factors. Accordingly, the WLSMV (weighted least squares mean- and variance-adjusted) estimator was employed, as it outperforms traditional maximum likelihood for ordered-categorical indicators with five or less response categories (Finney & DiStefano, 2006). Missing values percentages for each of the assessed variables were trivial ranging from 1% to 5% and excluded from the analysis using pairwise deletion approach which is default in Mplus when using the WLSMV estimator.

Following Morin et al. (2016), we successively assessed ICM-CFA, B-CFA, ESEM, and B-ESEM models. ESEM was conducted using oblique target rotation (Asparouhov & Muthén, 2009), while B-ESEM was estimated using bifactor orthogonal target rotation (Reise, 2012). In ICM-CFA and B-CFA models all cross-loadings were constrained to be exactly zero. In contrast, in ESEM and B-ESEM models all cross-loadings were “targeted” to be as close to zero as possible. In both B-CFA and B-ESEM, all items were allowed to load on a general anger rumination factor and on a specific a priori S-factor. In ESEM version items were allowed to cross-load, whereas they were not in the CFA version.

Measurement invariance of the best fitted model was tested across gender (boys vs. girls) and age group (children vs. preadolescents) to ensure equivalence of meaning across these groups (Putnick & Bornstein, 2016). The following sequential invariance testing strategy (Meredith, 1993) adapted for ordered-categorical indicators (Morin et al., 2013) was used: (a) configural invariance; (b) metric/weak invariance (invariance of the factor loadings); (c) scalar/strong invariance (loadings and thresholds); (d) strict invariance (loadings, thresholds, and uniqueness); (e) invariance of the latent variances–covariances (loadings, thresholds, uniqueness, and variances–covariances); (f) latent means invariance (loadings, thresholds, uniqueness, variances–covariances, and latent means). The size of all groups exceeded the generally recommended value of 200 observations for measurement invariance testing (Koh & Zumbo, 2008).

The fit of all models was assessed using the WLSMVχ², the CFI, the TLI, and the RMSEA and its 90% CI (Hu & Bentler, 1999). Traditional cutoff criteria with CFI and TLI values greater than 0.90 and 0.95 and RMSEA values lower than 0.08 and 0.06 were used to indicate adequate and excellent model fit, respectively. Model fit improvement as well measurement invariance across the nested models were evaluated using the Mplus DIFFTEST option for WLSMV (MDΔχ²; Asparouhov & Muthén, 2006). Given that χ² and MDΔχ² tend to be oversensitive to sample size, additional indices were used in tests of invariance (Chen, 2007): a CFI change of (ΔCFI) ≤ 0.010 or less accompanied by a change of RMSEA (ΔRMSEA) ≤ .015 or less between a model and the preceding one indicate to the more parsimonious model or that the measurement invariance hypothesis should not be rejected.

Construct replicability of the latent constructs was tested using H index with values (>.80) suggesting a well-defined latent variable (Hancock & Mueller, 2001). Composite reliability was measured using Omega (ω; McDonald, 1999) and Omega hierarchical (omegaH or ω_Η) estimates. Both ω and omegaH are indicators of the degree to which the scale scores precisely measure the target construct. In contrast with ω which estimates the proportion of variance in the total and subscale scores attributed to all “modeled” source of common variance, omegaH assesses the proportion of variance in total score exclusively attributable to a single general latent factor, whereas omegaHS (ω_HS) estimate the unique variance of each subscale score after controlling for the variance associated with the general factor (Reise et al., 2013a). Nevertheless, high values of omegaH (>.80; Reise et al., 2013a) should not be confused with “unidimensionality” of the data as they: (a) just inform on the percentage of variance in a uni-weighted total score that can be attributed to a general factor and (b) are positively related to the number of items (Rodriguez et al., 2016). Given the aforementioned limitations of OmegaH, the explained common variance (ECV) and the percentage of uncontaminated correlation (PUC) were also used for a more straightforward and clear measure of degree of dimensionality (Reise et al., 2013b). According to Rodriguez et al. (2016), when ECV and PUC are above > .70, the common variance can be considered as essentially unidimensional.

Test–retest reliability (see measures) and validity of the CARS (convergent, divergent and predictive) were examined using SEM analysis technique; the GBFQ-C-SF was treated as a five-factor ICM-CFA model whereas all others measures under study were treated as unidimensional ICM-CFA models. Various rules of thumb have been advanced in the literature for interpreting effect sizes coefficients (e.g., Cohen, 1988; Hemphill, 2003). In the present study, we employed the widely known guidelines proposed by Cohen (1988) for evaluating, correlation r (r < .30, small; .30 ≤ r <.50, medium; r >.50, large) and coefficient of determination (R²) effect sizes (R² < 0.13, weak; 0.13 ≤ R² < 0.26, medium; R² ≥ 0.26, substantial). Point estimates were based on 1,000 bootstrapping samples and 95% CI were generated.

Results

CFA Versus Bifactor CFA Versus ESEM

Model fit indices and the standardized parameter estimates for all models are presented in Table 1.

Table 1.

Goodness-of-Fit Statistics and Information Criteria for the Estimated Models on the Children’s Anger Rumination Scale.

Model	WLSMV χ²(df)	CFI	TLI	RMSEA	90% CI	Comparison	ΔWLSMVχ² (df)	ΔCFI	ΔRMSEA
M1. CFA 1-factor first-order model	500.83* (152)	0.96	0.95	0.06	[0.06, 0.07]	—	—	—	—
M2. CFA four-factor first-order model	488.82* (146)	0.96	0.95	0.07	[0.06, 0.07]	M2-M1	17.08* (6)	0.00	0.01
M3. CFA bifactor model	280.87* (133)	0.98	0.98	0.05	[0.04, 0.05]	M3-M2	204.73* (13)	0.02	0.02
M4. ESEM four-factor first-order model	190.87* (101)	0.99	0.98	0.04	[0.03, 0.05]	M4-M3	99.17* (32)	0.01	0.01
M5. ESEM bifactor model	150.02* (86)	0.99	0.98	0.04	[0.03, 0.05]	M5-M4	42.00* (15)	0.00	0.00
Gender invariance
Baseline Boys (n = 256)	134.77* (86)	0.99	0.97	0.05	[0.03, 0.06]	—	—	—	—
Baseline Girls (n = 296)	135.05* (86)	0.99	0.98	0.04	[0.03, 0.06]	—	—	—	—
M1. Configural	323.47* (196)	0.98	0.97	0.05	[0.04, 0.06]	—	—	—	—
M2. Weak (loadings)	348.33* (242)	0.99	0.98	0.04	[0.03, 0.05]	M2-M1	21.18 (46)	0.00	0.01
M3. Strong (loadings, thresholds)	378.06* (275)	0.99	0.98	0.04	[0.03, 0.05]	M3-M2	44.09 (33)	0.00	0.00
M4. Strict (loadings, thresholds, uniquenesses)	411.85* (294)	0.99	0.98	.04	[0.03, 0.05]	M4-M3	29.23 (19)	0.00	0.00
M5. Latent variance-covariance	372.86* (309)	0.99	0.99	0.03	[0.02, 0.04]	M5-M4	23.87 (15)	0.01	0.01
M6. Latent means	391.00 * (314)	0.99	0.99	0.03	[0.02, 0.04]	M6-M5	11.97 * (5)	0.00	0.00
Age invariance
Baseline children (n = 293)	122.35* (86)	0.99	0.98	0.04	[0.02, 0.05]	—	—	—	—
Baseline preadolescents (n = 259)	96.08* (86)	1.00	1.00	0.02	[0.00, 0.04]	—	—	—	—
M1. Configural	236.02* (196)	1.00	0.99	0.03	[0.01, 0.04]	—	—	—	—
M2. Weak (loadings)	321.43* (242)	0.99	0.99	0.03	[0.02, 0.04]	M2-M1	93.28* (46)	0.01	0.00
M3. Strong (loadings, thresholds)	355.72* (275)	0.99	0.99	0.03	[0.02, 0.04]	Μ3-Μ2	30.15 (28)	0.00	0.00
M4. Strict (loadings, thresholds, uniquenesses)	366.19* (294)	0.99	0.99	0.03	[0.02, 0.04]	Μ3-Μ2	7.42 (19)	0.00	0.00
M5. Latent variance-covariance	355.62* (309)	0.99	0.99	0.02	[0.01, 0.03]	M5-M4	23.44 (15)	0.00	0.01
M6. Latent means	348.45 * (314)	1.00	1.00	0.02	[0.00, 0.03]	M6-M5	1.97 (5)	0.01	0.00

Note. Bold entries indicate the final levels of invariance that were achieved. CFA = confirmatory factor analysis; ESEM = exploratory structural equation modeling; WLSMV = weighted least squares mean- and variance-adjusted estimator; χ² = chi-square; df = degrees of freedom; CFI = comparative fit index; TLI = Tucker–Lewis index; RMSEA = root mean square error of approximation; 90% CI = 90% confidence interval of the RMSEA; ΔWLSMVχ² = chi-square difference test based on the Mplus DIFFTEST function for WLSMV estimator; ΔCFI change in CFI value compared with the preceding model; ΔRMSEA = change in the RMSEA value compared with the preceding model.

p < .05.

The one-factor ICM-CFA model showed a reasonable representation of the data based on the approximate fit indices (CFI = 0.96; TLI = 0.95; RMSEA [90% CI] = 0.06 [0.06, 0.07]). Results also indicated an internally consistent (ω = .91) and well-defined factor (H = .94); all loadings (λ = .33-.79, Μ_λ = 0.64) exceeded the recommended cutoff of ǀ.32ǀ proposed by Tabachnick and Fidell (2001). Similarly the four-factor ICM-CFA solution fitted the data acceptably [CFI = 0.96; TLI = 0.95; RMSEA [90% CI] = 0.07 [0.06, 0.07]) yielding internally consistent and well-defined factors: Angry Afterthoughts (ω = .76; H = .85), Thoughts of Revenge (ω = .76; H = .81), Angry Memories (ω = .63; H = .75), Understanding of Causes (ω = .75; H = .83); items loaded strongly on their respective factors (λ = .37-.79, Μ_λ = .64). Based on the χ² difference test the four-factor ICM-CFA outperformed the one-factor ICM-CFA model, ΔWLSMVχ²₍₆₎ = 17.08, p < .05. Nevertheless, the aforementioned fit improvement was not replicated by the negligible observed changes in approximate fit indices (ΔCFI = 0.00; ΔRMSEA = 0.01). Most important, discriminant validity of the latent measures was not supported given that correlations (r = 0.92-1.00, p < .001; Μ_r = 0.96; see Table 2) were above the proposed cutoff of ǀ.80ǀ (Brown, 2015).

Table 2.

Latent Factor Correlations for the Four-Factor ICM-CFA and ESEM Model.

	AA	TR	AM	UOC
AA	—	.99***	.96***	.92***
TR	.55***	—	.97***	1.00***
AM	.56***	.60***	—	.95***
UOC	.43***	.42***	.56***	—

Note. CFA correlations are displayed above the diagonal and first-order ESEM correlations are displayed below the diagonal. CFA = confirmatory factor analysis; ESEM = exploratory structural equation modeling; ICM-CFA = independent cluster models–confirmatory factor analysis; AA = angry afterthoughts; TR = thoughts of revenge; = AM = angry memories; UOC = understanding of causes.

***

p < .001.

The B-CFA model fitted the data better (CFI = 0.98; TLI = 0.98; RMSEA [90% CI] = 0.05 [0.04, 0.05]) and appeared to be superior compared with the four-factor ICM-CFA solution, ΔWLSMVχ²₍₁₃₎ = 204.73, p < .05; ΔCFI = 0.02; ΔRMSEA = 0.02. Furthermore, the anger rumination GF showed acceptable factor loadings (λ = .32-.80, Μ_λ = .63; H = .94), whereas the SFs were weakly defined: Angry Afterthoughts (λ = .06 to −.63, Μ_λ = .01; H = .44), Thoughts of Revenge (λ = .00 to .69, Μ_λ = 0.32; H = .53), Angry Memories (λ = .07-.84, Μ_λ = .27; H = .72), Understanding of Causes (λ = −.00-.91, Μ_λ = .34; H = .82). More specifically, the B-CFA model yielded a pattern of small, insignificant, or even divergent item loads on the hypothesized SFs (e.g., cars_7 on Angry Afterthoughts; β = −.63, p <.001). Further three items (cars_4, cars_1, cars_12) were found to tap more highly into their respective SF instead of the GF (see Table 3). Omega coefficient levels were generally satisfactory, whereas omega hierarchical values displayed high variability with a very high proportion of variance exclusively attributed to the anger rumination GF and a very small one to the SFs after controlling for the GF (ω =.95; ω_H = .91); Angry Afterthoughts (ω = .91; ω_HS = .00); Thoughts of Revenge (ω = .82; ω_ΗS = .27); Angry Memories (ω = .84; ω_HS = .13); Understanding of Causes (ω = .72; ω_HS = .24). Additionally, an ECV value of ǀ.73ǀ and a PUC value of ǀ.78ǀ suggested a similar pattern of item loadings between the GF and that possibly obtained from the one-factor ICM-CFA model. This suggestion was supported by the high correlation between the two sets of factor loadings (r_{λone-factor CFA – GF B-CFA} = .99). Nevertheless, as it has already been mentioned, excluding cross-loadings in a B-CFA model could result to a misspecification regarding the true variance attributed to the GF (Murray & Johnson, 2013). Thus, we proceeded with the four-factor ESEM which yielded a very good representation of the data (CFI = 0.99; TLI = 0.98; RMSEA [90% CI] = 0.04 [0.03, 0.05]) but provided mixed results in regard to its fit improvement over the B-CFA model, ΔWLSMVχ²₍₃₂₎ = 99.17, p < .05; ΔCFI = .01; ΔRMSEA = .01. Furthermore, the four-factor ESEM model displayed reduced factor correlations (r = 0.42-0.60, Μ_r = .52; see Table 2) and a pattern of inflated target loadings, significant cross-loadings as well as items that tapped exclusively into nontarget factors. [e.g., cars_7 (Angry Afterthoughts_target = −.01; Thoughts of Revenge_nontarget = .54; Angry Memories_nontarget = .32)]. This loading pattern provided an extra statistical argument over the conceptual overlap of the four theoretically related anger rumination constructs as well as the existence of an unmodelled GF. Given that the selection of the best fitted model was not limited on model fit indices but included the parameter estimates and the underlying theory as well (Morin et al., 2016), the ESEM approach was retained in the next step of analysis.

Table 3.

Parameter Estimates for the CFA and ESEM Solutions of CARS.

	CFA one-factor model	CFA four-factor model	Bifactor CFA		ESEM				Bifactor ESEM
	(λ)^a	SF (λ)^a	AR (λ)	SF (λ)^a	AA (λ)	TR (λ)	AM (λ)	UOC (λ)	AR (λ)	AA (λ)	TR (λ)	AM (λ)	UOC (λ)
AA
cars_7	.72 ***	.72 ***	.77 ***	−.63 ***	−.01	.54***	.32***	.03	.70 ***	−.06	.30***	.16**	−.05
cars_8	.73 ***	.74 ***	.74 ***	.20 **	.50 ***	.20**	.01	.24***	.73 ***	.26 ***	.03	−.10*	.04
cars_9	.76 ***	.77 ***	.77 ***	.07	.46 ***	.06	.37***	.03	.79 ***	−.08	−.12*	−.05	.00
cars_17	.69 ***	.69 ***	.69 ***	.22 **	.48 ***	.09	.08	.21***	.69 ***	.22 ***	−.04	−.07	.06
cars_18	.79 ***	.79 ***	.80 ***	.06	.27 ***	.27***	.23***	.22***	.77 ***	.16 **	.09*	.09	.02
cars_19	.78 ***	.78 ***	.79 ***	.13 **	.32 ***	.15**	.27***	.23***	.76 ***	.25 ***	.01	.12**	.02
TR
cars_4	.71 ***	.79 ***	.66 ***	.69 ***	.11	.76 ***	.04	−.05	.69 ***	−.13*	.45 ***	−.09	−.06
cars_6	.49 ***	.54 ***	.49 ***	.00	.19**	.05	.30***	.05	.51 ***	−.14 *	−.07	.03	.03
cars_13	.58 ***	.64 ***	.56 ***	.23 **	.08	.53 ***	−.04	.17**	.53 ***	.28***	.39 ***	.08	−.00
cars_15	.71 ***	.79 ***	.67 ***	.39 ***	.12	.78 ***	.03	−.07	.69 ***	−.12	.44 ***	−.10	−.09*
AM
cars_1	.55 ***	.56 ***	.51 ***	.84 *	−.16*	−.16**	.88 ***	.08	.54 ***	−.07	−.15**	.52 ***	.02
cars_2	.53 ***	.55 ***	.52 ***	.18	−.10	.15*	.42 ***	.19**	.49 ***	.06	.08	.32 ***	.06
cars_3	.69 ***	.71 ***	.68 ***	.16	.35***	−.03	.51 ***	−.02	.70 ***	.01	−.13**	.11	−.05
cars_5	.76 ***	.79 ***	.76 ***	.11	.43***	.07	.51 ***	−.12*	.79 ***	−.10	−.10*	.02	−.09*
cars_14	.70 ***	.72 ***	.70 ***	.07	.12	.23***	.23 **	.30***	.67 ***	.10	.11*	.14 *	.14**
UOC
cars_10	.68 ***	.75 ***	.69 ***	−.00	.42***	.22***	.09	.11	.69 ***	.08	.04	−.10*	.00
cars_11	.33 ***	.37 ***	.32 ***	.22 *	−.15*	−.03	.24**	.39 ***	.31 ***	−.10	−.01	.21***	.30 ***
cars_12	.43 ***	.48 ***	.41 ***	.91 **	.12	−.10*	−.05	.67 ***	.41 ***	.04	−.06	−.01	.70 ***
cars_16	.51 ***	.56 ***	.50 ***	.22 *	.32***	−.08	.00	.45 ***	.50 ***	.15*	−.10	−.03	.27 ***

Note. Target factor loadings are in bold. CFA = confirmatory factor analysis; ESEM = exploratory structural equation modeling; AR = general anger rumination factor; AA = angry afterthoughts; TR = thoughts of revenge; AM = angry memories; UOC = understanding of causes; λ = standardized factor loadings; SF = specific factors of the Children’s Anger Rumination Scale.

Each item loaded on their respective factor, while cross-loadings were constrained to be zero.

p < .05. **p < .01. ***p < .001.

ESEM Versus B-ESEM

The B-ESEM solution yielded the best overall model fit to the data (CFI = 0.99; TLI = 0.98; RMSEA [90% CI] = 0.04 [0.03, 0.05]). Based on the χ² difference, it outperformed the ESEM model (ΔWLSMVχ² = 42.00, df = 15, p < .05). Nevertheless the trivial changes in approximate fit indices (ΔCFI = 0.00; ΔRMSEA = 0.00) brought into question B-ESEM’s fit superiority. The GF was well-defined (H = .94) by strong and significant item loadings (λ = .31-.80, Μ_λ = .63) but that was not accomplished by the majority of SFs: Angry Afterthoughts (H = .06; λ = −.06-.26, Μ_λ = .17), Thoughts of Revenge (H = .15; λ = −.07-.45, Μ_λ = 0.34), Angry Memories (H = .08; λ = .02 to .52, Μ_λ = 0.23), Understanding of Causes (H = .22; λ = .00-.27, Μ_λ = .32). In contrast to the generally high levels of coefficient omegas only the GF displayed a high level proportion of variance: GF (ω = .91; ω_H = .91); Angry Afterthoughts (ω = .68; ω_HS = .04); Thoughts of Revenge (ω = .87; ω_HS = .13); Angry Memories (ω = .90; ω_HS = .07); Understanding of Causes (ω = .80, ω_HS = .17). Finally, an ECV value of ǀ.81ǀ, a PUC value of ǀ.78ǀ and the high correlated sets of loadings (r_{λone-factor CFA-GF B-ESEM} = .99) strongly supported the strength of the GF as a single common factor and consequently the unitary factorial structure of CARS. In other words, most items were strongly represented and explained by the anger rumination general construct and not by the specific subdimensions.

Measurement Invariance

Measurement invariance was tested across gender (boys vs. girls) and age groups (children vs. preadolescents) on the best fitted bifactor ESEM model, and the findings were displayed in the lower portion of Table 3. Configural invariance was successfully estimated in all groups, and then more stringent constraints were progressively imposed on the models. None of these invariance conditions caused model fit deterioration. The latent mean invariance for gender and age group respectively were supported based on the recommended cutoff guidelines (ΔCFI, ΔRMSEA). More specifically, the latent means invariance across gender revealed that—when the latent means of the girls were constrained to be zero for the purpose of identification—girls’ anger rumination latent means did not significantly differentiated from boys. Similarly, no age significant differences were detected in anger rumination latent means.

B-ESEM or One-Factor ICM-CFA?

In the present study, B-ESEM provided the best fit to the multidimensional CARS data. Careful examination of various bifactor-derived statistics showed that most items were strongly represented and explained by the anger rumination general construct and not by the specific subdimensions. According to Reise et al. (2007), true BF models should not be used to account for residual (co)variance alone but applied when there are meaningful specificities constituting well-defined subfactors. In other words when subfactors are found to be insignificant then, “ . . . researchers may conclude that a unidimensional model should be adequate as the effect of the multidimensional is too trivial to merit a multidimensional model.” (Luo & Al-Harbi, 2016, p. 2, as cited in Decker, 2021). Given that our results justified the essential unidimensionality of the CARS without too much concern about structural parameter bias (Reise et al., 2013a), we proceeded with testing all types of CARS’s validity on the one-factor ICM-CFA CARS’s model.

Convergent and Discriminant Validity

Results showed that there was a significantly positive correlation between Anger Rumination and Neuroticism, r = 0.52, SE = 0.05, p < .001, 95% CI [0.41, 0.63]. Conversely, there was a significantly but albeit weak negative correlation between Anger Rumination and Energy/Extraversion, r = −0.18, SE = 0.05, p < .001, 95% CI [−0.27, −0.05], Conscientiousness, r = −0.24, SE = 0.07, p < .001, 95% CI [−0.38, −0.09], Intellect/Openess, r = −0.27, SE = 0.07, p < .001, 95% CI [−0.39, −0.13] and Agreeableness, r = −0.28, SE = 0.07, p < .001, 95% CI [−0.41, −0.14]. The overall fit of the model was acceptable, WLSMVχ²₍₁₁₁₂₎ = 1584.69, p < .001; CFI = 0.92; TLI = 0.92; RMSEA [90% CI] = 0.04 [0.03, 0.04]).

Predictive Validity

According to R² coefficient, anger rumination substantially predicted concurrent levels of depression (b = .71, β = .58, SE = 0.05, p < .001, 95% CI [0.45, 0.66]; R² = 0.33). Results also indicated a weak but significant proportion of variance shared by ruminative tendency toward anger and bullying behaviors (b = .37, β = .35, SE = 0.06, p < .001, 95% CI [0.21, 0.48]; R² = 0.12). The overall model fit of the two cross-sectional SEM models was satisfactory; anger rumination → depression symptoms, WLSMVχ²₍₉₄₄₎ = 1,269.28, p < .001; CFI = 0.94; TLI = 0.93; RMSEA [90% CI] = 0.03 [0.03, 0.04]; anger rumination → bullying, WLSMVχ²₍₃₄₉₎ = 473.71, p < .001; CFI = 0.97; TLI = 0.97; RMSEA [90% CI] = 0.034 [0.03, 0.04].

Discussion

Anger rumination represents a dysfunctional cognitive strategy, formed in childhood that is related to deleterious effects on individual’s psychological health. Thus, the early identification and treatment of youth’s tendency to dwell unintentionally on angry thoughts is of utmost importance to prevent the stabilization of this maladaptive response style in later life stages. To our knowledge, the CARS (S. D. Smith et al., 2016) is the first inventory adapted from the adult version (ARS) to be developmentally appropriate and psychometrically sound to target children’s tendency to ruminate on angry thoughts. Similarly with ARS, anger rumination in CARS is conceptualized as a multidimensional construct that comprised four dimensions—stages in the anger ruminative process: Angry Afterthoughts, Thoughts of Revenge, Angry Memories, and Understanding of Causes. Previous studies on both versions of the instrument, mainly employed CFA and to a lesser extent EFA approaches and yielded mixed results regarding its unitary or four-faceted structure (Repper, 2006; S. D. Smith et al., 2016). As it was aforementioned, CFA is considered an overrestrictive approach that challenges construct-relevant multidimensional data leading often to biased parameter estimates (Morin et al., 2017). On the other hand, the EFA, even though more realistic and flexible in nature, is a data-driven approach that is recommended in cases when there is no supporting theory guiding the analysis (Pasquali, 2012 as cited in Bido et al., 2018).

The present study, acknowledging the multidimensionality of the CARS, is the first study that successively contrasted ICM-CFA, B-CFA, ESEM, and B-ESEM models (Morin et al., 2016) in order to contribute essentially to the existing literature regarding CARS factorial structure. Literature suggests that a “good fitting” model does not always imply an adequate model in terms of generalizability or predictive validity (T. A. Schmitt et al., 2018). Thus, model selection, as it has already been mentioned, did not include only model fit indices but also the careful examination of parameter estimates (e.g., factor loadings) and the underlying theory as well (Morin et al., 2016). Furthermore, given the high propensity of bifactor models to fit any possible data, even with nonsense response patterns (Reise et al., 2016), evaluations were made with caution (Bonifay et al., 2017; Decker, 2021) and several psychometrically informative bifactor-derived statistics were considered (Rodriguez et al. 2016).

Results showed that both ICM-CFA models provided good representation of the data as well as internally consistent and well-defined factors. Nevertheless, in case of the one-factor ICM-CFA solution, unidimensionality could not be reliably supported because the size of item loads on a single factor often represent a common rather than a systematic source of variance for each item (Reise et al., 2010). Furthermore, the discriminant validity of the anger ruminative dimensions in the four-factor ICM-CFA model was not accomplished as their interrelation exceeded the recommended cutoff of .80 (Brown, 2015). Particularly the inflated factor correlations found in the present study are consistent with previous findings (S. D. Smith et al., 2016) suggesting a high degree of overlap between subdimensions of the CARS as well as the “existence” of a single underlying higher order anger rumination factor. In order to judge whether CARS’ s multidimensional item response data have a strong general factor to justify a unidimensional measurement model, the B-CFA approach was employed (Reise et al., 2007). The B-CFA model yielded a better representation compared with the four-factor ICM-CFA model and a similar pattern of loadings between the G-factor and that obtained from the one-factor ICM-CFA model. Nevertheless, unidimensionality of the CARS could not be strongly supported based exclusively on the B-CFA model. According to Murray and Johnson (2013) excluding cross-loadings between items and construct-relevant nontarget specific factors in a B-CFA model could inflate the variance of the GF. Additional support for the unitary factorial structure of the CARS was provided by the well-fitting ESEM model: the existence of cross-loadings suggested the conceptual overlap of the four theoretically related anger rumination constructs as well as the presence of an unmodelled GF. Finally, the best-fitting B-ESEM model justified the unidimensionality of the CARS because SFs did not retain their own specificity in addition to that accounted for by the G-factor, suggesting that they are ignorable nuisance dimensions adding no information to anger rumination GF. Our findings are congruent with the unidimensional CARS solution suggested by Repper (2006) and seem to contradict Sukhodolsky et al.’s (2001) theoretical framework in which anger rumination represents a dynamic emotional–cognitive process comprised of four interactive but distinct stages.

Similarly with previous findings (S. D. Smith et al., 2016), measurement invariance (e.g., invariance on the level of latent means) of the CARS across gender and age-groups was supported. As for gender differences, the similar rates of anger rumination displayed by boys and girls contradict previous studies suggesting that boys tend to ruminate more on angry thoughts relative to girls (Harmon et al., 2019; S. D. Smith et al., 2016). Partially consistent to our findings are the results obtained from two meta-analyses on youth gender differences in rumination (Rood et al., 2009; Tamres et al., 2002). More specifically, Rood et al. (2009) reported that the differences are quite small in childhood and become significant and larger in magnitude through adolescence. Additionally, in another meta-analysis on coping mechanisms, including rumination, results yielded a significantly trivial effect of gender on rumination, with females reporting higher ruminative levels (Tamres et al., 2002). Furthermore in line with previous studies suggesting adolescence as the life stage in which rumination increases in intensity and becomes more rigid (Hampel & Petermann, 2005; Hankin, 2008) no significant differences were detected between children and preadolescents regarding their tendency to ruminate on anger.

Given that our results justified the essential unidimensionality of the CARS without too much concern about structural parameter bias (Reise et al., 2013b) we proceeded with testing all types of CARS’s validity on the one-factor ICM-CFA CARS’s model. To our knowledge, our study is the first that assessed the convergent and divergent validity of the CARS. Based on the guidelines proposed by Cohen (1988) both forms of validity were confirmed. Particularly, as it was expected Anger Rumination was found to be highly correlated with the personality trait of Neuroticism. This finding is in line with previous studies supporting the positive relationship between negative affectivity and anger ruminative response style (Mezulis et al., 2011; Sauer-Zavala et al., 2013; Sukhodolsky et al., 2001). Particularly, the anger rumination, neuroticism link has been attributed to both genetic and environmental factors. More precisely, du Pont et al. (2019) in a longitudinal study conducted with 439 same-sex twin pairs found that rumination and neuroticism share common genetic influences. Additionally, Sachs-Ericsson et al. (2014) in a study including 375 biological parent–offspring dyads supported that parental neuroticism contributes positively to the offsping’s rumination by cultivating an environment that promotes dysfunctional coping strategies such as rumination. The pattern of negative and small correlations between anger rumination and the other personality traits, namely Energy/Extraversion, Intellect/Openess, Consciousness, and Agreeableness was also confirmed in previous researches (e.g., Fresnics & Borders, 2016; Oral & Arslan, 2017).

The substantial depressogenic role of rumination that was supported in the present study is consistent with previous findings underscoring the importance of assessing anger rumination in understanding youth’s risk for depression (Gilbert et al., 2005; Harmon et al., 2019; Patel et al., 2017). A possible cognitive mechanism to explain anger rumination—depression link is victim justice sensitivity, a personality trait reflecting people’s tendency to react emotionally to incidents of injustice for the self (M. Schmitt et al., 2010). Thus, individual’s high propensity to ruminate on an angry experience may intensify preexisting cognitive appraisals of being unfairly treated which in turn may lead to depression symptoms of worthlessness and helplessness (Bondü et al., 2017).

In consistency with our prediction, Anger Rumination seemed to have a positive weak, yet significant effect on bullying behaviors (Caprara et al., 2007; Zsila et al., 2018; Vasquez et al., 2012). One possible explanation could be attributed to the vengeful prolonged thinking that usually characterizes anger rumination. More specifically, according to the anger ruminative theory (Sukhodolsky et al., 2001), thoughts of retaliation represent a way for handling the high levels of emotional intensity caused by recycling angry thoughts. Indeed, Sarićam (2017) in a cross-sectional study conducted with 318 secondary school students found that thoughts of revenge partially mediated the link between victimization and bullying. In other words, the unsettling experience of victimization can generate a distorted cognitive–affective cycle of retaliation thoughts (Manasse & Ganem, 2009) which in turn may predispose individuals to behave aggressively in order to resolve them. Another explanation of the anger rumination-bullying link is provided by the Emotional Cascade Model (Selby et al., 2008). According to this model, negative affect initiated by an emotion-provoking event interacts with rumination processes resulting in an “emotional cascade.” Consequently, individuals may engage in several dysregulated behaviors such as binge eating, self-injury, yelling, and threatening in an effort to distract themselves and short-circuit this emotional cascade (Selby et al., 2009).

The present study contributes to existing literature in several ways. First, CARS’s factorial structure was tested using both conventional and more recent and analytic techniques, such as the B-ESEM modeling approach to resolve some issues associated with instrument’s latent structure. Second, to our knowledge it is the third study (Repper, 2006; S. D. Smith et al., 2016) that examined the psychometric properties of the CARS in children and adolescence. Third, reliability and validity of the instrument were examined using SEM analysis, which reduces the impact of measurement error. Finally, our results provide a strong empirical justification for the unidimensionality of the Anger Rumination construct.

Limitations and Recommendations

In the present research, a number of important limitations should be also acknowledged. First, given that our results were specific to a nonclinical sample of Greek students enrolled in public schools of Crete, generalization to the broader Greek youth population is difficult to be attained. Future research should include more representative samples (e.g., other geographic regions; private schools). Second, acknowledging the role that ethnicity plays in anger expression coping styles (Perry-Parrish et al., 2017; Pittman, 2011), it would be recommendable to assess the factorial structure of the CARS in different cultural settings in order to draw a more certain conclusion regarding the nature of anger rumination. Third, by relying exclusively on single-source (children/preadolescents) and single-method (self-report) data collection, concerns regarding response bias (e.g., Holmbeck et al., 2002) and common method bias (e.g., Podsakoff et al., 2003) are raised. A remedy for these types of bias could be to employ alternative multisource (e.g., parents, teachers) and multimethod assessment modalities (e.g., semistructure interviews, rumination diary). For example, the diary methodology is becoming a valuable tool in research on rumination (Riley et al., 2019) to gather information regarding children’s angry rumination thoughts (e.g., intensity and specific content). Two relevant questions can be put forward in this context: (1) “What if this multisource and multimethod approach eventually provided evidence against the proposed unidimensional structure of CARS? and if so, (2) “Is there any clinical value to assessing distinct subdimensions of rumination (e.g., Angry Memories)? The fact that our results did not yield any support over the distinctiveness of the four cognitive ruminatory mechanisms does not preclude future research from uncovering other underlying dimensions or clinical important features of rumination. Thus, there is evidence suggesting that each of the aforementioned subdimensions serves a distinct role in the anger rumination process, associated with different outcomes and treatments. For example, high levels of Angry Afterthoughts may indicate potential deficits in cognitive shifting, an executive function necessary for ameliorating negative emotions (Holder et al., 2020). Thus, implementing programs that teach adolescents adaptive emotion regulation strategies (e.g., distraction and cognitive reappraisal) would help them reduce negative thinking and affect (e.g., Volkaert et al., 2020). Furthermore, the “Forgiveness Therapy” has been found to help individuals release Angry Memories and Thoughts of Revenge (Baskin & Slaten, 2010) and thus, cope with difficulties in forgiving oneself and another (Barber et al., 2005). On the other hand, the depressogenic feelings of regret implied in high levels of self-referential CFT (Understanding of Causes) have been found to be treated effectively with the “emotion-focused therapy” (Broomhall & Phillips, 2018). Finally, a longitudinal research design would be fruitful in uncovering the temporal stability of the CARS inventory and/or the bidirectional relationship between anger rumination, depression, and bullying (e.g., a cross-lagged panel model analysis).

Overall, our results suggest that the CARS is a reliable and valid instrument to assess children’s and preadolescent’s tendency to ruminate toward anger.

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

Ethical Approval

The present study was approved by the Greek Ministry of Education (No: Φ15/30515/40339/Δ1)

Informed Consent

Informed consent was obtained from all individual participants included in the study.

ORCID iD

Theodoros Giovazolias

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