Facet level effects of extraversion on leadership behaviours rated by subordinates

Abstract Several meta-analyses have shown extraversion to be an important predictor of leadership emergence, effectiveness, and behaviour. However, in recent years researchers have shown that in some settings, introverts are equal or even superior leaders. There have also been several calls for researchers to focus on narrower personality traits, as these might be more valid predictors than broader traits. For that reason, the relationship between facets of extraversion and leadership behaviour was investigated. In this study, both leaders and their subordinates (N = 234) participated. Leaders completed the NEO personality inventory and the change, production, employee (CPE) leadership behaviour instrument, while subordinates rated their leader using CPE. Regression analyses showed that the domain extraversion mostly followed the same patterns as in previous studies, being positively related to change and production leadership behaviour. The facets were, however, differently related to leadership behaviours. Assertiveness was positively related to subordinate rated change and production, while excitement seeking was negatively related to self-rated production and subordinate rated employee focused behaviour. The negative relations of excitement seeking illustrates the value of facet-level analysis of personality.

ABOUT THE AUTHOR Håvard Karlsen and Eva Langvik are part of the Occupational, Psychocardiology and Sleep research group (OPS) at the Norwegian University of Science and Technology. They both have expertise in personality psychology, vocational psychology, and psychometrics. OPS are involved in various multi-disciplinary projects, and they use a diverse set of methodologies, analyses and data sources, including large health studies, experimental designs, big data analysis and in-depth interviews. One of their research topics besides personality is the the association between anxiety, depression and risk of cardiovascular disease.

PUBLIC INTEREST STATEMENT
Many think of leaders as typically extraverted people, and that leaders must be extraverted to do a good job. Likewise, several researchers have found links between the personality trait extraversion and good leadership. Extraversion is made up of lower traits, like warmth, excitement seeking, assertiveness, and sociability. In this study, we asked leaders in various fields to take a personality test and evaluate themselves on leader qualities. Additionally, we asked their employees to describe them as leaders. We found that those leaders who were assertive were also considered to be engaged in more positive leader behaviour. However, those leaders who scored high on excitement seeking were less focused on the employees. This means that not all aspects of extraversion are positive in terms of leadership, and that for some aspects lower extraversion scores are better.

Introduction
Leadership concerns the interaction process where subordinates are influenced to change their behaviour to accomplish organisational goals and leadership include both distinct leadership styles and various leadership behaviour (Andersen, 2006;Yukl, 2009). Extraversion has a prominent place in both lay perceptions and academic research concerning personality and leadership performance (Barrick & Mount, 1991;Bono & Judge, 2004;DeRue et al., 2011;Mann, 1959;Watson & Clark, 1997). Sociability is often considered the core tenet of extraversion (McCrae & Costa, 1987;Wilt & Revelle, 2008). In a systematic review, relational leadership style was associated with higher employee job satisfaction (Cummings et al., 2018), and hence, identifying those who have the right dispositions is of great interest for the organisations. People high in sociability, as well as other traits like assertiveness, are often perceived as the stereotypical leader-type, socially fluent and assertive. Indeed, extraversion has often implicitly and explicitly been linked to leadership: Extraverts often express confidence, assertiveness and enthusiasm, and they are attributed high status, especially in initial meetings (Bendersky & Shah, 2013). Consequently, they often emerge as leaders (C. Anderson et al., 2001;C. Anderson & Kilduff, 2009;Barry & Stewart, 1997;Hogan et al., 1994;Ones & Dilchert, 2009;Riggio et al., 2003;Spark & O'Connor, 2020;Zaccaro et al., 2004).
Executives differ from non-executives on the personality traits conscientiousness, emotional stability and Extraversion (Wille et al., 2018). Extraversion has also been linked to leadership effectiveness and performance (Barrick & Mount, 1991;Barrick et al., 2001;DeRue et al., 2011;Do & Minbashian, 2020;Hurtz & Donovan, 2000;Kornør & Nordvik, 2004;Mohammed et al., 2002;Oostrom et al., 2011;Silverthorne, 2001). As with the other traits in the FFM, extraversion has a bright side and a dark side, and the trait is associated with aspects of narcissism (Gruda et al., 2021). Watson et al. (2019) observed that while the social and positive aspect of extraversion was negatively associated with social dysfunction and pathology, the more agentic aspect (e.g like taking charge, excitement seeking) was associated with mania and narcissism, and that aspect-level analyses generated substantial increases in predictive power compared to domain-level use of extraversion.
Most studies investigate the relationship between leadership and personality at the domain level, and some have even argued that leadership performance is best predicted at even higher orderfactor analysis, i.e. as a general factor of personality (Do & Minbashian, 2020). Before the 2000s, few studies included personality facets alongside the domains in their models . The Five Factor Model (FFM) has received criticism concerning its ability to predict leadership performance. More specifically, it is argued that the domains are too broad to be used to predict leadership criteria. Among others, Bono and Judge (2004) advocated the application of narrower personality traits. Specific facets might be more important than others in explaining the relationship between extraversion and leadership performance. Others have found that narrower personality dimensions explained more variance in leadership behaviour than the broad domains of the FFM (Bergman et al., 2014;Bergner et al., 2010). Despite the calls for an increased focus on facets or lower-level analysis for several years, both in health psychology (Watson et al., 2019) and in managerial settings (Chapman, 2007;Do & Minbashian, 2014;Judge, Piccolo, & Kosalka, 2009), few studies have investigated the relationship between extraversion and leadership at the facet level. In this study we therefore examine the effects of the six facets of extraversion on subordinate and self-rated leadership behaviour, in an attempt to forward our understanding of personality and leadership performance. We apply the Change, Production, Employee model (CPE) by Ekvall and Arvonen (1994) in this study, a behaviour-focused approach that makes a clear distinction among "employee-oriented", "production-orientated" and "change-oriented" leadership behaviours.

Measuring leadership behaviour and efficiency
A variety of measures exist when it comes to leadership efficiency (Madanchian et al., 2017). Leadership can be assessed through self-ratings or other-ratings: Self-ratings by leaders themselves are often more affordable and easier to collect, because researchers only need one observation per leader. Other-ratings constitute ratings from superiors, subordinates, or peers of the leader (Vecchio & Anderson, 2009). In the latter two cases, it is often necessary to collect several observations per leader from different subordinates/peers in order to achieve a more complete picture (Hensel et al., 2010). Both forms of ratings are associated with their respective set of biases and errors (e.g., Campbell & Sedikides, 1999;Ross et al., 1977). Kim and Yukl (1995) found that subordinate ratings were more related to actual effectiveness than self-ratings were. They are, however, also subjective and influenced by several factors like the halo effect, selective recall, how well liked the leader is, and the implicit leadership theories inherent/ embedded in those who rate (Lord et al., 1984;Sandal, 2002)-i.e. which traits they implicitly or unconsciously associate with leadership. Another potential bias in asking subordinates to rate their leaders on leadership behaviour as well as effectiveness is common method variance (Avolio et al., 1991;Binning et al., 1986). As the observations stem from the same source, they are not independent and may influence one another (Podsakoff et al., 2003). A subordinate who rates leadership behaviour favourably may therefore also rate the leader as effective regardless of actual effectiveness.

Extraversion and leadership performance
Extraversion is characterised by sociability and positive emotions (Walker, 2020). Among the personality traits, extraversion has most frequently been found to be related to various leadership criteria (C. Anderson et al., 2001;C. Anderson & Kilduff, 2009;Barrick et al., 2001;Barry & Stewart, 1997;Hogan et al., 1994;Nicholson, 1998;Riggio et al., 2003;Silverthorne, 2001;Son Hing et al., 2007;Watson & Clark, 1997). For ease of flow, and in keeping with tradition, we use the description extravert for individuals scoring high on the extraversion scale, and introvert for individuals with a low score. In reality, people are scored along a continuum instead of categorically, and most people will be some degree of ambivert, meaning that they fall somewhere in the middle of the extraversion scale. Similarly, leadership can be thought of in many ways, for instance, as transformational, or as effectiveness or behaviour. Individual level of leadership activities includes behaviour like such as motivating, evaluating and inspiring others. Transformational leadership differ from basic goal-achievement, referred to as transactional leadership, as it refers to transforming the follower's mind-set and motivating others to achieve beyond what they are expected to (Bass, 1985). Bono and Judge (2004) cite extraversion as the strongest and clearest correlate of transformational leadership. This is not unexpected, as several of the defining criteria of the transformational leader matches the behaviours of extraverts: the optimistic and enthusiastic nature of extraverts help them emerge as group leaders Judge, Erez et al., 2002;Kickul & Neuman, 2000;Riggio et al., 2003;Taggar et al., 1999) and be perceived as leaderlike (Hogan et al., 1994). Extraversion has been significantly related to transformational leadership (Bono & Judge, 2004;D'Alessio, 2008;Lim & Ployhart, 2004), at both maximum and typical performance (Ployhart et al., 2001), and to charismatic, ethical and supportive leadership (De Vries, 2012). It has also been related to job performance for managers (Barrick & Mount, 1991;Barrick et al., 2001;Hurtz & Donovan, 2000;. In a cross-cultural study, Silverthorne (2001) found that effective leaders across the U.S., Taiwan and Thailand were more extraverted than ineffective leaders. Do and Minbashian (2014) found through meta-analysis that agentic aspect of extraversion was positively related to leadership, while the affiliative aspect was unrelated to transformational leadership and negatively associated with effectiveness.
Extraversion has been linked to a number of leadership roles (Watson & Clark, 1997), and especially to interpersonal leadership (Oostrom et al., 2011). Studies have found that the ideal leadership profile was the open and relations-oriented leader, characterised by being extraverted, possessing good social skill, being change-oriented and being low in anxiety (Einarsen et al., 2002;Sandal, 2002). Kornør and Nordvik (2004) found that extraversion was significantly associated with self-rated change and employee leadership behaviour, as well as a total score of CPE leadership. However, when controlling for the other four traits, extraversion was only a significant predictor of production and total CPE leadership behaviour. Using factor analysis, they concluded that extraversion, alongside openness and neuroticism, comprised a factor with the change dimension of leadership. A recent study found that meeting interaction mode moderated the effect of extraversion on leadership emergence in team meetings: Extraversion was related to leadership emergence only in the face-to-face meetings and not in virtual meetings (Wilson et al., 2021).
On the other hand, some studies have found that extraversion was unrelated to management performance Rothmann & Coetzer, 2003) or that other personality traits were more helpful than extraversion in predicting the three CPE leadership styles (Bergman et al., 2014). Andersen (2006) concluded after a literature review that the research on leadership and personality was too inconsistent and often showed small effects. Several researchers (e.g., Atamanik, 2013;Judge & Zapata, 2015) have presented conflicting results concerning leader effectiveness for introverts and extraverts in competitive settings. Grant et al. (2011) found that extraversion was related to group effectiveness, but that this relationship was moderated by group members' proactivity. However, several large-scale meta-analyses have concluded that extraversion is linked to leadership (Barrick & Mount, 1991;Barrick et al., 2001;Bono & Judge, 2004;DeRue et al., 2011;Hurtz & Donovan, 2000;, and extraversion continues to be perceived as important in leadership performance both in the research field and lay perceptions (Grant et al., 2011). Personality traits may be divided into subfacets. While facets of a trait are correlated, people may still show substantial divergence among their facet scores. Few studies include facet scores of personality, and it is reasonable to suggest that some of the inconsistences in the research on extraversion and leadership performance are due to failure to incorporate analysis at the facet-level.

Extraversion at the facet level
The bandwidth-fidelity dilemma (Chapman, 2007;Cronbach & Gleser, 1965;Judge et al., 2013) concerns whether a lower order (narrower) or higher order (broader) construct best predicts a criterion. Facet level analysis of extraversion has shown to be superior to dimension level concerning mental health (Watson et al., 2019) and physical functioning (Kekäläinen et al., 2020). Since facet scores on personality are summarised to compromise factor scores, the factor scores may mask differences at the level of individual traits. In spite of increased reliability due to the aggregation of inter-correlated facets, broader traits do not necessarily show better predictive power than narrower traits (Ashton, 1998;Chapman, 2007). Though one facet of the domain is related to a criterion, this may be overshadowed by the other facets that are not related to the criterion but still constitute the domain, causing the domain to show less predictive power than the individual facets (Ashton, 1998;Chapman, 2007;Weiss & Costa, 2005). Some have suggested a bandwidth effect, where the personality traits drive global performance while the facets drive specific performance (Ellershaw et al., 2016). These aspects of the bandwidth-fidelity dilemma illustrate the need to examine whether the facets of personality are related to leadership, in addition to the need to explore the level of the domain.
Research has indicated that narrow traits are equal or even superior to broad traits in predicting job performance and leadership (Do & Minbashian, 2014;Rothstein & Goffin, 2006). There is less agreement on how to divide traits into facets. In the NEO inventories, the extraversion domain in six facets: activity, assertiveness, excitement seeking, gregariousness, positive emotions and warmth (Costa. & McCrae, 1995). While the facetstructure used by various researchers differ, they often contain similarities that allow for comparisons.  found that the facets of sociability and dominance predicted leadership better than the overall measure of extraversion did-though they did not include other extraversion facets in their analysis. Kornør and Nordvik (2004) showed that the facets were significantly correlated with several aspects of self-rated CPE leadership behaviour. Vickers (1995) argued that assertiveness and activity were positively related to leadership and that sociability was negatively related to advancement. He interpreted this alongside previous studies to indicate that the exhibitionistic elements of extraversion, exemplified by being noisy and showing off, were detrimental to leadership. Nicholson (1998) found that leaders were more active than the general population, but that they were not more excitement seeking. The Hogan Development Survey (Hogan & Hogan, 2001) includes excitability, related to excitement seeking, as one of the traits associated with destructive leadership. Gough (1990) found that sociability and dominance were linked to both peer and self-ratings of leadership. There is some evidence that charisma, a part of extraversion and also transformational leadership, is linked to compensation packages (salaries, bonuses, etc.) but not to organisational performance (Agle et al., 2006;Tosi et al., 2004). Rubin et al. (2005) found that positive affectivity was related to transformational leadership. In a study of U.S. presidents, positive emotions and activity were shown to be related to presidential greatness, though assertiveness was the strongest predictor (Rubenzer et al., 2000).

Dominance/assertiveness and sociability/gregariousness
High scores on assertiveness are associated with dominant, forceful and socially ascendant behaviour, and with speaking without reservation (McCrae & Costa, 2010). Extraverts prefer to gain influence through dominance over others rather than being receptive to their ideas (Peterson et al., 2003). Assertiveness/dominance has been linked to leadership Nicholson, 1998;Vickers, 1995) and to leadership emergence (McCrae & Costa, 2010;Son Hing et al., 2007). Nicholson (1998) concluded that assertiveness was one of the strongest requirements for leaders. Dominance has been related to how leaders rate their own behaviour and effectiveness (Brutus et al., 1999). Bendersky and Shah (2013) showed that extraverts were initially attributed high status and expectations as a result of their dominance and assertiveness at the start of a team project, relating it to leadership emergence. As extraverts failed to live up to these expectations, their statuses were eventually reduced. Driskell et al. (2006) suggested that dominance might be related to leadership through the exertion of power and control, though they also noted the need to suppress the tendency for social dominance in order to be a good team player. Insofar as leadership concerns a mutual effort between leaders and subordinates-if one considers the leader as part of the team-leaders should not be overly assertive. This was supported by Ames and Flynn (2007), who found negative outcomes for leadership effectiveness when leaders scored both high and low on assertiveness, and that for ideal effectiveness, leaders should have an average score on assertiveness. Excessive assertiveness had adverse social outcomes, while insufficient assertiveness had adverse instrumental outcomes (Ames, 2008;Ames & Flynn, 2007). Hu et al. (2019) found that warmth and assertiveness had a curvilinear relationship to advice-seeking by peers and peer liking, and that this again was related to leadership emergence in self-managed teams. This implies that the ideal degree to which these traits are expressed is somewhere in the middle of the scale.
Sociability concerns the preference for social stimulation: High scorers enjoy and seek out the company of other people, whereas low scorers are less inclined to such behaviour (McCrae & Costa, 2010). Sociability has been offered as the core facet of extraversion (McCrae & Costa, 1987;Wilt & Revelle, 2008), and though this claim has been contested (cf. Ashton et al., 2002;Cunningham, 1988;Lucas et al., 2000;Watson & Clark, 1997), the perception of an extravert as a sociable and outgoing person seems firmly rooted in the minds of laypeople. There also seems to be a general perception of the leader as being sociable and outgoing (Ones & Dilchert, 2009;Zaccaro et al., 2004). Although sociable leaders may be perceived as friendly and caring to subordinates, they may also be disposed to spending time talking rather than working. Vickers (1995) therefore found that sociability was negatively related to leadership. Contrary to this, the results of a meta-analysis by  showed that extraversion was positively related to leadership. Riggio et al. (2003) found that social skills were related to leadership effectiveness perceived by subordinates, but not to other measures of effectiveness.
However, a relational leadership style has been identified as important for outcome patterns of the workforce in other studies (Cunnings et al., 2018). Warmth (interest in and friendliness towards others), and gregariousness (preference for the company of others) can be thought to affect the compassion and consideration a leader shows her subordinates, thus being related to the employee dimension of leadership, which contains similar aspects (Arvonen, 2002). Indeed, friendliness has been found to be related to perceptions of leadership (Malloy & Janowski, 1992), and warmth was the strongest predictor of self-rated employee and total CPE in Kornør and Nordvik (2004) study. In summary, assertiveness and gregariousness are the facets that most often are associated with leadership in the literature. Depending on how sociability is operationalised, warmth and positive emotions may also be included. Activity has occasionally been referenced as an antecedent of leadership, while excitement seeking has been related to destructive leadership.
To sum up, it is evident that extraversion has an important role in terms of leadership. However, it is unclear whether this is due to the broader factor of extraversion or certain of the individual facets. If the facets diverge in effect from the factor, then future research and theory would be recommended to study extraversion facets instead of extraversion as a whole. Knowing that certain facets are more important to extraversion will allow organisations in search of a "perfect leader" to narrow their focus to these facets instead of the broader trait. Identifying aspects of extraversion in leadership that represent the dark side of leadership can facilitate better selection procedures, avoiding unnecessary economic and human costs. An investigation into this topic is therefore of practical and theoretical interest.

Summary and research questions
Extraversion has consistently been related to various leadership criteria. Despite calls for the need to examine the narrower aspects or facets of personality (Do & Minbashian, 2014;Judge et al., 2013), there are to our knowledge no studies linking the facets of extraversion to leadership behaviour dimensions assessed both with self-and other reports. The literature suggests that some facets are more strongly related to various leadership domains than others (cf. Watson et al., 2019). As extraversion in general is usually positively related to leadership (cf. Do & Minbashian, 2020;Wille et al., 2018), it is of interest to see if this applies to all of its facets as well. Some studies have documented negative effects of extraversion, which could potentially be manifested at the facet level (cf. Ames & Flynn, 2007;Vickers, 1995. Specifically, we are interested in these research questions: Is the domain of extraversion positively related to the leadership behaviours? Do the facets of extraversion follow the same pattern across the domain? How is the relationship between extraversion and leadership behaviour influenced by the source (i.e. self or other) of leadership evaluation?

Sample and procedure
The sample consisted of leaders, as well as their subordinates, in various locations and enterprises in Norway. Potential respondents were contacted either through social media or via e-mail with a request to participate. If they agreed, they then received an e-mail explaining that the purpose of the study was to examine the relation between leaders and their subordinates with respect to the former's personality. They also received instructions for how to participate, and a link to the online survey. The e-mail also contained instructions for their subordinates and a link to a special survey designed for them. Leaders who participated were asked to forward the e-mail to all their subordinates, with instructions that at least five had to answer. In return for their participation, the leaders were offered the results of their personality scores along with an explanation of the Five-Factor Model, which 89% accepted. The recruitment phase lasted from October to December 2015. This study was approved by the NSD (Norwegian Center for Research Data).
The businesses the invitees hailed from ranged across various fields like health care, consulting, education, student organisations, and building maintenance and were located all over Norway. As the invitation to participate was sent to several large firms with an undisclosed number of leaders, it is difficult to calculate exactly how many leaders received the invitation and therefore the response rate. Forty-seven leaders responded to the survey, though one was disqualified for not completing the personality inventory. Of those 46 that remained, 37 also had one or more subordinates who completed the subordinate survey. Nineteen (41%) of the 46 leaders were female. The average age of the leaders was 41 (SD = 13), and their average tenure as leader was 10 years (SD = 9). Fifteen percent had seven or fewer subordinates, 61% had 8-20 subordinates, 11% had 21-50 subordinates and 13% had more than 50 subordinates. A total of 188 subordinates participated, 59% were female, and their mean age was 38 (SD = 13). The average amount of years spent working with a leader was 2.7 (SD = 3.2). For the 37 leaders with responding subordinates, the mean number of subordinates was 3.9 (SD = 2.9).

Instruments
The NEO PI-R. The extraversion domain and its facets were measured using the NEO PI-R (McCrae & Costa, 2010). The other four personality domains were also measured to be able to control for their effect on leadership behaviours. In order to make the survey less time-consuming and increase the completion rate, the short form NEO-FFI was used for these domains. For both of these, Norwegian translations were used. The total number of NEO items was 96 (48 from each version of the instrument). Only the leaders were asked to fill out the NEO inventory, assessing their own personality. T-scores for the NEO traits were calculated on the basis of the Norwegian norm scores (Martinsen et al., 2011). Table 1. Alpha values were generally high. Agreeableness had the smallest alpha of the personality domains, at α = .69, while the other domains had alpha values well above .70. Among the extraversion facets, most had α values above .70, with the exception of excitement seeking (α = .60) and warmth (α = .54).

Cronbach's alpha for the scales on NEO domains and extraversion facets is presented in
The CPE Instrument. The Change, Production, Employee Instrument was developed by Arvonen and Ekvall and has been validated in Nordic samples (Ekvall & Arvonen, 1994;Kornør & Nordvik, 2004;Skogstad, 1997). It is used to measure leadership behaviour across three dimensions: change, production and employee. The three domain scores were also combined into a total CPE score, representing the "complete manager" (in accordance with Arvonen, 1995). Leadership behaviour is thought to affect organisational outcomes indirectly, through other organisational and psychological processes (Arvonen & Pettersson, 2002;Yukl, 2009). The 15-item version of the CPE (Arvonen & Pettersson, 2002;Ekvall & Arvonen, 1994;Sverke et al., 1999) was used. The original instrument used other-ratings, which were adapted to self-ratings for the leadership questionnaire. Both leaders and subordinates were asked to rate the leaders on the CPE scales. For leaders whose subordinates rated them on CPE, the subordinate ratings were aggregated, which can attenuate the standard deviations and amplify coefficients calculated from these scores (Scullen, 1997). This is discussed in more detail in the limitations section. Alpha values are shown in Table 1. They were acceptable, above .80 for the subordinate ratings, and above .70 for the self-ratings. Before aggregation of the subordinate ratings, intra-class correlations were calculated to check the inter-rater reliability. According to the classifications of McGraw and Wong (1996), ICC(1,k) were calculated for absolute agreement among the raters. Average measures were used because the CPE dimensions were averaged scores from multiple items. The ICC for both change and production was 0.44, and for employee it was 0.35.
The structure of the CPE Instrument was tested using factor analysis, and it was found to replicate the structure of earlier studies.

Analysis
In the analysis of subordinate rated leadership, all leaders with responding subordinates were included. Correlation analysis of all personality variables as well as subordinate and self-rated leadership variables was performed. Multiple linear regression analysis of domain and facet scores was applied in order to control for the effect of the other personality variables. .52 Note. *p < .05, **p < .01, ***p < .001. N = 37-46. CPE is scored 1-5, personality traits use T-scores

RESULTS
Descriptive statistics and correlations between personality domains, extraversion facets and leadership behaviour are shown in Table 1, alongside Cronbach's alpha for the NEO and CPE instruments. The mean T-scores of the personality traits show how the sample differed from the population. Among the personality domains, only extraversion seemed to match the Martinsen et al. study, with a mean T-score of 50.2. The leaders in the current sample scored higher on openness, agreeableness and conscientiousness and lower on neuroticism. Intercorrelations among the three CPE dimensions were small to moderate in size, and the subordinate and selfratings of respective CPE dimensions were small to moderately correlated with each other.
Regression analyses were performed with the three domains of CPE regressed on the five personality traits. Additionally, a sum score of CPE, indicating total CPE, was calculated and included as a dependent variable. A total of eight regression models were tested, for both subordinate and self-ratings of CPE, and the results are displayed in Table 2. The Durbin-Watson statistic was within acceptable range (Durbin & Watson, 1951), ranging from 1.7-2.3 for the analyses. VIF and tolerance were also within acceptable ranges. None of the models with subordinate ratings as the dependent variables had significant F values, despite some of the predictors having significant and large β coefficients. In contrast, all the models with self-ratings were significant. All the models had moderate to large amounts of explained variance (i.e. R 2 ), ranging from .10 for subordinate rated employee, to .52 for self-rated total CPE. Extraversion predicted subordinate and self-rated change, subordinate rated production and subordinate rated total CPE. Openness was negatively related to production for both ratings of production, and positively to self-rated employee. Conscientiousness was related to self-ratings of change, production and total CPE, but not to any of the subordinate rated CPE. Agreeableness was significant in predicting self-rated employee, while neuroticism had no significant effects.
A series of regression analyses were performed on the effect of the personality domains and extraversion facets on CPE dimensions. Due to the limited statistical power, and to adhere to keeping the predictors in the regression model to a minimum, only facets that were significant in the correlation analysis were included. The personality domains that were significant in previous correlation analyses were controlled for (not listed in the table). These were openness and conscientiousness for change; conscientiousness for production; openness, agreeableness and conscientiousness for employee; and agreeableness and conscientiousness for total CPE. Only self-rated CPE had significant correlations with personality domains other than extraversion. The results are shown in Table 3. The Durbin-Watson statistic ranged from 1.7 to 2.4, which is within the acceptable values. VIF and tolerance were also within acceptable ranges for the predictors in the analyses. Assertiveness was significantly related to subordinate rated change and production. Excitement seeking had a negative effect on subordinate rated employee and self-rated production.

DISCUSSION
Despite the popularity of the trait theory of leadership and the emerging evidence that narrower facets are important in explaining job and leader performance, few studies have investigated the effects of the NEO facets on leadership. In order to examine the effects of the personality trait extraversion and its facets on leadership behaviour, correlation and regression analyses were performed using observations from both the leaders themselves and their subordinates. The results emphasised the benefit of examining the narrower facets of personality domains.

Self-and other ratings of leadership performance
The results differed depending on who did the rating, as has been observed in similar studies using the same measures of leadership (Bergman et al., 2014). At the domain level, we observed a stronger relationship between the leaders score on extraversion and leadership behaviour rated by the subordinate ratings than self-ratings, which was reflected in smaller β values in the models with self-rated CPE as dependent variables. Contrary, conscientiousness was strongly related to several of the self-rated CPE dimensions. An explanation for this may be that extraversion is a more interpersonally focused personality trait, marked by sociability and positive affectivity. Conscientiousness, on the other hand, has a more internal orientation, characterised by orderliness, self-discipline and deliberation (Langvik & Martinsen, 2015;McCrae & Costa, 2010). It could be easier for subordinates to observe leaders' extraversion rather than leaders' conscientiousness. This might explain why conscientiousness did not predict subordinate rated leadership behaviour, while extraversion did.

Extraversion and leadership behaviour
Various studies have related extraversion to transformational leadership (Bono & Judge, 2004;Lanaj et al., 2016), to leadership emergence Kickul & Neuman, 2000;Ng et al., 2008;Taggar et al., 1999;Wille et al., 2018), and to leadership effectiveness (Barrick & Mount, 1991;Barrick et al., 2001;DeRue et al., 2011;Do & Minbashian, 2014;. In this study, comparatively, our focus was on leadership behaviour. The regression analyses of personality domains and CPE showed that self-ratings explained more variance than subordinate ratings, in line with previous studies (Bergman et al., 2014), though this may be partly explained by common method variance. Extraversion predicted change-oriented leadership behaviour for both self-ratings and subordinate ratings, in line with Kornør and Nordvik (2004). However, when looking at the facets of extraversion, the results were ambiguous: Assertiveness was positively related to subordinate rated change and production. Excitement seeking was negatively related to self-rated production, and to subordinate rated employee.
A skewed power balance characterises the relationship between leaders and subordinates, as the former holds formal power over the latter. Popular leadership theories like the CPE model of leadership and transformational leadership emphasise that leaders inspire and empower their subordinates, contrary to dominating and outright controlling them (Arvonen, 2002;Men & Stacks, 2013;Yukl et al., 2002). Despite this, the current results indicate that the leader's assertive personality positively influences the degree to which subordinates see them as engaging in change and production oriented leadership behaviour. As assertiveness/dominance often has been shown in research to be related to leadership, this is not too surprising. More surprising is the fact that sociability did not show any significant relations in the regression analyses, despite also frequently being shown in research to relate to leadership .
Excitement seeking was negatively related to subordinate rated employee and self-rated production in the regression analyses. Interestingly, excitement seeking was the only facet that was negatively related to any of the leadership dimensions. Excitement seeking is related to risk-taking and risky behaviour (Horvath & Zuckerman, 1993) and also mania and narcissism (Gruda et al., 2021;Watson et al., 2019). It might therefore be related to poor employee relations as leaders might engage in risky behaviours that cause them harm in some way. An alternative scale for excitement seeking found that high scores were related to aggressive behaviour (Arnett, 1994). Moreover, excitement seeking might be detrimental to production as it may make leaders less motivated to engage in the normal day-to-day maintenance. In the current study, only self-rated production was related to excitement seeking. This negative relationship might therefore be reflected in a level of detail in production behaviour that goes unnoticed by employees, but not by the leaders themselves. Beauducel et al. (2006) showed that extraverts had poorer performance than introverts during monotonous tasks, and also that they had to invest more effort into it. The excitement seeking extravert might struggle to maintain her enthusiasm for the more mundane tasks and interactions with her subordinates. Extraversion and the other facets had only positive associations with leadership variables, which is to be expected from earlier studies that mainly reported positive relationships. High scores on excitement seeking will contribute to a high score on the extraversion domain, and while the latter is usually considered to benefit employees, effectiveness and the organisation in general, the former may actually be detrimental to employee relations and production leadership. In this case, the positive effect of the domain may mask the negative effect of a facet. This demonstrates the benefits of studying personality at the facet level in organisations.

Implications and future research
This study builds upon previous results (Kornør & Nordvik, 2004) by showing that analysing personality at the facet level yields different relationships to leadership compared to analyses at the domain level. In relation to the bandwidth-fidelity dilemma, this study shows that by focusing on the broad-band traits (domain), effects of the narrow-band traits (facets) may be masked.

Theoretical implications
A recurring topic in personality trait theories is the discussion of the number of traits a model, and the search for broader dimensions like the general factor of personality (Do & Minbashian, 2020). In terms of extraversion, taking the results of this study alongside the results from earlier studies (Bergner et al., 2010;, there is evidence that the facets explain unique variance in leadership criteria. Hence, people investigating leadership and extraversion should try to measure facets if possible. Further studies might show that only a few of the facets are strong predictors of leadership, and that the others are unrelated. In that case, only the strong predictors need to be assessed, which removes unnecessary items and makes for a shorter questionnaire. This study further demonstrates the need to focus on both self-and other rating when it comes to personality and leadership behaviour. The results from Wilson et al. (2021) findings that meeting interaction mode affects the relationship between extraversion and leadership emergence indicate that future studies should also examine possible moderating or mediating effects of personality on leadership behaviour. Similarly, Hu et al. (2019) findings of the curvilinear and moderated effects of warmth and assertiveness on leadership emergence also support this.

Managerial implications
Extraverted leaders are often selected with the assumption that they are better at people management. However, in this study extraversion was unrelated to subordinate rated employeeorientated behaviour, and the facet excitement seeking was negatively related to this dimension of behaviour when rated by subordinates. One area that will benefit from this knowledge is personnel selection. A candidate for a managerial position might have a very high score on excitement seeking, positive emotions and warmth, and thereby have an overall high score on extraversion. Despite not having high scores on the facets that were shown to be relevant for change leadership (assertiveness, activity and gregariousness), employers might get the impression that the candidate is a good fit based solely on the domain score.
The extent to which extraversion is valued as a dispositional feature varies among cultures (cf. Kim et al., 2018). Especially for cultures that value extraversion more highly, the results of the current study show that specific aspects of extraversion seem more important for good leadership than others. Thus, it could help leaders and organisations realise that other traits and qualities are equally, or more, important in determining great leadership. Further, this study draws attention to possible dark sides of commonly portrayed bright sides of personality when it comes to leadership behaviour.

Limitations
There are some limitations associated with this study: First, though a truly random sample is difficult to achieve in studies of specific groups such as this one, there are some issues related to self-selection. Nevertheless, the design is suitable for a preliminary study like this one. Secondly, the low number of leaders participating limits the statistical power of the analyses (Aiken & West, 1991;Cohen, 1992). Thirdly, individual subordinate scores were aggregated to form a composite mean score for each leader. There are methodological issues related to this, as described by Scullen (1997), due to attenuation of standard deviations. Consequently, the subordinate ratings have higher reliabilities and stronger relationships to outcome variables. To examine the effect of the single-aggregate approach, separate analyses were performed on a dataset in which individual scores of the subordinates were used, with each leader's individual scores appearing once for each subordinate. These analyses showed roughly the same pattern of relationships, though the coefficients were weaker. The standard deviations of the single-aggregate approach were only slightly smaller than for the individual subordinate scores. For these reasons, the original analyses based on the initial single-aggregate approach were used. The ICCs showed low to moderate agreement between the subordinates in their ratings of the leaders' behaviours. This could mean that the CPE instrument is not a reliable instrument to measure leadership behaviour, though it could also be an indication of how challenging it is to determine whether a leader is engaged in good or bad leadership behaviour, and the importance of not relying on self-report only.
Two of the extraversion facets, excitement seeking and warmth, had low reliability coefficients, so care should be taken when interpreting the results. Despite this, the scales have shown good cross-cultural reliability and validity (McCrae & Costa, 2010).

Conclusion
In closing, the results demonstrate the value of analysing personality traits in relation to leadership at the facet level, as this may reveal patterns invisible at the domain level. The extraversion domain was positively related to change behaviour, and unrelated to employee and production orientation. Although most facets were positively related to leadership behaviours in the correlation and regression analyses, excitement seeking showed a pattern of negative relations to production-and employee-oriented behaviour. This has important implications for personality research, as it has usually been shown that extraversion is positively related to leadership variables. Due to the limitations of the study, the results must be considered as preliminary. Nevertheless, the findings support the importance of narrower facets in understanding the relationship between extraversion and leadership behaviour.