Dark Triad dirty dozen: psychometric properties and measurement invariance in Peruvian adolescents

ABSTRACT Dark Triad is a term used to describe a group of three aversive personality traits – Machiavellianism, psychopathy, and narcissism. This study evaluates the utility of the Dark Triad Dirty Dozen for Peruvian adolescents through the evaluation of its psychometric properties; specifically, its factorial structure, measurement invariance according to gender and age group, and reliability. A total of 440 adolescents participated in the study (female: 48.2%; male: 51.8%); their ages ranged from 12 to 17 (Mage = 14; SDage = 1.38). The results showed a three-factor structure invariant by gender and age group and adequate internal consistency, although it was necessary to eliminate item 8. The findings suggest that the 11-item version of the Dark Triad Dirty Dozen is a measure with adequate psychometric properties, reliable and useful for the study of Peruvian adolescents. The theoretical and practical implications of the study are then discussed.


Introduction
Personality is one of the most studied areas of psychology.It is particularly relevant due to its influence on people's decision making and behaviour; specifically, the study of dysfunctional personality tendencies has attracted the attention of researchers in recent years (Jonason et al., 2012).Paulhus and Williams (2002) coined the term Dark Triad to refer to the constellation of three negative personality traits and study their similarities and differences -Machiavellianism, subclinical psychopathy, and subclinical narcissism.Machiavellian traits are characterized by a tendency to use strategies to deceive and manipulate others for personal gain.Meanwhile, psychopathic traits are linked to emotional insensitivity, impulsiveness, and lack of remorse, which can be reflected in aggressive behaviour or behaviours that diverge from the interests of others.Finally, narcissistic traits are characterized by a propensity towards self-centeredness, selfishness, high ambition, and a grandiose view of the self (Jones & Paulhus, 2010;Paulhus & Williams, 2002).
Since the introduction of the Dark Triad in the field of psychology, scholars have discussed whether it is a unitary construction or three independent dimensions of personality (Furnham et al., 2013).Those who defend the conception of a composite construct argue that there is evidence of Dark Triad unification because the three traits are associated with adaptive mating strategies (Jonason et al., 2010(Jonason et al., , 2012)); Furthermore, Jones and Figueredo (2013), through structural equation modelling, found that manipulation and insensitivity thoroughly explained the associations between Machiavellianism, psychopathy, and narcissism.However, from a critical stance of the Dark Triad, it is argued that there is evidence that other personality constructs that are not included in this theoretical model also correlate with short-term mating strategies, such as sensation seeking, risk taking, and impulsivity (Glenn & Sellbom, 2015).Furthermore, questions have also been raised about the differences between Machiavellianism, narcissism and psychopathy (Furnham et al., 2013).In this regard, although some research findings support their individuality, for example, by finding differences in the use of aggression in response to environmental threats (Jones & Paulhus, 2010) or differences in the use of tactics -'hard' (e.g.threats) or 'soft' (e.g.compliments) -of manipulation (Jonason et al., 2012), there are authors who raise theoretical concerns regarding the Dark Triad approach and argue that the concepts of Machiavellianism and grandiose narcissism are included as characteristics or traits of psychopathy (Glenn & Sellbom, 2015).Furthermore, it is argued that measures of Machiavellianism are indistinguishable from measures of psychopathy (Miller et al., 2019).Therefore, research on Dark Triad and its measurement instruments is still needed in different populations and cross-cultural contexts to provide further empirical evidence to aid in its understanding.
Although the Dark Triad traits are considered socially aversive, they are present in the general population and are not restricted to clinical samples (Paulhus & Williams, 2002).In addition, there is evidence that these traits apply to adolescents and correlate with maladaptive behaviours in this population (Klimstra et al., 2014).For example, it has been found that subclinical psychopathy is an essential predictor of cybernetic aggression (Pabian et al., 2015) and that adolescents scoring higher in Machiavellianism are more likely to be aggressors and subdue victims through bullying (Berger & Caravita, 2016).A study in a nonclinical sample of adolescents found that Dark Triad traits are associated with aggressive and delinquent behaviour (Muris et al., 2013).These findings highlight the importance of studying the pathogenesis of disruptive and antisocial behaviour.
Despite the relevance of studying the Dark Triad to understand maladaptive behaviour in adolescents, few studies have evaluated the usefulness and relevance of the measurement instruments for this construct among this population.Further, in the Peruvian context, the discussion about the complexity and multidimensionality of the Dark Triad in adolescent population is still in its infancy.
The measurement of the Dark Triad in the general population began with considering instruments that measure the traits of Machiavellianism, subclinical psychopathy, and subclinical narcissism independently, such as the Machiavellian IV Scale (MACH-IV), the Narcissistic Personality Inventory (NPI), and the Self-Reported Psychopathy (SRP) scale.However, joint administration of these instruments can generate response biases associated with the use of extensive measures, in addition to a significant amount of time required.Given these difficulties, some instruments have been proposed that measure the components of the Dark Triad together, such as the Dark Triad Dirty Dozen (DTDD; Jonason & Webster, 2010), a brief measure comprising 12 items (four items measuring each factor).
Studies on the psychometric properties of the DTDD has revealed the robustness of its threedimensional structure and supported its use in different contexts and languages, such as English (Maples et al., 2014;Webster & Jonason, 2013), Japanese (Tamura et al., 2015), Polish (Czarna et al., 2016), Turkish (Özsoy et al., 2017), French-Canadian (Savard et al., 2017), Portuguese (De Medeiros et al., 2017), Serbian (Dinić et al., 2018), Italian (Chiorri et al., 2019), Bengali (Ahmed et al., 2020), and Spanish (Pineda et al., 2020); as well as in clinical and nonclinical samples from Canada (Faucher et al., 2023).In Peru, Copez-Lonzoy et al. (2019) found evidence supporting its validity and reliability in a sample of adults.However, a few psychometric studies conducted on samples of adolescents such as the study by Klimstra et al. (2014) showed that the DTDD three-factor model fitted satisfactorily and obtained adequate reliability indices for each factor in a sample of Dutch-speaking adolescents and also reported factorial invariance by gender.Similar results were obtained by Pechorro et al. (2021), who found that the psychometric properties of the DTDD were adequate in terms of internal consistency, validity based on internal structure and relationships with other variables, and factorial invariance according to gender in a sample of adolescents and young people at-risk in Portugal.In the Peruvian context, no instrumental studies of DTDD in adolescents have been reported.
Research that corroborates the usefulness and relevance of personality measurement instruments in adolescents is relevant, given the evidence that responses to self-reported personality factors become more differentiated the older adolescents get, perhaps as a reflection of a more differentiated view of their own personality traits (Soto et al., 2008).In this regard, Klimstra et al. (2014) found that for older adolescents, the characteristics of the Dark Triad are better distinguished from each other, that is, lower interfactorial correlations are present.Therefore, in addition to studies of the factorial structure of the DTDD, evaluating factorial invariance according to age range is relevant to make comparisons by age and obtain results highlighting the real differences that show changes in the Dark Triad during adolescence.
In addition, the previous study has reported significant differences in the scores of the DTDD factors according to gender, with males presenting higher scores in the three traits of the Dark Triad compared to females in adult (Czarna et al., 2016;Furnham et al., 2013;Webster & Jonason, 2013) and adolescent samples (Klimstra et al., 2014;Pechorro et al., 2021).However, few studies have verified the measurement invariance of the DTDD to corroborate that the differences are indeed explained by gender and are not product of measurement bias.Therefore, to better understand the effect of gender in the Dark Triad, studying the equivalence of the factorial structure for males and females is relevant.
Therefore, considering that the study of the Dark Triad in Peruvian adolescents is still in its infancy, this study aims to evaluate the psychometric properties of the DTDD in a sample of Peruvian adolescents through the analysis of its content, dimensionality, measurement invariance according to gender and age group, and the analysis of its reliability, taking into account that emphasis is placed on the inspection of the basic aspects for the evaluation of its internal structure.This study has theoretical and methodological relevance as it is the first step to contribute to studies of the Dark Triad in adolescents in Peru, verifying the usefulness and significance of one of the most used instruments internationally in order to provide psychometric evidence for rigorous measurement in future studies.

Participants
Through convenience sampling, 450 adolescents from Metropolitan Lima participated although 10 cases were excluded in the data cleaning process.Two of them were excluded because they were over 18 years old and eight of them because they were foreign adolescents.Finally, for data analysis, 440 adolescents from Metropolitan Lima participated in the study, 228 males (48.2%) and 212 females (51.8%), aged 12-17 years (M age = 14; SD age = 1.38).The adolescents were studying in the 1st to 5th year of secondary school in private educational institutions.In addition, 70.9% lived with both their parents, 23.1% lived with their mother, 3% with their father, and 3% lived with other relatives.

Measurement instrument
The DTDD (Jonason & Webster, 2010) is an instrument of North American origin.The version translated by Copez-Lonzoy et al. (2019) into the Spanish spoken by the general population of Lima was considered.The measure comprises 12 items assessing the traits of subclinical psychopathy, Machiavellianism, and subclinical narcissism.It has a Likert-type response format, with five multiple options, ranging from never to almost always.Copez-Lonzoy et al. (2019) found evidence in favour of a structure of three oblique factors, invariant according to gender, and adequate reliability indices for the three factors.

Procedures
To evaluate the relevance and clarity of the contents of the DTDD for its application to adolescents in Lima, five expert judges were consulted; all of them had experience in research in the field of personality.Their review consisted of analysing the content of the DTDD in the criteria of relevance (the degree to which the item is essential or important and should therefore be included in assessing the construct) and clarity of items (the degree to which the item is clear and understandable considering the target population), through the completion of a form that presented the conceptual description of the three traits measured by the DTDD and the description of the evaluation criteria.The experts had to evaluate the content of each item by answering the questions, How relevant is item 'x' to the measurement of dimension 'y'? and How clear or understandable is item 'x' for the measurement of dimension 'y' in adolescents?considering a rating scale, whose values were in the range of 1 to 5, being 1 Not at all relevant or Not at all clear and 5 Completely relevant or Completely clear, Aiken's V was calculated for each item based on the judges 'responses.
After obtaining the expert judges' responses, adolescents with characteristics similar to those of the study sample were called to conduct a focus group.The objective of the focus group was to evaluate only the clarity and comprehension of the content of the items by the adolescents.In addition, 10 adolescents participated in the focus group and completed a form which presented 12 items of the DTDD, together with the instructions for their evaluation: You should mark on a range from 1 (not at all) to 5 (completely), how clearly do you think the item is written.The responses to the form allowed the calculation of Aiken's V for each item.According to the information collected, modifying the content of the items was unnecessary because the adolescents found them understandable and clear.
Subsequently, the authorities of educational institutions of Lima were contacted to access the study sample.Authorization was received from the parents or guardians of the adolescents through the signing of informed consent; in addition, the adolescents signed their informed assent.These documents disclosed the research's objective, the participants' role, and the anonymous and voluntary nature of participation.Data collection was performed in person, using coded protocols, and was conducted in the classrooms of the adolescents who agreed to participate in the research.The study was approved by the Teaching Review Board corresponding to the Psychology Program Department of the Universidad San Ignacio de Loyola based on ethical guidelines within the institutional regulations, the Helsinki Convention, and the Colegio de Psicólogos del Perú (2017).

Data analysis
The relevance and clarity of the content of the items were analysed through Aiken's V coefficient, considering values of V > .70asadequate (Ventura-León, 2019).For confirmatory factor analysis, the ordinal nature of the items was assessed by calculating the polychoric correlation matrix.The estimator used was weighted least squares with mean and variance adjusted (WLSMV), the recommended procedure for ordinal variables (Beauducel & Herzberg, 2006;Gana & Broc, 2019).The global evaluation of the fit of the model was obtained with the comparative fit index (CFI), root mean square error of approximation (RMSEA), and standardized root mean square residual (SRMR).CFI values > .90 are interpreted as favourable evidence of fit to the model (Bentler, 1990), as well as RMSEA < .080(MacCallum et al., 1996) and SRMR < .080(Browne & Cudeck, 1992).
For the mediation invariance analysis and the ordinal nature of the items, the recommendations of Wu and Estabrook (2016) and Svetina et al. (2020) were followed for the analysis of invariance for ordinal variables.Thus, three restrictive models were evaluated hierarchically between the groups according to gender and age group, these being configural, threshold, and threshold and loading invariance, all of them tested using WLSMV estimator for ordinal data.In addition, for measurement invariance testing, a set of criteria, consisting of change in CFI < .010,RMSEA < .015or SRMR < .005(Chen, 2007), were evaluated.
Finally, for reliability analysis, the internal consistency method with the omega coefficient (ω) was used, considering values greater than .70.Statistical analysis was conducted using 'R' program, version 4.2.2, specifically the 'lavaan' library in version 0.6-13 (Rosseel, 2012).

Results
The results of evaluating the relevance and clarity of the content of the DTDD are shown in Table 1, which shows that all the scores given to the items are adequate, obtaining Aiken's V values between .80 and .95for all the items, taking into account the rating of the expert judges and of the group of adolescents.Therefore, the content of the DTDD items is relevant, understandable, and can be applied to adolescents in Metropolitan Lima.
Prior to the structural analysis, the descriptive results and the polychoric correlation matrix of the items were obtained as shown in Table 2. Initially, the values of skewness (g1) and kurtosis (g2) were observed.They were within the values suggested, i.e. less than 3 and 10 in absolute value, respectively (Kline, 2016).The intercorrelations were between .01 and .72 in absolute value.
Measurement invariance analysis was performed for two groups determined by gender, they were then pooled to estimate and evaluate the first level of invariance.The configurational invariance resulted in an acceptable fit, (χ 2 (82) = 144.2,p < .001,CFI = .969,RMSEA = .059,SRMR = .064),continuing with the invariance levels proposed for equal threshold, and equal loading and threshold, and it was noted that the criteria for changes in CFI, Note: V = Aiken's V; Ll = Lower limit; Ul = Upper limit.
RMSEA, and SRMR were met (Chen, 2007).Similarly, the measurement invariance analyses were performed according to age group, initially obtaining a good fit in the configurational invariance (χ 2 (82) = 159.6,p < .001,CFI = .959,RMSEA = .066,SRMR = .067),resulting in adequate values in the differences of the fit indices that confirmed the equivalence up to the suggested levels of equal loading and thresholds for ordinal variables.These results can be seen in Table 4.

Discussion
The proliferation of studies addressing the Dark Triad in recent years highlights its relevance in understanding socially aversive personality patterns in the clinical and nonclinical population.Despite growing interest in research, research on the Dark Triad in Peruvian adolescents is still in its infancy.Therefore, valid and reliable measurement instruments that can be used in research and professional fields are required.Hence, the objective of this study was to evaluate the psychometric properties of the DTDD in a sample of Peruvian adolescents through the analysis of its content, internal structure, measurement invariance according to gender and age group, and reliability analysis.
Regarding content-based validity, through the experts' judgement and the information collected from a focus group, the Aiken's V coefficients were calculated and appropriate values for all the DTDD items (V > .70)were obtained.Therefore, its items have relevance to evaluate the traits of the Dark Triad in Peruvian adolescents, from the perspective of expert judges; in addition, they are understandable, from the opinion of the adolescents themselves.
Regarding internal structure, the three-factor model had a good fit, although in the study sample, it was necessary to eliminate item 8 (Ser cínico [Being cynical]), which corresponds to the psychopathy factor, since it was observed that it had a negative factor loading and the magnitudes of the correlations with the other items of the same factor were below what is expected, and when incorporated into the factorial structure, a reasonable fit was not obtained.These findings can be compared with previous studies (Ahmed et al., 2020;Chiorri et al., 2019;Savard et al., 2017), where low to moderate correlations were reported between item 8 and the other items of the psychopathy factor, and Jonason and Luévano study (Jonason & Luévano, 2013), where item 8 had the lowest factor loading.In these studies, the ambiguous meaning of the word 'cynical' and the social desirability associated with said term are suggested as potential explanations for these results, difficulties that we believe could have increased in a sample of adolescents.In fact, in the study conducted by Muris et al. (2013) with a sample of adolescents, item 8 was modified by the statement 'I am cynical and mocking towards others'.However, the existence of two statements in the same item can also be problematic.Therefore, its psychometric properties and ability to represent the construct need further exploration.
Another relevant aspect to discuss is that, the intercorrelations found between the DTDD factors are different from those expected, since, according to the review by Furnham et al. (2013), although the correlations between the factors may vary in samples, most studies found the highest correlations are between the factors of psychopathy and Machiavellianism and the lowest correlations are between the factors of narcissism and Machiavellianism.In this study sample, not only were no significant relationships found between psychopathy and Machiavellianism but also the highest correlation was found between narcissism and Machiavellianism.Other studies in adolescents have also found unexpected correlations between the DTDD factors, such as the study conducted by Pechorro et al. (2021) in Portuguese adolescents, in which the lowest correlation was found between Machiavellianism and psychopathy and the highest correlation was found between Machiavellianism and narcissism, or the study conducted by Muris et al. (2013) for Dutch-speaking adolescents, in which negative correlations were reported between narcissism and the factors of Machiavellianism and psychopathy.In general, the findings indicate that the response pattern of adolescents is not the same as that of adults.In particular, in the study sample, the data collected suggest that Peruvian adolescents report higher scores on psychopathy items, with the exception of item 8, compared to Machiavellianism items, that is, they report having committed more frequent actions related to psychopathy.Although these results may question the validity of the DTDD for the adolescent population, this finding may also reflect a generational and cultural difference indicating that adolescents adopt more egocentric and insensitive standards that can be perceived as more attractive characteristics to establish romantic relationships, as previous studies have shown that narcissism and psychopathy, but not Machiavellianism, are positively correlated with the number of romantic partners.In addition, narcissism is associated with self-perceived attractiveness in young men and women (Borráz-León & Rantala, 2021).Along the same lines, it has been reported that narcissism and psychopathy are positively linked to greater sexual motivation, self-esteem, and assertiveness in young people (Steininger & Pietschnig, 2022).With all the above and having eliminated item 8, the structure of the three factors received empirical support through the confirmatory factor analysis (CFA); that is, the Dark Triad traits measured with the DTDD should be considered as three unique traits.These findings support those of previous studies (Ahmed et al., 2020;Chiorri et al., 2019;Copez-Lonzoy et al., 2019;De Medeiros et al., 2017;Dinić et al., 2018;Klimstra et al., 2014;Pechorro et al., 2021, Pineda et al., 2020;Tamura et al., 2015).However, it is necessary to replicate psychometric studies of the DTDD in Peruvian adolescents in order to evaluate the consistency of the findings in relation to unexpected interfactor correlations and to provide more evidence to contribute to the understanding of these results.
The factorial invariance of the DTDD was evaluated through multigroup factorial analysis.With regard to gender, the three-factor structure is equivalent for males and females in terms of factor loadings and the pattern of means between items.These results are consistent with those of previous research (Ahmed et al., 2020;Chiorri et al., 2019;Copez-Lonzoy et al., 2019;Faucher et al., 2023;Klimstra et al., 2014;Pechorro et al., 2021); therefore, it is possible to make comparisons of the DTDD measurement according to gender.
Regarding factorial invariance according to age group, equivalence of the factorial structure of the DTDD was found for the two groups considered (12-14 and 15-17 years old), complying with the assumptions of configural, metric and strict invariance.Therefore, the construct and its indicators measured through the DTDD do not present significant differences in meaning for adolescents of different ages.This finding is relevant as it allows us to affirm that it is possible to draw valid conclusions from the comparisons of the DTDD according to age group, an aspect addressed in a few previous studies (Faucher et al., 2023).
Conversely, regarding the reliability analysis from the perspective of internal consistency, adequate reliability coefficients were found for the three factors, although, as in previous studies, the psychopathy factor had the lowest reliability values (Copez-Lonzoy et al., 2019, Özsoy et al., 2017;Tamura et al., 2015).In this regard, although a value below .70 can be considered low, the coefficient of .65 obtained is relevant for a scale composed of only three items.In spite of this, it should be questioned that one of the reasons for low internal consistency in the psychopathy dimension in various studies may be that this trait is more complex (Lilienfeld & Andrews, 1996), so that its measurement with a brief scale may be underrepresented, since the multifaceted nature of psychopathy (Miller et al., 2019), which is a broad construct that includes interpersonal, affective, and behavioural traits, is not recognized (Glenn & Sellbom, 2015).
The practical implications of this study are related to the fact that it has provided psychometric evidence regarding the internal structure, reliability and measurement invariance according to gender and age groups of a tool for the measurement of Dark Triad traits in Peruvian adolescents, considering its relevance and usefulness for cross-cultural research.
Despite the mentioned strengths, some limitations should be reported.First, the nonprobabilistic nature of the sampling method prevents the generalization of the results.In future studies, representative samples of Peruvian adolescents are recommended, including students from public educational institutions, as different response patterns can be observed in more heterogeneous samples.Second, the cross-sectional design of the study does not allow evaluation of the temporal stability of the DTDD scores or changes in their factorial structure over time.Therefore, developing studies with longitudinal designs to estimate test -retest reliability and analyse developmental changes in adolescents with low and high scores in the Dark Triad traits is essential.Third, only evidence of validity based on the content and internal structure of the DTDD was explored and the evaluation of validity based on relationships with other variables, considering external criteria, is still pending.Therefore, future research should explore concurrent validity considering different measures of Dark Triad traits and measurement of variables with proven associations with these personality traits, such as aggressive tendencies or disruptive behaviours.Moreover, measures that recognize the multifaceted nature of Dark Triad traits can be used as external criteria.Finally, although measurement invariance according to age ranges has been addressed in this study, this analysis is limited to the adolescent population.Therefore, future research could consider the study of measurement invariance taking into account groups of adolescents and adults.
Despite these limitations, the study's objectives were achieved and the results allow us to conclude that the DTDD, comprising 11 items, has adequate psychometric properties and replicates its three-factor structure in Peruvian adolescents.Therefore, there is preliminary evidence of the usefulness of the DTDD in order to explore the traits of the Dark Triad in Peruvian adolescents, especially in research contexts where brief measures are required, to thus understand the relationship between these traits with variables related to the adjustment and adaptation of the population.

Disclosure statement
No potential conflict of interest was reported by the author(s).

Notes on contributors
Susana K. Lingán-Huamán She holds a Master's degree in Educational Psychology from the Universidad Nacional Mayor de San Marcos, a Bachelor's degree in Psychology and a PhD in Psychology from the same university.She has experience in university management and research related to education and psychology.She has published books and scientific articles in indexed journals and is a reviewer of articles in national and international research journals.Currently, she is a research professor in the Psychology Department at Universidad San Ignacio de Loyola.Ronald Castillo-Blanco He holds a Bachelor's degree in Psychology from the Universidad Nacional Mayor de San Marcos and Master's degree in Organizational Psychology from the same university.Currently, he works as an Educational Information Analyst at the Universidad del Pacífico and at the same time, he is an undergraduate-and graduate-level teacher, and he is a thesis advisor on aspects related to applied statistical analysis.He is also a lecturer on quantitative research methodology, as well as a trainer in workshops and courses on applied statistics, structural equation modelling and psychometric analysis.

Dayana Charún-Puémape
She holds a Bachelor's degree in Psychology from the Universidad San Ignacio de Loyola.Psychologist at the 'Cognitive' Stimulation and Empowerment Centre and works in the area of neurodevelopmental disorders.Milady Pajuelo-Almuerón She holds a Bachelor's degree in Psychology from the Universidad San Ignacio de Loyola.Recruiting intern at NTT Data in the area of recruitment and selection.

Table 2 .
Descriptive and polychoric correlations of the scale items.

Table 3 .
Factor loadings of the standardized solution of the confirmatory factor analysis for the final model.

Table 4 .
Measurement invariance of the final model regarding gender.