Theoretical Background

The internal structure of an assessment tool indicates the level of association between the variables that compose the test (e.g., items), how these variables are grouped, and to what extent a latent construct explains them. The observed associations between items indicate the common variance, i.e., how much they measure similar constructs (AERA et al., 2014; ^{Rios & Wells, 2014}; ^{Thompson, 2007}).

Indicators of the internal structure are commonly investigated in psychological tests to explore or confirm the structure formed by variables composing the scale, and whether this structure is consistent with the expected structure (AERA et al., 2014; ^{Thompson, 2007}). Besides the level of association between the variables, another indicator of the proper functioning of the internal structure is the interpretability of the group of variables observed through data analysis. For instance, the pathological trait narcissism is multidimensional, composed of grandiose tendency (i.e., grandiose narcissism) and vulnerable tendency (i.e., vulnerable narcissism) (^{Stoeber, Sherry, & Nealis, 2015}). From this perspective, it is expected that studies investigating the structure of scales assessing narcissism should find factorial solutions composed of two factors reflecting the two dimensions of the construct.

The analytical strategy typically used to verify the internal structure is the factor analysis. There are two major classes of factor analysis, exploratory (EFA) and confirmatory (CFA; ^{Yong & Pearce, 2013}). In EFA, the items are grouped without restrictions, and cross-loadings are allowed. CFA models are more restrictive, cross-loadings are not allowed, and factors are previously defined based on empirical studies and theory (^{Brown, 2014}; ^{Thompson, 2007}). Both EFA and CFA enable to verify different factor structures (e.g., unidimensional, bifactor; ^{Rios & Wells, 2014}).

In the context of internal structure verification, the bifactor factor structure has been tested as a suitable model for dimensional constructs, as pathological traits composing personality disorders (PD). This structure has also been tested in self-report scales (^{Gouveia et al., 2018}). This structure represents an approach of data modeling that reconciles multidimensionality and the existence of a general factor. In bifactor models, each item is free to simultaneously load on a general (and orthogonal) factor and one or more specific factors (see Figure 1 for a graphical representation). The high comorbidity among PD (e.g., ^{Clark, 2007}; ^{Widiger & Trull, 2007}) can indicate a common latent construct, supporting the use of a bifactor structure to investigate the internal structure of scales to measure pathological traits. The bifactor can also be interpreted as a general factor composed by the social desirability variance of items or a predominant response style present in the sample (^{Reise, 2012}; ^{Reise, Morizot, & Hays, 2007}; ^{Sharp et al., 2015}). Contrasting with a hierarchical factor model, the bifactor provides the direct loading estimates of each item on the general factor. This information is useful because it affords the identification of the most discriminative items, which can guide item selection to compose an abbreviated version of the scale. Furthermore, advantages of the bifactor structure include whether subscales should be maintained or excluded after controlling for a general factor, investigating construct dimensionality (^{Reise et al., 2007}), and assessing the predictability of the overall score and speciic scores according to criterion variables (^{Canivez, 2016}).

Figure 1 Bifactor structure. 

Although the investigation of bifactor structures has grown in the last ten years (e.g., ^{Preti et al., 2015}; ^{Tackett, Daoud, De Bolle, & Burt, 2013}), for most of the assessment tools of pathological traits, this model remains unverified. An example of this is the Dimensional Clinical Personality Inventory, currently in its second version (IDCP-2; ^{Carvalho & Primi, in press; Carvalho, 2019}). It is a self-report scale composed of 206 items to measure pathological traits from a dimensional perspective. Validity based on internal structure and relationship to external criteria has been observed in previous studies (e.g., ^{Carvalho & Costa, 2018}; ^{Carvalho, Sette, & Miguel, 2018}; ^{Carvalho, Zuanazzi, & Miguel, 2019}). Previous literature provides only fragments of the internal structure of IDCP-2 (e.g., ^{Carvalho, 2018}; ^{Carvalho & Arruda, 2016}; ^{Carvalho & Sette, 2017}), indicating a structure of 47 factors grouped in 12 dimensions.

A more recent study (Pianowski, ^{Carvalho, & Miguel, 2019}) has verified the suitableness of IDCP-2 factors according to the Hierarchical Taxonomy of Psychopathology (HITOP; ^{Kotov et al., 2017}), which represents a current dimensional proposal for mental disorder taxonomy, including PD. The HITOP constructs psychopathological disorders and their components based on the observed covariation of symptoms and traits. In this evidence-based model, symptoms are grouped in disorders and co-occurring disorders into spectra. Each spectrum is larger constellations of disorders (e.g., the internalizing spectrum is composed of disorders from fear, distress, eating pathology, and sexual problems subfactors). Almost all spectra are composed of PD, internalizing, thought disorder, disinhibited externalizing, antagonistic externalizing, and detachment, expecting the somatoform spectrum. Although the obsessive-compulsive PD is not present in the HITOP model, the literature supports a sixth spectrum representing this disorder (^{Forbes et al., 2017}), called the compulsivity factor. In this study, we were guided by both previous studies indicating the structure of IDCP-2 and the five HITOP spectra with the addition of the compulsivity factor presenting the obsessive-compulsive PD. We could not find studies investigating the IDCP-2 internal structure using all its factors, as well as studies verifying bifactor structures for this measure.

Our aim in this study was to verify the internal structure of IDCP-2, including its 47 factors. As confirmatory models, we tested the original 12 factors structure (^{Carvalho & Primi, 2015}; Carvalho & Primi, in press), and an alternative structure based on the HITOP five spectra and a compulsivity factor. Besides, we conducted an exploratory investigation also testing the original and HITOP structures, but without restrictions on the item loadings. The veriications included testing for bifactor solutions. We expected that the confirmatory models (original and HITOP structures), should present good fit indices, especially the bifactor models, considering the multifactorial perspective of PD (^{Clark, 2007}; ^{Reise, 2012}; ^{Widiger & Trull, 2007}) and previous evidence of the suitableness of this structure to personality (^{Sharp et al., 2015}; ^{Preti et al., 2015}). Exploratory models were tested for cases where the confirmatory models did not present a good fit.

Methods

Results

We conducted CFA and EFA. Table 1 presents fit indexes of four tested models, exploratory and conirmatory.

Although any of the conirmatory models presented good it indexes, the bifactor model with 12 speciic factors was the one to show the best it. According to that, we tested exploratory models and the best it model was the bifactor with 12 specific factors. The loadings and reliability of this model are presented in Table 2.

Table 2 Factorial Loadings of the Exploratory Bifactor Model With 12 Specific Factors 

Note: Loadings > .30 are in bold and grey; AC = Aggressiveness; ax = Anxiety; DT = Detachment; DP = Depression; AI = Avoidance of Intimacy; EG = Eccentricity; sm = Seduction and Manipulation; IN = Interpersonal Need; GO = Conscientiousness; NA = Need for Attention; ss = Self-sacrifice; AU = Audacity.

Excepting Thoroughness, measures presented loadings in the general factor. We found 12 factors, namely, Aggressiveness, Anxiety, Detachment, Depression, Avoidance of Intimacy, Eccentricity, Seduction and Manipulation, Interpersonal Need, Conscientiousness, Need for Attention, Self-Sacriice, and Audacity. We sought to avoid cross-loading. However, three measures loaded on two factors: Attention Seeking, Insecurity, and Interpersonal Superficiality. The decision was to maintain these measures in two factors due to their interpretability. Internal consistency was assessed by alpha ranging from .40 to .91 for specific factors, and alpha equal to .96 for the general factor. Omega coefficient ranged from .41 to .91 for specific factors and was equal to .94 for the general factor.

Discussion

Our aim in this study was to investigate the internal structure of IDCP-2, using the 47 factors composing the scale. We tested for diferent structures based on the instrument's previous literature (e.g., ^{Carvalho, 2018}; ^{Carvalho & Arruda, 2016}; ^{Carvalho & Primi, 2015}; Carvalho & Primi, in press; ^{Carvalho & Sette, 2017}), as well as the HITOP model (^{Kotov et al., 2017}). Therefore, we used CFA and EFA models. Among the tested models, the one presenting the best it to data and the best interpretability of the factors was the bifactor exploratory model with 12 specific factors.

CFA models composed by 12 factors (IDCP-2 original structure; ^{Carvalho & Primi, 2015}; Carvalho & Primi, in press) and by six factors (HITOP model with an extra compulsivity factor; ^{Kotov et al., 2017}; ^{Forbes et al., 2017}), did not present satisfactory it indices, indicating that the predeined factor structures were not adjusting to the data. These results can be explained by the features of CFA restricting cross-loadings and requiring prior setting of all parameters, making this kind of analysis less flexible (^{Thompson, 2007}; ^{Brown, 2014}) in comparison to exploratory models. We could observe the existence of cross-loadings in some factors (e.g., Self-Devaluation and Depressivity) that may have occurred due to the similarity of the composing pathological traits. Previous ind-ings using IDCP-2 factors under the perspective of the HITOP observed cross-loadings (^{Pianowski, Carvalho, & Miguel, 2019}).

The EFA models were tested with the same number of factors of the CFA models (i.e., ix factors and 12 factors solutions). However, the parameters were not fixed for EFA, and the items were freed to grouping based on their correlations (^{Ferguson & Cox, 1993}; ^{Yong & Pearce, 2013}). The bifactor with 12 speciic factors model was the best regarding it indices and theoretical interpretability of factors (^{Carvalho, 2019}). The literature demonstrates that the bifactor model is indicated for constructs that are admittedly multidimensional (^{Clark, 2007}; ^{Reise, 2012}; ^{Widiger & Trull, 2007}). Furthermore, studies corroborate that the bifactor model is suitable for scales that measure pathological traits (^{Sharp et al., 2015}; ^{Preti et al., 2015}), and the high comorbidity rate among PD indicates to a general factor (^{Sharp et al., 2015}). The results found in our study corroborate the use of bifactor models for self-report tests that assess pathological traits, specifically the IDCP-2. Expressly, our findings indicated that (a) factors that compose IDCP-2 show a common ground, probably respecting a broad pathological functioning of personality; (b) the specific 12 factors of IDCP-2 remain significant even after controlling for this general factors. This last inding is clinically relevant, as indicates the usability of IDCP-2 scores for measuring pathological traits.

The 12 observed factors (i.e., Aggressiveness, Anxiety, Detachment, Depressivity, Avoidance of intimacy, Eccentricity, Seduction and manipulation, Interpersonal need, Conscientiousness, Need for attention, Self-sacrifice, and Audacity), agree with the core domains that characterize PD (e.g., APA, 2013; ^{Kotov et al, 2017}). Besides, these factors approximate the original dimensions of IDCP and IDCP-2 (^{Carvalho & Primi, 2015}; in press; ^{Carvalho, 2019}). Although some factors do not precisely reflect IDCP-2'S original dimensions, as Anxiety and Audacity, they do identify coherent and consistent groups of variables, and are similar to some IDCP-2 dimensions (e.g., Criticism avoidance and Inconsequence). For instance, Anxiety is composed of Avoidance of Abandonment, Anxious Concern, and Anxiety. These factors share a common trait, the anxiety related to concerns about the future. The correspondence between the observed actors and IDCP-2 original 12 factors are presented in Table 3.

The reliability estimates were generally high, indicating homogeneity among items composing the same factor (^{Tavakol & Dennick, 2011}). An exception to it was the Need for attention factor, presenting low internal consistency, probably related to the restricted number of variables composing this factor. This issue should be investigated in future studies.

Our results indicated the bifactor with 12 speciic factors as the best model. Although the original structure of IDCP-2 is not based on a bifactor model, the specific factors reflect, in general, the original factors of the scale, as observed in Table 3. Future studies should investigate the meaning of the general factor. Moreover, future studies should investigate the clinical use of the new factors presently observed, especially those showing compositions dissimilar to the original dimensions (e.g., Anxiety).

The main limitations of this study should be highlighted. The sample of this study did not have people with PD diagnoses, this may have restricted the variability of the items. Furthermore, we observed the presence of a general factor, corroborating the literature. However, we could not establish the meaning of this factor. For instance, it could represent a pathological common ground between specific factors, social desirability, or response style bias. Future studies should be conducted to investigate this issue further.