The investigation sample consisted of 255 male adolescents in conflict with the law, evaluated while complying with socio-educational measure of deprivation of liberty or provisional detention. Data were collected during the period from 2008 to 2010.

The inclusion criteria used were: age between 12 and 19 years old; being in socio-educational condition of deprivation of liberty or in provisional detention at Fundação de Atendimento Socioeducativo (FASE, Socio-Educational Care Foundation); voluntarily agreeing to participate in the investigation. On the other hand, exclusion criteria were: active psychotic signs or symptoms, intellectual disability or hearing impairment clinically detected or described in the medical records; refusal to complete the application of the instruments at any stage of the process.

Hare's Psychopathy Inventory: Youth Version (Gauer, Vasconcellos, & Werlang, 2006) includes an interview guide, plus the technical manual and a response form to be completed by the evaluator, consisting of 20 items that investigate affection, interpersonal aspects and lifestyle. Brazilian studies, although incipient, indicate adequate inter-rater reliability for PCL: YV (Ronchetti, Davoglio, Salvador-Silva, Vasconcellos, & Gauer, 2010). The instrument is scored considering the adolescent's usual functioning since late childhood/early adolescence except for one item that also considers the functioning prior to the first decade of life. Each item is scored on a three-point grading: zero (0) characteristics are not present, or oppose, or are inconsistent with the intent of the item; one (1) when the item partially applies but not to the degree required for a higher score; or when there is uncertainty about the application of the item, or there are conflicts between sources of information that cannot be resolved in favor of 0 or 2; two (2) when the item applies perfectly in its most fundamental aspects. Exceptionally, when there is not enough information to score an item, the item's score may be omitted, but omissions may never exceed five out of twenty.

The objectives of the analyses performed are: to obtain the PCL: YV item parameters in a generalized partial credit model, and to build a scale using anchor levels established from the selected items.

Item Response Theory

Although it includes behavioral aspects, the construct called psychopathy cannot, of course, be directly observed. In this connection, statistical models of latent traits (variables that cannot be directly observed but inferred from observable variables) are one of the main objects of investigation for quantitative methods in social sciences. In particular, the Item Response Theory (IRT) proposes to connect a person's probability of correctly answering an item with a combination of that person's ability and the attributes of that item (Andrade, Tavares, & Valle, 2000). For Pasquali (2003), IRT adopts two fundamental axioms: 1) Performance on a test item is the effect and latent traits are the cause; 2) The performance-latent trait relationship can be described by an increasing monotonic equation called the Item Characteristic Curve (ICC).

Interpretation

The interpretation of the parameters is made as follows: for Ayala (2009), a “reasonably good” discrimination parameter (α) varies approximately between 0.8 and 2.5. Baker and Kim (2017) claim as moderate α between 0.65 and 1.34. The α discrimination of each item reaches its maximum value in the difficulty level of this item's ability. The difficulty parameter β corresponds to the point on the ability scale where P (θ) = 0.5; when an item is easy; this occurs at a low skill level; when it is difficult, it occurs at a high level. These skill levels are usually set out as a function of the standard deviation from the mean on the scale (0, 1), and then each level is given a qualitative interpretation (so that data presentation becomes more pedagogical) and are then called anchor levels.

The number of anchor levels is not known a priori. To determine at which level an item is anchor (or even if an item is anchor at some level), Beaton and Allen (1992) indicate the following conditions: 1) positive answer by a large percentage of individuals (at least 65%) with this skill level; 2) be answered positively by a smaller percentage of individuals (maximum 50%) with the immediately previous skill level; 3) the difference between these two proportions must be at least 0.30.

Model selection

PCL: YV is an instrument with polytomic items, requiring consistent modeling. Choosing not to consider the hypothesis of items with the same discrimination (the case of Rasch models), one has to choose between two polytomic models: the Generalized Partial Credit Model (GPCM) (Masters, 1982; Muraki, 1992) or the Graded Response Model (GRM) (Samejima, 1968). According to Tsang, Piquero, and Cauffman (2014), although appropriate for categorical responses, GRM assumes that the likelihood of responding to a higher category increases as the latent trait increases.

In fact, this is expected. However, this hypothesized ordering may not be reflected in the empirical data. In polytomic items, if the probabilities do not increase along with the latent trait, at least one response category will never be the most likely (for any point on the θ scale; Andrich, 1988). The assumption of ordered categories made by the GRM implies that this model is unable to detect these “disorganized thresholds” (Tsang et al., 2014). The GPCM, while making the same assumption, does not force the thresholds to be ordered.

In the interpretation of the discrimination parameter the criterion of Baker and Kim (2017), accepting as moderate or higher an α ≥ 0.65 was adopted. The α discrimination of each item reaches its maximum value at the difficulty level of the item. The difficulty parameter β of the item corresponds to the point on the ability scale where P (θ) = 0.5: when an item is easy, this occurs at a low skill level; when it is difficult, it occurs at a high level. In polytomic models, as in the case of this paper, each score of an item (as in the case of PCL: YV; 0, 1, and 2) is called a category and exhibits its own characteristic curve. The intersection parameter δ_j of one category with the previous one indicates the latent trace levels where it is equally likely to answer either score (0 or 1, 1 or 2). This parameter refers to the exact points of intersection, not to the category as a whole. An item with m _j categories exhibited m_j-1 intersection points. As Muraki (1992) arbitrarily defined δ₁ = 0, we work with δ₂ as an intersection between categories 0 and 1, and δ₃ as an intersection between 1 and 2, in the case of PCL: YV. In the interpretation of anchor levels, since there were few items left, the criteria 2 and 3 previously described were relaxed: percentages of up to 55% in the previous skill level were accepted, as well as differences greater than 0.25, a procedure also adopted by Mafra (2011).

The study with polytomic data considered the twelve items that presented discrimination parameter (α) higher than 0.65. The categories δ of the items, reviewed by the generalized partial credit model, referred to a three-point Likert Scale, covering the scores “0”, “1” and “2” equivalent to “The item does not apply to the individual”, “The item applies to some degree, but not to the point of representing a score 2, or “there are many conflicting exceptions or information” and “The item reasonably applies to the individual in the most essential aspects”, respectively. Table 1 presents (a) the discrimination and location parameters of the categories of all items, considering the application in GPCM by the R Software (R Core Team, 2013), through the ltm package (Rizopoulos, 2006); and (b) the recalculated parameters of the remaining items after the elimination of the items with low discrimination (1, 2, 4, 13, 14, 16, 17 and 19).

Figure 1 presents the characteristic curves of the categories of the 12 selected items. Items 8, 6, and 18 presented the greatest discrimination parameters (αs = 3.00, 2.00, and 1.75, respectively), resulting in steeper curves and suggesting that they are more sensitive to different levels of psychopathy traits than items 9, 3 and 11, which presented the lowest αs among the selected items, for example (0.71, 0.74 and 0.80, respectively).

Figure 1 Note: θ (theta): latent trait

The data in Table 1 and Figure 1 also show the difficulty parameters of the categories and the latent trait range that each test response is most likely to meet. For example, in item 9, “Parasitic Lifestyle”, a score 2 answer (“The item applies reasonably well to the individual in the most essential aspects”) only becomes the most likely answer from point 1.89 on the latent trait scale (and yet it is only close to 0.5); on the other hand, an individual with the same θ approaches the probability of 1 for a response of item 6, “Lack of Remorse/Guilt”.

Table 1

Items	α	αR	δ2	δ2R	δ3	δ3R
1	0.364		-3.077		0.020
2	0.496		-1.991		0.134
3	0.764	0.748	-1.690	-1.712	-0.064	-0.075
4	0.446		-1.768		0.769
5	0.919	0.902	-0.618	-0.625	0.267	0.259
6	1.758	2.005	-1.087	-1.068	-0.020	-0.006
7	1.613	1.655	-1.176	-1.171	0.425	0.415
8	2.703	3.002	-0.794	-0.791	0.280	0.275
9	0.801	0.716	0.132	0.161	1.777	1.892
10	1.019	1.054	-1.264	-1.255	-0.204	-0.199
11	0.809	0.802	-0.277	-0.283	0.359	0.353
12	1.046	1.063	-0.478	-0.486	0.029	0.028
13	0.604		-1.272		0.789
14	0.605		-2.231		-1.023
15	1.642	1.522	-1.920	-1.977	0.039	0.025
16	0.460		-0.291		0.666
17	0.605		-1.011		1.310
18	1.828	1.753	-1.703	-1.715	-0.738	-0.764
19	0.552		2.204		-0.244
20	1.252	1.176	-0.610	-0.616	0.257	0.237
Log.Lik: original = -4663.968, reestimated = -2690.084

Note: α (alpha): discrimination parameter. δ (delta): intersection parameter. Log.Lik: model fit statistic: likelihood logarithm to convergence of the model parameter estimation algorithm. R: parameters reestimated after exclusion of the items with low discrimination, composing a second model. Bold values: α < 0.65.

Figure 2 presents the Item Information Functions (IIFs); the IIF peaks indicate where an individual with a latent trait truly at that level can be accurately estimated (Baker & Kim, 2017). The smaller the amount of information, the lower the accuracy of θ estimates. Item 3, for example, is more accurate (with information close to 15) in the latent trait range between -1 and 0, and loses accuracy as it approaches extremes. Figure 2 also shows at which points on the latent trace scale the test provides more accurate estimates on individuals. It is clear that the test is positioned to the left in relation to the mean and that most of the information is located approximately between -1 to 1 on the latent trace scale. The test provides little information about respondents located outside this range, which are in significant numbers and whose interviews represent a considerable spending of time in prison surveys. In summary, these results suggest two conclusions: (a) the short version of the instrument offers similar levels of information as the full test and (b) the instrument is more informative at medium latent trace levels and is not indicated for use in the clinical setting.

Figure 2 Note: θ (theta): latent trait

As stated above, by definition δ₁ = 0: the probability of obtaining a score “0” or higher is always 1, regardless of the position on the scale. After calculating the cumulative probabilities for δ2R and δ3R (the probability of obtaining the score “1” or “2” at each level of the latent trace scale) and only of the upper category δ3R (score “2”), it was possible to establish five anchor levels: -1, 0, 1, 2 and 3.

Table 2 shows a synthesis of the anchor items for the categories equivalent to the scores “1” and “2”, according to the values found for δ₂R and δ₃R, and the relevant levels that determine anchor categories.

Table 2

Item	Description	Group
Level -1
Item 3 (δ2R)	Need for stimulation - ‘1’	Behavioral
Item 9 (δ2R)	Parasitic lifestyle - ‘1’	Behavioral
Item 10 (δ2R)	Poor behavioral controls - ‘1’	Antisocial
Item 15 (δ2R)	Irresponsibility - ‘1’	Behavioral
Item 18 (δ2R)	Juvenile delinquency - ‘1’	Antisocial
Level 0
Item 5 (δ2R)	Conning/manipulative - ‘1’	Interpersonal
Item 6 (δ2R)	Lack of remorse or guilt - ‘1’	Affect
Item 7 (δ2R)	Shallow affect - ‘1’	Affect
Item 8 (δ2R)	Callous/lack of empathy - ‘1’	Affect
Item 11 (δ2R)	Promisc. Sex Behavior - ‘1’	Interpersonal
Item 12 (δ2R)	Early behav. problems - ‘1’	Antisocial
Item 18 (δ3R)	Juvenile delinquency - ‘2’	Antisocial
Item 20 (δ2R)	Criminal versatility - ‘1’	Antisocial
Level 1
Item 3 (δ3R)	Need for stimulation - ‘2’	Behavioral
Item 6 (δ3R)	Lack of remorse or guilt - ‘2’	Affect
Item 7 (δ3R)	Shallow affect - ‘2’	Affect
Item 8 (δ3R)	Callous/lack of empathy - ‘2’	Affect
Item 10 (δ3R)	Poor behavioral controls - ‘2’	Antisocial
Item 12 (δ3R)	Early behav.problems - ‘2’	Antisocial
Item 15 (δ3R)	Irresponsibility - ‘2’	Behavioral
Item 20 (δ3R)	Criminal versatility - ‘2’	Antisocial
Level 2
Item 11 (δ3R)	Promisc. Sex Behavior - ‘2’	Interpersonal
Level 3
Item 9 (δ3R)	Parasitic lifestyle - ‘2’	Behavioral

Note: δR (delta): reestimated intersection parameter.

According to Table 2, individuals at level -1 are characterized for achieving a score of “1” or higher for the items “Need for Stimulation”, “Parasitic lifestyle” and “Irresponsibility”, which fall into the Behavioral group, and also in the items “Poor behavioral controls” and “Severe criminal behavior”, which fall into the Antisocial group. Likewise, in the following levels, the categories of each item that correspond to certain items are successively exposed. It is important to note that this does not mean that a respondent of any level will necessarily respond in this exposed pattern, since these are probabilities: anchor levels have the function of allowing a more accessible and pedagogical interpretation of the data.

Table 2 also shows that the vast majority of item categories are characterized as providing more information about individuals between levels -1 and 1. Only the δ₃R categories of the items “Promiscuous sexual behavior” and “Parasitic lifestyle” define levels 2 and 3 respectively. It is an issue that a complex-use instrument such as PCL: YV, which requires a lot of time to apply and to train the surveyors, has such a limited range of information. In fact, this may represent an under-representation of precisely the portion of the population that requires more attention from mental health professionals in socio-educational institutions.