Identifying potentially marker symptoms of attention-deficit/hyperactivity disorder

Participants

The sample was composed of 474 children, aged between six and fifteen years (mean = 10.3; standard deviation = 2.3), of which 42% were male. The sample was obtained through the mediation of two schools from two regions of Chile, which voluntarily agreed to participate in the study. Usual parent meetings were used to discuss the objectives of the research and invite the parents to participate. Parents (89% mothers) who agreed to participate were informed about how to respond to the questionnaire, which they completed with the direct support of the main researcher or one of the project collaborators. There were no cases with missing data due to the monitoring performed during data collection. In all cases, we obtained an informed consent for using the data in the research, with an acceptance rate of 100%. All procedures performed in this study were in accordance with the ethical standards of the institutional research committees (University of Talca, number 11140524) and the 1964 Helsinki Declaration and its later amendments or comparable ethical standards.

Instrument

We used the ADHD subscale of the Child and Adolescent Behavior Inventory (CABI; Burns et al., 2015). This subscale is composed of 18 items corresponding to the ADHD symptoms proposed by the DSM-5 (inattention and hyperactivity/impulsivity). Each symptom was rated on a 6-point scale (i.e., almost never (never or about once per month), seldom (about once per week), sometimes (several times per week), often (about once per day), very often (several times per day), and almost always (many times per day)), choosing the option that best described the frequency of their children’s usual behavior (i.e., such behaviors cannot be explained by the presence of behavioral problems or by the children’s misunderstanding of tasks and instructions). Earlier studies with children from Chile and Spain provide support for the reliability and validity of scores for the ADHD-IN and ADHD-HI scales of the CABI (e.g., Belmar et al., 2017; Burns et al., 2013; Sáez et al., 2018).

Data analysis

The data were analyzed with the IRTPRO 4.0 software (Cai, Du Toit & Thissen, 2011), using the graded response model (GRM; Samejima, 1997; Samejima, 2010). The GRM assumes, in addition to the usual IRT assumptions, that the categories to which the individual responds (or in which the individual is rated, as is in this case) can be ordered or hierarchized, as is the case, for example, of probability scales with summative estimates, or Likert-type scales. The model aims to obtain more information than available with only two response levels (e.g., “yes”—“no”), and in that sense, it is an extension of the two-parameter logistic model (2-PLM) to ordered polytomous categories.

The GRM specifies the probability of a person being rated with a category ik or higher as opposed to being rated with a lower category when the rating scale has at least three categories, and is expressed as (1)${\displaystyle P_{ik}^{\ast }\left({\theta }_j\right)=\frac{e^{D_{\alpha i}\left({\theta }_j-{\beta }_{ik}\right)}}{1+e^{D_{\alpha i}\left({\theta }_j-{\beta }_{ik}\right)}}}$ (2)${\displaystyle P_{ik}\left({\theta }_j\right)=P_{ik}^{\ast }\left({\theta }_j\right)-P_{ik+1}^{\ast }\left({\theta }_j\right)}$ where k is the ordered response option; P_ik(θ_j) is the probability of responding to option k of item i with a latent trait level θ_j; $P_{ik}^{\ast }\left({\theta }_j\right)$ isthe probability of responding to option k or higher in item i with a latent trait level θ_j; θ_j is the latent trait level of the person; β_ik isthe location parameter of the alternative k of item i; α_i is the discrimination parameter of item i, and D is the constant 1.702.

Prior to the estimation of the GRM models, it was verified that the data complied with the necessary criteria of unidimensionality and local independence by means of a parallel analysis based on minimum rank factor analysis (Timmerman & Lorenzo-Seva, 2011) implemented in FACTOR 10.8 (Lorenzo-Seva & Ferrando, 2013), where the variance extracted in the first factor was compared with that obtained from 500 permutations of the sample values, and the inspection of the standardized LD-χ2 values of the matrix of expected and observed response frequencies to each item (LD-χ2 values greater than 10 suggest a substantial violation of local independence) (Cai, Thissen & Du Toit, 2011).

For the assessment of model fit, we examined the statistic M2 (Maydeu-Olivares & Joe, 2006), its associated root mean square error of approximation (RMSEA), and the differences between the response frequencies observed and expected by the model in each item by the inspection of the significance of S-χ2 (Orlando & Thissen, 2000). In the case of M2, non-significant values (p > 0.01) and associated RMSEA values close to zero (<.08; Hu & Bentler, 1999) are expected for a good model fit. In the case of S-χ2, good fit requires most items to have non-significant values (p > 0.01).

Unidimensionality and local independence

Figure 1 shows the result of the parallel analysis. For each sub-scale, the presence of a single clearly dominant factor can be observed, since only one eigen-value of each scale exceeds those obtained from random matrices (500 permutations). The LD-χ2 values associated with the expected frequencies against those values observed in both subscales were between .10 and 15.4 (M = 5.1, SD = 3.04). Two of the 42 contrasts were greater than 10, without observing clusters of extreme LD-χ2 values that could suggest the presence of substantive sources of non-modeled systematic error. As a result, the criteria of unidimensionality and local independence can be considered adequately complied with, and estimation of the GRM models proceeded.

Fitting of the data to the GRM model

To assess the fit of the data to the GRM model, the M2 and RMSEA statistics were examined for each of the scales. The results for both the IN scale (M2 = 1, 529.9, df = 891; p = .0001, RMSEA =. 04) and for the HI scale (M2 = 1, 285, GL = 891; p = .0001, RMSEA = .03) may indicate some lack of fit. However, the low associated RMSEA values suggest that this misfit may be due to a limited amount of unmodeled error (Cai, Thissen & Du Toit, 2011). Most of the items reached non-significant S-χ2 values (p > .01), in both sub-scales (six cases in IN and nine in HI).

Estimation of the parameters

To estimate the item parameters α_i and β_ik, a marginal maximum likelihood method was used, given the sufficiently large sample size. Figure 2 shows, as an example, the response category curves corresponding to item 2 (sustained attention) of the IN scale. The abscissa represents the latent variable θ (M = 0; SD = 1). For each item, six curves are drawn, each of which represents the probability, represented on the ordinate axis, of being located in each of the response categories conditionally to the trait level. Thus, in the symptom discussed, for the most likely response to be “many times a day” (highest category), the child must present a very high level of inattention (approximately 2 standard deviations or more above the mean). On the other hand, the most likely score of a child near the mean (Theta = 0) would be “once a week” (category 2).

Table 1 shows the values of the parameters α_i and β_ik. Since, according to Baker (2001), α_i values from 0.01 to 0.24 are very low, from 0.25 to 0.64 are low, from 0.65 to 1.34 moderate, from 1.35 to 1.69 high, and more than 1.7 are very high, we conclude that, in absolute terms, the discrimination parameters have been very high (>1.70). In relative terms, we observe that in the IN scale the most discriminative items have been 2 (sustained attention, α_i = 3.73) and 8 (easily distracted, α_i = 3.44). On the contrary, while maintaining a reasonable level, symptom 7 (loses things, α_i = 1.73) has presented substantially less discriminative power than the rest, so that its relative contribution to the test information has been lower. In the case of the HI scale, the three most discriminative symptoms were 5 (driven by a motor/on the go, α_i = 3.62) 2 (leaves seat, α_i = 2.96) and 7 (blurts answers, α_i = 2.94). No symptom has been clearly less discriminative than the others.

Figure 3 shows the cumulative information functions of the items, where the relative contribution of each symptom to the total information of the test is illustrated (the upper curve—dotted line—simultaneously represents the cumulative information of the last item and the information function of the complete test; the items are sorted from bottom (item 1) to top (item 9) in the same order as in Table 1). As shown in Fig. 3A (IN sub-scale), items 2 (sustaining attention) and 8 (easily distracted) contribute more information to the test, while item 7 (loses things) contributes little information relative to the other symptoms. The complete test provides the largest amount of information ranging between approximately −.5 and 2 standard deviations, producing the peak of maximum information in high areas of the latent variable (between 1 and 2 standard deviations above the mean). Figure 3B shows the items on the hyperactivity-impulsivity sub-scale. Clearly, item 5 (on the go/driven by a motor) provides the most information to the test set, and no symptoms are observed that provide substantially less information than the rest. The test acquires the maximum informative power in a range between the mean and +1.7 standard deviations.

Regarding the parameters β_ik (Table 1), the values range from approximately −1 SD to +2 SD. As seen, the symptoms differ substantially in the degree of severity they represent. This result is illustrated in Fig. 4. Figure 4A shows the characteristic curves of the more and less severe inattention items (assuming category 4—“very often, several times a day”—as a threshold to consider the potential adhesion to the symptom). In the least severe item (IN8, easily distracted), an observed score of 4 is expected in children with a level of inattention approximately 1.4 standard deviations above the mean. On the other hand, for the most severe item (IN1, fails to give close attention), the same observed score is expected for substantially higher levels of inattention (2.2 standard deviations above the mean). The hyperactivity scale shows similar results (see Fig. 4B), with differences close to one standard deviation of severity between the most severe (HI3, runs and climbs θ = 1.3) and least severe (HI7, talks excessively, θ = 2.1).