Confirmatory Factor Analysis
Based on previous research on the parental- and self-report-versions of the ICU, four main models of the ICU were tested in a CFA: a 3-bifactor model (Essau et al.
2006; Roose et al.
2010; Waller et al.
2015), an IRT-shortened 2-factor model (S. W. Hawes et al.
2014b), a unidimensional model (Ray and Frick
2018) and an IRT-shortened unidimensional model (Ray et al.
2016). To account for any method-variance effect of standard- and reverse-scored items, the Unidimensional and 3-bifactor models were also tested with the addition of a method-variance bi-factor loading on all reverse-scored items (Paiva-Salisbury et al.
2017). This addition was not relevant for the IRT-shortened 2-factor model, as the Uncaring factor comprised all reversed-scored items. In the IRT-shortened Unidimensional model, eight of the ten items are reverse-scored, and it was therefore more parsimonious to test for method variance in this model by specifying shared method variance between the two standard-scored items on this scale.
The DIFFTEST function showed significant reductions of the
X2 test statistics for the models when method-variance was accounted for. This applied in both parent-reported data: 3-bifactor model (
∆X2 = 53.15,
df = 12,
p < .001), unidimensional model (
∆X2 = 100.956,
df = 12,
p < .001), and unidimensional short model (
∆X2 = 5.194,
df = 1,
p = .023, marginally significant); in self-reported data: 3-bifactor model (
∆X2 = 182.669,
df = 12,
p < .001), unidimensional model (
∆X2 = 163.030,
df = 12,
p < .001) and unidimensional short model (
∆X2 = 60.269,
df = 1,
p < .001); and in two of three models in the teacher-reported data: the 3-bifactor model (
∆X2 = 63.900,
df = 12,
p < .001) and the unidimensional model (
∆X2 = 152.841,
df = 12,
p < .001), but not the unidimensional short model (
∆X2 = 1.793,
df = 1,
p = .181). All other fit indices were also improved when a method-variance element was included in the model, again except for the unidimensional short model in the teacher-data. Subsequently, all analysis and model comparisons were made between models accounting for method-variance. Table
1,
2 and
3 show the fit-indices for these models when analyzing the ICU by parent-, self- and teacher-report, respectively. The fit-indices of the models without a method-variance element can be found in Online Resource
1.
Table 1
Fit-indices in the parent-reported data of ICU models including a method variance element
Unidimensional | 695.671 / 240 | .808 | .779 | .110 [.100–.119] | 1.39 |
Unidimensional short | 104.454 / 34 | .932 | .909 | .115 [.090–.104] | 0.97 |
2-factor | 116.770 / 53 | .956 | .946 | .088 [.066–.109] | 0.80 |
3-bifactor | 387.455 / 216 | .928 | .908 | .071 [.059–.082] | 0.91 |
Table 2
Fit indices in the self-reported data of ICU models including a method variance element
Unidimensional | 519.807 / 240 | .842 | .818 | .087 [.077–.097] | 1.17 |
Unidimensional short | 116.791 / 34 | .918 | .891 | .126 [.101–.151] | 0.94 |
2-factor | 109.768/ 53 | .952 | .940 | .083 [.061–.105] | 0.86 |
3-bifactor | 408.400 / 216 | .891 | .861 | .076 [.065–.087] | 0.98 |
Table 3
Fit-indices in the teacher-reported data of ICU models including a method variance element
Unidimensional | 767.219 / 240 | .817 | .790 | .139 [.128–.150] | 1.52 |
Unidimensional short | 189.327 / 34 | .864 | .820 | .200 [.173–.228] | 1.36 |
2-factor | 134.161 / 53 | .957 | .947 | .116 [.092–.140] | 0.87 |
3-bifactor | 481.843/ 217a | .908 | .883 | .103 [.091–.116] | 1.06 |
Across all responder groups, the full unidimensional model displayed overall poor model fit. The IRT-shortened unidimensional model showed adequate fit in relation to the CFI, the TLI and the WRMR indices in both parent- and self-data, while these indices showed marginal fit in the teacher data. In all datasets however, the RMSEA indicated inadequate fit of this model. The 2-factor model showed good fit in parent, self and teacher data based on the CFI, the TLI and the WRMR indices. The RMSEA indicated marginal fit for this model across datasets. The 3-bifactor model showed adequate fit in the parent data and marginal fit in the self and teacher data.
The RMSEA indicator favors models with higher degrees of freedom, and in our study the 3-bifactor model with a method-variance factor by far has the highest degrees of freedom. This could explain why this model has the lowest RMSEA scores. Typically, it would require a larger sample size to have enough power to detect significant findings related to RMSEA scores on models such as the 2-factor model with 53 degrees of freedom (MacCallum et al.
1996). The CFI and TFI indices tend to be less sensitive to sample size. The 2-factor model was therefore assessed as the overall better fitting model for ICU across datasets, despite the slightly lower RMSEA values observed for the 3-bifactor model.
The interpretation of the 2-factor model in relation to method variance effects is not clear cut. The model embeds a method variance effect within the 2-factor structure with standard- and reverse-scored items separately constituting each factor. Arguably, the 2-factor structure could be a method-variance artefact and could alternatively be modeled as a unidimensional CU construct constituting the 12 items, and a method variance bi-factor related to the five reverse-scored “Uncaring”-items. Post-hoc CFA-analysis of this alternative model yielded very similar model fit indices as for the 2-factor model in both parent- (X2 = 125.655, df = 51, CFI = .949, TLI = .934, RMSEA = .097, 90% CI = [.075–.118], WRMR = 0.87), self- (X2 = 101.730, df = 51, CFI = .957, TLI = .944, RMSEA = .080, 90% CI = .[057–.103], WRMR = 0.82), and teacher-reported data (X2 = 130.869, df = 51, CFI = .958, TFI = .946, RMSEA = .117, 90% CI = [.093-.142], WRMR = 0.87). Thus, the results of our confirmatory factor analyses alone cannot make the distinction on whether the 2-factor model represents two interrelated factors, or a unidimensional construct with method-variance effects between items. Therefore, all subsequent analysis of convergent validity used both full scale and factor scores to enable a comparison of the scores’ correlational patterns.
Reliability and Subscale Correlations
Reliability analyses of the ICU12 were run separately for each respondent group. For the ICU12-P (parent-report), Cronbach’s α was .869 for the full scale, .816 for the 7-item Callousness subscale, and .791 for the 5-item Uncaring subscale. For the ICU12-S (self-report), the Cronbach’s αs were .810 (total scale), .848 (Callousness-subscale), and .811 (Uncaring-subscale). For the ICU12-T (teacher-report), the Cronbach’s αs were .901 (total scale), .855 (Callousness-subscale), and .839 (Uncaring-subscale). For all ICU12 versions, all items showed corrected item-total correlations (CITCs) > .30 to both the total scale and its respective subscale. While the two subscales correlated strongly on the ICU12-P, r(155) = .623, p < .001, and the ICU12-T, r(88) = .707, p < .001, the correlation was weak and not statistically significant on the ICU12-S, r(151) = .174, p = .031. Due to the observed inter-correlation between the ICU12 subscales, partial correlation was applied when subsequently assessing the convergent validity of the subscale scores.
Cross- and Inter-Rater Reliability
The cross-rater reliability of the ICU12 was weak, both between parent- and self-report, ICC of .170, 99% CI [−.04, .37], F(149, 149) = 1.41, p = .018, and between teacher- and self-report, ICC of .226, 99% CI [−.05, .47], F(85, 85) = 1.59, p = .018. The cross-rater correlations between the ICU12-P and -S subscales were similarly weak for both the Callousness, ICC = .067, 99% CI [−.15, .27], F(149, 149) = 1.14, p = .209, and the Uncaring subscales, ICC = .141, 99% CI [−.07, .34], F(150, 150) = 1.33, p = .042. The inter-rater reliability of the ICU12 between parents and teachers was also weak, ICC = .204, 99% CI [−.07, .45], F(87, 87) = 1.51, p = .028.
Age and Gender Effects
While self-reported CU showed a small negative correlation to age, r(155) = −.192, p = .017, this was not observed for parent-report, r(157) = .061, p = .446, nor teacher-report, r(93) = .045, p = .665. The 99% CI for the gender difference in ICU12 scores between boys and girls was [−3.70, 2.43], p = .592 for parent-report, [0.73, 6.25], p = .001 for self-report and [−.50, 7.93], p = .023 for teacher-report. On average boys obtained scores that were approximately 0.5 SD higher on the ICU12-S and the ICU12-T when compared to girls, while they were 0.08 SD higher for boys on the ICU12-P.
Convergent, Divergent and Discriminative Validity
Externalizing Problems and Aggression
The results of the correlation analyses between parent, self- and teacher-reported CU and the main measures of externalizing problems are shown in Table
4. By parent- and teacher-report we found strong within-rater correlations between ICU and measures of aggression and rule breaking behavior. The cross-rater correlations were weak and for self- and teacher-reported CU only observed for the rule breaking scale. Age of onset had a weak negative correlation to the ICU-P only. Moderate correlations were seen between self-reported delinquency and the various ICU scores. On a subscale level, the associations appeared more marked for the Callousness subscale.
Table 4
Convergent validity of the ICU-scales to measures of behavior problems
ICU12-Parent | .475** | .196 | .433** | .118 | −.203 | .270* | .212 |
-callousness | .290** | .080 | .356** | .124 | −.186 | .117 | .123 |
-uncaring | .163 | .108 | .032 | −.021 | .015 | .125 | .062 |
ICU12-Self | .007 | .084 | .162 | .163 | .064 | .284* | .334** |
-callousness | −.003 | .182 | .103 | .149 | .132 | .303* | .270* |
-uncaring | .013 | −.106 | .113 | .046 | −.074 | .045 | .156 |
ICU12-Teacher | .105 | .392* | .219 | .539** | .044 | .248 | .358* |
Spearman rank-order correlations showed the expected convergent validity of self-reported CU to coercive and thrill-seeking aggression, r(155) = .286, p < .001 and r(155) = .285, p = .001, respectively. The ICU12-S also had a small to moderate positive correlation to the Vengeful aggression scale, r(155) = .224, p = .005, while the correlation to the Explosive aggression scale was smaller, r(155) = .137, p = .088. Parent-reported CU showed small to negligible correlations to the aggression scales (rs = .035–.149, ps = .065–.675), while teacher-reported CU correlated somewhat with thrill-seeking aggression only, r(91) = .226, p = .035.
Logistic regression controlling for age and gender effects was applied to study the relationship between the ICU12-scores and indicated problematic alcohol use (AUDIT-score ≥ 5). Self- and teacher-reported, but not parent-reported, CU showed a significant association to problematic alcohol use: OR = 1.09, p = .008; OR = 1.11, p = .008, and OR = 1.04, p = .173, respectively. When both subscales were entered in the model instead of the total ICU12-S score, the Uncaring subscale had a higher odds ratio, OR: 1.13, p = .045, compared to the Callousness scale, OR:1.07, p = .101.
Anxiety and Punishment Sensitivity
The partial correlations of the ICU-scores to measures of anxiety and punishment sensitivity when controlling for concurrent levels of externalizing problems are seen in table
5. While the ICU12-S and the ICU12-T showed some small to moderate negative correlations to both within- and cross-rater measures of anxiety and punishment sensitivity, the ICU12-P only demonstrated a within-rater negative relationship to anxiety. On a subscale level, the associations were observed mostly for the Uncaring subscale.
Table 5
Relationship of the ICU-scales to measures of anxiety and behavioral inhibition
ICU12-Parent | .001 | −.187 | −.038 | .009 |
-callousness | .033 | .034 | .041 | .100 |
-uncaring | −.035 | −.228* | −.086 | −.099 |
ICU12-Self | −.206 | −.188 | −.230 | −.368** |
-callousness | −.066 | −.049 | −.101 | −.179 |
-uncaring | −.228 | −.224 | −.227 | −.346** |
ICU12-Teacher | −.234 | −.140 | −.208 | −.329* |
Discriminant Validity
Overall, the ICU12-S demonstrated discriminative validity to the WHO-5 Well-being index and the withdrawn-depressed and somatic complaints scales on the CBCL/TRF (rs = −.090–.034, ps = .336–.918). Both the ICU12-P and ICU12-T showed discriminative validity to subjective well-being and parent- and teacher-reports of somatic complaints (rs = −.146–.091, ps = .088–.996), but moderate strength positive correlations to within-rater withdrawn-depressed scales were observed, r(157) = .323, p < .001, and r(93) = .415, p < .001, respectively.