1997 2002 2000 2004 1989 1989 1993 1993 2001 In this study, we conducted confirmatory factor analyses (CFA) of data from a large general population sample of 7-year-old twins, rated by their teachers on ADHD and ODD. Two questions are addressed. First is the measurement model that relates differences in the latent constructs of ADHD and ODD to the observed behavior problem scores identical in boys and girls, i.e., is MI tenable? Second, do the magnitudes of the genetic and environmental influences differ, or do different genes play a role in boys and girls? Methods Subjects and procedure 2002 2006 1995 2004 t p F p 1998 Measure 2001 1998 1994 2001 2001 Distribution of the items 1994 1998 Criteria of MI 1993 For ordinal data, MI can be tested by constraining the thresholds and factor loadings, and residual variances to be equal in boys and girls. These constraints allow estimation of group differences in the means and variances of the common factor. To this end, the mean and variance of the common factor are fixed at 0 and 1, respectively, in an arbitrary reference group. We chose to estimate the mean and variance in girls, and to use boys as the reference group. In doing so, we are modeling the observed group differences as a function of the differences in the latent liability. Statistical analyses 1996 2003 p p 1981 To test if the Conners scales are MI with respect to sex, the factor structure was constrained to be identical in boys and girls. The ODD, IN, and HI scales resulted from factor analyses, and a single factor was fit to these scales. In contrast, the ADHD-I contains items related to problems with inattention and hyperactivity, and thus a two-factor model was fitted. To detect prevalence differences in ADHD and ODD across sex, the means and variances of the latent factors were constrained to be equal in boys and girls. χ α 2002 χ χ χ 1995 χ 1999 2004 1996 2003 1998 2004 Sex differences in genetic and environmental influences were examined in two ways. First, we investigated if the estimates of the genetic and environmental variances are equal in boys and girls. Secondly, we investigated if the same genes influence phenotypic variation in boys and girls. These qualitative sex differences were evaluated by constraining the genetic correlation in opposite sex twins at 0.5 (similar as in same-sex DZ twins). If different genes play a role in boys and girls, the genetic correlation is expected to be lower than 0.5 in opposite sex twins. Results Measurement invariance χ p χ χ p χ p 2002 1 2001 2001 Table 1 Promax rotated factor loadings and thresholds (T) of the best-fitting factor model for the four subscales of the CTRS-R:S  Items Loadings factor 1 Loadings factor 2 2001 N T1 T2 T3 Oppositional 2. Defiant 0.91 — 0.48 0.71 1.65 2.45 6. Defies 0.88 — 0.50 1.02 2.00 2.74 10. Spiteful 0.69 — 0.30 1.49 2.32 3.13 15. Argues 0.84 — 0.51 0.82 1.80 2.52 20. Explosive 0.78 — 0.41 1.20 1.92 3.12 Cognitive problems-Inattention 4. Forgets things 0.93 — 0.55 0.34 1.29 1.82 8. Poor spelling 0.81 — 0.50 0.27 0.95 1.44 13. Poor reading 0.71 — 0.45 0.39 0.87 1.21 18. Lacks interest 0.70 — 0.47 1.01 1.65 2.27 22. Poor arithmetic 0.82 — 0.49 0.55 1.22 1.68 Hyperactivity 3. Restless 0.73 — 0.62 0.10 0.94 1.51 7. Always on the go 0.79 — 0.57 0.66 1.31 1.87 11. Leaves seat 0.82 — 0.58 0.62 1.37 1.83 17. Difficulty waiting 0.83 — 0.65 0.12 0.91 1.58 21. Runs about 0.79 — 0.44 1.21 1.89 2.51 24. Difficulty playing 0.87 — 0.52 0.34 1.17 2.03 27. Excitable 0.86 — 0.66 0.40 1.12 1.84 ADHD index AP 1. Inattentive 0.99 −0.09 — −0.36 0.76 1.47 14. Attention span 0.95 −0.03 — 0.03 0.87 1.55 16. Only pays attention 0.45 0.23 — 0.36 1.20 1.88 19. Distractibility 0.94 −0.01 — 0.59 1.54 2.25 25. Fails to finish 0.72 0.09 — 0.24 1.27 1.99 26. Not follow instructions 0.68 0.09 — 0.38 1.30 1.86 HI 5. Disturbs 0.05 0.80 — 0.20 1.03 1.52 9. Remain still 0.05 0.88 — 0.92 1.68 2.24 12. Fidgets 0.16 0.67 — 0.12 0.94 1.53 23. Interrupts −0.05 0.85 — 0.54 1.37 2.07 27. Excitable −0.09 0.91 — 0.46 1.15 1.83 28. Restless −0.06 0.97 — 0.50 1.19 1.81 AP HI The thresholds are constrained to be equal in boys and girls. The means and variances of the latent factors in boys are constrained at 0 and 1, respectively. The means and variances of the latent factors are freely estimated in girls. The variances in girls were not significantly different from 1. The means of the latent factors are estimated at −0.60 (oppositional), −0.86 (hyperactivity), −0.42 (ADHD-I AP), and −0.52 (ADHD-I-HI). The mean of the cognitive problems-inattention factor is not significantly different between boys and girls Genetic analyses 2 3 1998 Table 2 Polychoric twin-correlations of the CTRS rated by same teachers (ST) versus different teachers (DT)  Oppositional Cognitive problems-inattention Hyperactivity ADHD index ST DT ST DT ST DT ST DT Monozygotic males 0.86 0.53 0.90 0.76 0.81 0.59 0.85 0.59 Dizygotic males 0.50 0.49 0.64 0.29 0.42 0.14 0.49 0.19 Monozygotic females 0.87 0.43 0.92 0.64 0.83 0.47 0.87 0.52 Dizygotic females 0.66 0.10 0.60 0.42 0.34 0.25 0.45 0.24 Opposite-sex twins 0.37 0.13 0.44 0.23 0.30 0.17 0.37 0.27 Table 3 Genetic model fitting results on CPRS-R:S ratings Model Parameters -2 LL With model Δdf Δχ² p Oppositional behavior in 7-year-old children 1. Fully saturated 84 4779.36 — — — — 2. Equal correlations same and different teachers 78 4812.26 1 6 32.91 <0.001 3. ACE model, estimates of ACE are allowed to be different between same and different teachers 44 4817.94 1 40 38.58 0.534 4. ACE, ACE same teacher = ACE different teacher 40 4853.84 3 4 35.90 <0.001 5. Correlated errors ACE model 42 4819.80 1 42 40.44 0.540 6. Correlated errors AE model 40 4823.93 5 2 4.13 0.127 7. Correlated errors AE model, AE boys = AE girls 38 4829.76 6 2 5.83 0.054 8. Correlated errors AE model, AE boys = AE girls, opposite-sex genetic correlation-free 37 4821.86 7 1 7.90 0.005 Cognitive problems-inattention in 7-year-old children 1. Fully saturated 84 6785.90 — — — — 2. Equal correlations same and different teachers 78 6822.57 1 6 36.67 <0.001 3. ACE model, estimates of ACE are allowed to be different between same and different teachers 44 6815.94 1 40 30.04 0.874 4. ACE, ACE same teacher = ACE different teacher 40 6843.87 3 4 27.93 <0.001 5. Correlated errors ACE model 42 6815.85 1 42 29.95 0.918 6. Correlated errors AE model 40 6820.01 5 2 4.16 0.125 7. Correlated errors AE model, AE boys = AE girls 38 6821.99 6 2 1.98 0.372 8. Correlated errors AE model, AE boys = AE girls, opposite-sex genetic correlation-free 39 6817.50 7 1 4.49 0.034 Hyperactivity in 7-year-old children 1. Fully saturated 84 6880.07 — — — — 2. Equal correlations same and different teachers 78 6906.97 1 6 26.90 <0.001 3. ACE model, estimates of ACE are allowed to be different between same and different teachers 44 6914.59 1 40 34.42 0.715 4. ACE, ACE same teacher = ACE different teacher 40 6942.35 3 4 27.76 <0.001 5. Correlated errors ACE model 42 6924.12 1 42 44.05 0.385 6. Correlated errors AE model 40 6926.76 5 2 2.64 0.267 7. Correlated errors AE model, AE boys = AE girls 38 6929.06 6 2 2.30 0.317 8. Correlated errors AE model, AE boys = AE girls, opposite sex genetic correlation-free 37 6919.99 7 1 9.07 0.003 ADHD in 7-year-old children 1. Fully saturated 84 7420.21 — — — — 2. Equal correlations same and different teachers 78 7458.10 1 6 37.89 <0.001 3. ACE model, estimates of ACE are allowed to be different between same and different teachers 44 7472.59 1 40 52.38 0.091 4. ACE, ACE same teacher = ACE different teacher 40 7507.40 3 4 34.81 <0.001 5. Correlated errors ACE model 42 7477.78 1 42 57.57 0.055 6. Correlated errors AE model 40 7479.14 5 2 1.36 0.507 7. Correlated errors AE model, AE boys = AE girls 38 7480.72 6 2 1.58 0.454 8. Correlated errors AE model, AE boys = AE girls, opposite-sex genetic correlation-free 37 7475.93 7 1 4.79 0.029 4 Table 4 Standardized estimates of the genetic and environmental effects on problem behavior  % Additive genetic effects (A) % Non-shared environmental effects (E) Genetic correlation opposite-sex twins Oppositional 56 44 0.16 Cognitive problems-inattention 71 29 0.35 Hyperactivity 58 42 0.21 ADHD index 61 39 0.32 Discussion The purpose of this study was twofold. First, we investigated if teacher ratings on ADHD and ODD are measurement invariant with respect to sex. Secondly, genetic and environmental influences on variation in ADHD and ODD were compared between boys and girls. Measurement invariance 1997 2000 2004 Quantitative and qualitative differences in the heritability among boys and girls More than half the variance in ADHD and ODD in boys and girls is attributable to genetic influences. The remaining variance is attributable to unique environmental influences. The magnitude of the influences of genes and environment is the same in boys and girls. However, part of the variance in ADHD and ODD is attributable to different genes in boys and girls. We base this on the fact that the genetic correlation between DZ opposite-sex twins was significantly lower than 0.5, which is the theoretical value (in the absence of assortative mating), if the same genes influence behavior in boys and girls. We observed a genetic correlation lower than 0.5 in DZ opposite-sex twins for oppositional behavior, cognitive problems-inattention, hyperactivity, and the ADHD index. 2005 2004 2004 2005 The finding of sex-specific genetic variation has implications for gene-finding studies of ADHD and ODD. The fact that the genes which influence the behavior of boys and girls do not completely overlap indicates that some quantitative trait loci may explain variation in boys but not in girls and vice versa. Therefore, the data from boys and girls cannot be collapsed when studying genetic effects in teacher ratings. In the NTR, teacher data are collected at the ages 7, 10, and 12 years. The sample sizes at the ages 10 and 12 are currently relatively small. In the future, we plan to address the issue of qualitative sex differences in teacher ratings in a longitudinal framework. The results of such a study will reveal if the finding of sex differences in the specific genes that play a role is also present in older children. Another important issue that may be addressed is the MI of ADHD with respect to age. 1998 2001 2002 Assessment of ADHD and ODD symptoms, through teacher reports on the CTRS-R:S, provides a solid starting point for measuring sex differences in mean scores or in heritabilities. Variation in teacher ratings of children’s problem behavior is mainly influenced by genetic factors. The size of the genetic influences does not depend on the child’s sex, but partly different genes are expressed in boys and girls. Future studies should reveal if these findings generalize to children from different age groups.