This original study of a population-based cohort investigates the associations between child mental health problems (age 6) and IQ-achievement-discrepancy in adolescence (age 12-13) in 1577 children.
The total child mental health problems, internalizing and externalizing problems, and the specific problem-syndromes are measured with the well-known CBCL and TRF scales from the Achenbach System of Empirically Based Assessment (ASEBA), which provides a comprehensive and valid approach for assessing maladaptive functioning in large samples of children in the general population.
The method used to examine the longitudinal associations of parent- and teacher-reported problems (CBCL/TRF scales) with academic underachievement or overachievement relative to IQ is new and elegant.
The outcome of interest is the IQ-achievement-discrepancy measured by the standardized residuals that were derived from a linear regression analysis of academic achievement as function of IQ. This way the associations between mental health problems and IQ-achievement-discrepancy ca be modelled in stead of looking separately on academic achievement and IQ (the latter os also done to enable direct comparison with the existing literature).
There is a clear line of thought throughout aims, methods, results, and discussion, and I only have minor suggestions that may further improve the paper.

The topic is highly relevant and results are useful for the planning of early intervention in school-aged children by using the parent- and teacher- reported problems as early warning signs of maladaptive functioning, indicating a need for intervention. The specific prognostic significance of attentional problems has major importance for understanding the burden of ADHD, the related risk of academic underachievement, and hence the scope for prevention by early psychological, pedagogical, and pharmacological interventions.
Minor comments and suggestions:
1) There are no attrition analyses. Although the study sample is large and probably representative, I suggest that the authors predictors of participation (versus no participation) in CBCL/TRF, academic achievement (Cito), and IQ (WICS) measurements. It’s highly likely that missing data on the teacher-report (N=1824) and the Cito test (N=765) may reflect school problems, and therefore the included participants may be positively selected. Please add attrition analyses and discuss the risk of selection bias.
2) The background and discussion should explain that the association between mental health disorders and lower likelihood of a later participation in school examinations and lower school grades have been documented, see suggested reference below (Dalsgaard at al, JAMA Psychiatry 2020)
3) Please also explain if children with known intellectual deficits (mental retardation) were included in this study, and if so, how this might have inflated the associations between CBCL/TRF scores and IQ-Cito-scores? Perhaps they were excluded from the normal elementary education and Cito test?

Minor editing and suggested references:
Page 5: Under significant outcomes: I would delete “(Cito)” and “(WISC)”, because most readers don’t know Cito, and you did not perform a complete WISC.
Page 6-7: Regarding background literature: Longitudinal associations between subclinical mental health problems in school-aged children and lower participation in examination as well as lower academic achievement (grades) were already reported by: Wolf RT, Jeppesen P, Gyrd-Hansen D, The CCC2000 Study Group, Oxholm AS (2019) Evaluation of a screening algorithm using the Strengths and Difficulties Questionnaire to identify children with mental health problems: A five-year register-based follow-up on school performance and healthcare use. PLOS ONE 14(10): e0223314. https://doi.org/10.1371/journal.pone.0223314
Regarding the longitudinal associations between mental health disorders in children and lower participation in school examination and lower academic achievement, please add reference to Dalsgaard S, McGrath J, Østergaard SD, et al. Association of Mental Disorder in Childhood and Adolescence With Subsequent Educational Achievement. JAMA Psychiatry. 2020;77(8):797–805. doi:10.1001/jamapsychiatry.2020.0217
Page 12: Please explain for “dummies” how the IQ-achievement-discrepancy is expressed as a Z-scores? The change per SD of CBCL/TRF in standardized residuals?
Page 13: Explain the “simultaneous model” including the mother-reported scores and additionally the teacher-reported scores of the same subscale. Are scores from the two informants mutually adjusted?
Page 14: Explain the correction for multiple testing better. The level of significance was α = 0.03 based on the number of independents tests. How did you estimate the number of tests (19.12) using random permutations?
Table 2 and Figure 2: Legend should clarify that each row corresponds to one model of the independent contribution of parent-scores and of teacher-scores, separately? or after mutual adjustment?
Page 16: Please rephrase the sentence “we did not find strong indicators for multiplication interaction effects. Only Thought Problems showed a nominally significant sex interaction”. Fewer statistical technical expressions would be helpful. I agree that the finding don’t survive correction for multiple testing. Please comment on the power to analyze effect modification.
Also discuss that the distribution of subclinical problems (like attention problems) in the general population show less differences by sex compared to the sex-distribution of clinical ADHD diagnoses.
Page 16: please use consistent presentation: teachers, teacher, or B-teacher
Supplementary table 1: Here analyses are repeated with IQ and academic achievement as separate outcomes, so why does the legend say “lower actual achievement than would be expected based on IQ”?
Supplementary table 1: Again, as reader, I am not sure, if we look at the independent contribution of parent-scores and of teacher-scores with or without mutual adjustment?