Correction to: Nature Mental Health (2023) 1:304-315 https://doi.org/10.1038/s44220-023-00057-5, published online 10 May 2024.

In the version of the article initially published, in Box 1, equation (1) was for true score sample variance as a function of observed scored variance, and error variance, rather than the formula for an individual’s true score as a function of their observed score and measurement error. We also incorrectly wrote that the error term includes systematic error. However, the error term captures only random error, such that the true score can include systematic error unrelated to the construct of interest. In the “Phenotypic complexity” section, we amended the text to clarify that a three-tiered hierarchical structure is not an intrinsic property of the CBCL, but one that is imposed by specification of a bifactor model, which we applied because it roughly reflects the scoring structure of the CBCL (i.e., Total Problems, Internalizing, and Externalizing composite scales, and eight empirical syndrome scales), and enables this measure to be partitioned into unique sources of variance for further analysis. We incorrectly specified the bifactor model (Supplementary Fig. 1) with a negative correlation between the Internalizing and Externalizing group factors and with too many error covariances (i.e., correlations between variances in the observed variables not explained by the factors). We re-estimated the model without specifying these additional parameters and obtained an adequate fit to the data. Based on the re-estimated parameters of this model, we recalculated the proportion of reliable variance unique to each of the three composite scales, and the residual variance unique to each of the eight CBCL syndrome scales. In the “Measurement non-invariance” section, we did not explicitly mention configural invariance, which is tested prior to weak invariance. We similarly omitted configural invariance from Supplementary Table 3, and the incorrect labels were assigned to each level of invariance. This, along with definitions, have been corrected. Under the solution column in Table 1 and the third box of Data Analysis in Fig. 3, we mistakenly wrote “measurement invariance” instead of “measurement non-invariance.” These corrections have been made to the HTML and PDF versions of the article.