Application of the Bifactor S – 1 Model to Multisource Ratings of ADHD/ODD Symptoms: an Appropriate Bifactor Model for Symptom Ratings

  • G. Leonard BurnsEmail author
  • Christian Geiser
  • Mateu Servera
  • Stephen P. Becker
  • Theodore P. Beauchaine


The symmetrical bifactor model is often applied to attention-deficit/hyperactivity disorder (ADHD)-hyperactive/impulsive (HI), ADHD-inattentive (IN), and oppositional defiant disorder (ODD) symptoms, but this model frequently yields anomalous or inadmissible results. An alternative model, the bifactor S – 1 model, is more appropriate for examining the hierarchical structure of ADHD/ODD symptoms. Both models were applied to ADHD-HI, ADHD-IN, and ODD symptom ratings by mothers, fathers, and teachers for 2142 Spanish children (49.49% girls; ages 8–13 years). The symmetrical bifactor model yielded the typical anomalous loadings, with a weakly defined ADHD-HI specific factor and difficult to interpret associations of general and specific factors with correlates. In contrast, the bifactor S – 1 model with ADHD-HI symptoms as general reference factor produced clearly interpretable results. For mothers and fathers, slightly more than 50% of true score variance in ADHD-IN and ODD symptoms represented specific residual variance not shared with the general ADHD-HI reference factor. For teachers, approximately 69% and 39% of true score variance in ADHD-IN and ODD symptoms, respectively, represented specific residual variance not shared with the general ADHD-HI reference factor. The general ADHD-HI reference factor and specific ADHD-IN and ODD residual factors showed convergent and discriminant validity across sources, along with unique associations with peer rejection, social impairment, and academic impairment factors. The bifactor S – 1 model also yielded results consistent with predictions from trait-impulsivity theory of ADHD/ODD development. Researchers should use the bifactor S – 1 model rather than the symmetrical bifactor model if hypotheses involve the latent hierarchical structure of ADHD/ODD symptoms.


Attention-deficit/hyperactivity disorder Bifactor model Bifactor S – 1 model Disruptive behavior disorders Oppositional defiant disorder P factor Trait impulsivity theory 



This research was supported by two grants from the Ministry of Economy and Competitiveness of Spanish Government under award numbers PSI2014-52605-R and PSI2017-82550-R (AEI/FEDER, UE), and a predoctoral fellowship co-financed by MINECO (Spanish Government) and the European Social Fund (BES-2015-075142). Stephen Becker is supported by award number K23MH108603 from the National Institute of Mental Health (NIMH). The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health (NIH) or the Spanish Government. We thank Cristina Trias for assistance with the study.

Compliance with Ethical Standards

Conflict of Interest

The authors of the current study have no conflicts of interest.

Ethical Approval

The research protocol was approved by the Research Ethics Committee (Institutional Review Board [IRB]) of the University of the Balearic Islands.

Informed Consent

Mothers, fathers, and teachers provided written informed consent.

Supplementary material

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of PsychologyWashington State UniversityPullmanUSA
  2. 2.Utah State UniversityLoganUSA
  3. 3.University of the Balearic IslandsPalmaSpain
  4. 4.Cincinnati Children’s Hospital Medical Center and University of Cincinnati College of MedicineCincinnatiUSA
  5. 5.The Ohio State UniversityColumbusUSA

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