Issues in Estimating Interpretable Lower Order Factors in Second-Order Hierarchical Models: Commentary on Clark et al. (2021)

2021 ◽  
pp. 216770262110351
Author(s):  
Tyler M. Moore ◽  
Benjamin B. Lahey
Keyword(s):  
Lower Order ◽  
Hierarchical Modeling ◽  
Simulated Data ◽  
Second Order ◽  
General Factor ◽  
Bifactor Models ◽  
Specific Factors ◽  
Factor Modeling ◽  
Highly Correlated ◽  
Criterion Variables

In a previous issue of Clinical Psychological Science, Clark and colleagues asserted that lower order factors in second-order models are comparable with specific factors in bifactor models when residualized on the general factor. Modeling simulated data demonstrated that residualized lower order factors are correlated with bifactor-specific factors only to the extent that factor loadings are proportional. Modeling actual data with violations of proportionality showed that specific and residualized lower order factors are not always highly correlated and have differential correlations with criterion variables even when both models fit acceptably. Because proportionality constraints limit only second-order models, bifactor models should be the first option for hierarchical modeling.

scholarly journals Criterion Validity and Relationships between Alternative Hierarchical Dimensional Models of General and Specific Psychopathology

2020 ◽  
Author(s):  
Tyler M. Moore ◽  
Antonia N. Kaczkurkin ◽  
E. Leighton Durham ◽  
Hee Jung Jeong ◽  
Malerie G. McDowell ◽  
...  
Keyword(s):  
Lower Order ◽  
Statistical Models ◽  
Child Psychopathology ◽  
Criterion Validity ◽  
Second Order ◽  
Specific Factor ◽  
General Factor ◽  
External Criterion ◽  
Bifactor Models ◽  
External Variables

ABSTRACTPsychopathology can be viewed as a hierarchy of correlated dimensions. Many studies have supported this conceptualization, but they have used alternative statistical models with differing interpretations. In bifactor models, every symptom loads on both the general factor and one specific factor (e.g., internalizing), which partitions the total explained variance in each symptom between these orthogonal factors. In second-order models, symptoms load on one of several correlated lower-order factors. These lower-order factors load on a second-order general factor, which is defined by the variance shared by the lower-order factors. Thus, the factors in second-order models are not orthogonal. Choosing between these valid statistical models depends on the hypothesis being tested. Because bifactor models define orthogonal phenotypes with distinct sources of variance, they are optimal for studies of shared and unique associations of the dimensions of psychopathology with external variables putatively relevant to etiology and mechanisms. Concerns have been raised, however, about the reliability of the orthogonal specific factors in bifactor models. We evaluated this concern using parent symptom ratings of 9-10 year olds in the ABCD Study. Psychometric indices indicated that all factors in both bifactor and second-order models exhibited at least adequate construct reliability and estimated replicability. The factors defined in bifactor and second-order models were highly to moderately correlated across models, but have different interpretations. All factors in both models demonstrated significant associations with external criterion variables of theoretical and clinical importance, but the interpretation of such associations in second-order models was ambiguous due to shared variance among factors.General Scientific SummarySome investigators have proposed that viewing the correlated symptoms of psychopathology as a hierarchy in which all symptoms are related to both a general (p) factor of psychopathology and a more specific factor will make it easier to distinguish potential risk factors and mechanisms that are nonspecifically related to all forms of psychopathology versus those that are associated with specific dimensions of psychopathology. Parent ratings of child psychopathology items from the Adolescent Brain Cognitive Development (ABCD) Study were analyzed using two alternative statistical models of the proposed hierarchy. All factors of psychopathology defined in both bifactor and second-order models demonstrated adequate psychometric properties and criterion validity, but associations of psychopathology factors with external variables were more easily interpreted in bifactor than in second-order models.

scholarly journals Riskier Tests of the Validity of Bifactor Models of Psychopathology

2019 ◽  
Author(s):  
Ashley L. Watts ◽  
Holly Poore ◽  
Irwin Waldman
Keyword(s):  
Community Sample ◽  
General Factor ◽  
Symptom Dimensions ◽  
Bifactor Models ◽  
Specific Factors ◽  
Psychopathology Symptom ◽  
Using Data ◽  
P Factor ◽  
Correlated Factors ◽  
Additional Variance

We advanced several “riskier tests” of the validity of bifactor models of psychopathology, which included that the general and specific factors should be reliable and well-represented by their indicators, and that including a general factor should improve the correlated factor model’s external validity. We compared bifactor and correlated factors models using data from a community sample of youth (N=2498) whose parents provided ratings on psychopathology and external criteria (i.e., temperament, aggression, antisociality). Bifactor models tended to yield either general or specific factors that were unstable and difficult to interpret. The general factor appeared to reflect a differentially-weighted amalgam of psychopathology rather than a liability for psychopathology broadly construed. With rare exceptions, bifactor models did not explain additional variance in psychopathology symptom dimensions or external criteria compared with correlated factors models. Together, our findings call into question the validity of bifactor models of psychopathology, and the p-factor more broadly.

scholarly journals The p Factor and the n Factor: Associations Between the General Factors of Psychopathology and Neuroticism in Children

2019 ◽  
Author(s):  
Cassandra M Brandes ◽  
Kathrin Herzhoff ◽  
Avante J Smack ◽  
Jennifer L Tackett
Keyword(s):  
Mental Disorders ◽  
Age Groups ◽  
Negative Emotionality ◽  
General Factor ◽  
General Psychopathology ◽  
Bifactor Models ◽  
Specific Factors ◽  
Latent Dimension ◽  
P Factor ◽  
Internalizing And Externalizing

Research across age groups has consistently indicated that psychopathology has a general factor structure, such that there is a broad latent dimension (or p factor) capturing variance common to all mental disorders, as well as specific internalizing and externalizing factors. This research has found that the p factor overlaps substantially with trait negative emotionality (or neuroticism). However, less is known about the psychological substance of the specific factors of the general psychopathology model, or how lower-order facets of neuroticism may relate to each psychopathology factor. We investigated the structure of neuroticism and psychopathology, as well as associations between these domains in a sample of 695 pre-adolescent children using multi-method assessments. We found that both psychopathology and neuroticism may be well-characterized by bifactor models, and that there was substantial overlap between psychopathology (p) and neuroticism (n) general factors, as well as between specific factors (Internalizing with Fear, Externalizing with Irritability).

scholarly journals Bifactor Models for Predicting Criteria by General and Specific Factors: Problems of Nonidentifiability and Alternative Solutions

2018 ◽  
Vol 6 (3) ◽  
pp. 42 ◽  
Author(s):  
Michael Eid ◽  
Stefan Krumm ◽  
Tobias Koch ◽  
Julian Schulze
Keyword(s):  
Factor Models ◽  
Formal Proof ◽  
Bifactor Model ◽  
First Order ◽  
Applied Model ◽  
Measurement Models ◽  
Bifactor Models ◽  
Specific Factors ◽  
Order Factor ◽  
Criterion Variables

The bifactor model is a widely applied model to analyze general and specific abilities. Extensions of bifactor models additionally include criterion variables. In such extended bifactor models, the general and specific factors can be correlated with criterion variables. Moreover, the influence of general and specific factors on criterion variables can be scrutinized in latent multiple regression models that are built on bifactor measurement models. This study employs an extended bifactor model to predict mathematics and English grades by three facets of intelligence (number series, verbal analogies, and unfolding). We show that, if the observed variables do not differ in their loadings, extended bifactor models are not identified and not applicable. Moreover, we reveal that standard errors of regression weights in extended bifactor models can be very large and, thus, lead to invalid conclusions. A formal proof of the nonidentification is presented. Subsequently, we suggest alternative approaches for predicting criterion variables by general and specific factors. In particular, we illustrate how (1) composite ability factors can be defined in extended first-order factor models and (2) how bifactor(S-1) models can be applied. The differences between first-order factor models and bifactor(S-1) models for predicting criterion variables are discussed in detail and illustrated with the empirical example.

scholarly journals The p Factor and the n Factor: Associations Between the General Factors of Psychopathology and Neuroticism in Children

2019 ◽  
Vol 7 (6) ◽  
pp. 1266-1284 ◽  
Author(s):  
Cassandra M. Brandes ◽  
Kathrin Herzhoff ◽  
Avanté J. Smack ◽  
Jennifer L. Tackett
Keyword(s):  
Mental Disorders ◽  
Age Groups ◽  
Negative Emotionality ◽  
General Factor ◽  
General Psychopathology ◽  
Bifactor Models ◽  
Specific Factors ◽  
Latent Dimension ◽  
P Factor ◽  
Internalizing And Externalizing

Research across age groups has consistently indicated that psychopathology has a general factor structure such that a broad latent dimension (or p factor) captures variance common to all mental disorders as well as specific internalizing and externalizing factors. This research has found that the p factor overlaps substantially with trait negative emotionality (or neuroticism). However, less is known about the psychological substance of the specific factors of the general psychopathology model or how lower-order facets of neuroticism may relate to each psychopathology factor. We investigated the structure of neuroticism and psychopathology as well as associations between these domains using multimethod assessments in a sample of 695 preadolescent children. We found that both psychopathology and neuroticism may be well characterized by bifactor models and that there was substantial overlap between psychopathology (p) and neuroticism (n) general factors as well as between specific factors (Internalizing with Fear, Externalizing with Irritability).

Bifactor Models of Attention-Deficit/Hyperactivity Disorder (ADHD): An Evaluation of Three Necessary but Underused Psychometric Indexes

Assessment ◽  
2016 ◽  
Vol 25 (7) ◽  
pp. 885-897 ◽  
Author(s):  
Víctor B. Arias ◽  
Fernando P. Ponce ◽  
Daniel. E. Núñez
Keyword(s):  
Attention Deficit Hyperactivity Disorder ◽  
Attention Deficit ◽  
Measurement Model ◽  
Clinical Samples ◽  
General Factor ◽  
Common Variance ◽  
Hyperactivity Disorder ◽  
Bifactor Models ◽  
Specific Factors ◽  
Inattention And Hyperactivity

Background: In the past decade, the bifactor model of attention-deficit/hyperactivity disorder (ADHD) has been extensively researched. This model consists of an ADHD general dimension and two specific factors: inattention and hyperactivity/impulsivity. All studies conclude that the bifactor is superior to the traditional two-correlated factors model, according to the fit obtained by factor analysis. However, the proper interpretation of a bifactor not only depends on the fit but also on the quality of the measurement model. Objective: To evaluate the model-based reliability, distribution of common variance and construct replicability of general and specific ADHD factors. Method: We estimated expected common variance, omega hierarchical/subscale and H-index from standardized factor loadings of 31 ADHD bifactor models previously published. Results and Conclusion: The ADHD general factor explained most of the common variance. Given the low reliable variance ratios, the specific factors were difficult to interpret. However, in clinical samples, inattention acquired sufficient specificity and stability for interpretation beyond the general factor. Implications for research and clinical practice are discussed.

scholarly journals Going “Up” to Move Forward: S-1 Bifactor Models and the Study of Neurocognitive Abilities in Psychopathology

2021 ◽  
Vol 18 (14) ◽  
pp. 7413
Author(s):  
Darren Haywood ◽  
Frank D. Baughman ◽  
Barbara A. Mullan ◽  
Karen R. Heslop
Keyword(s):  
Structural Models ◽  
General Factor ◽  
Neurocognitive Performance ◽  
Diagnostic Stability ◽  
Psychopathological Symptoms ◽  
Simulation Techniques ◽  
Wide Range ◽  
Bifactor Models ◽  
Specific Factors ◽  
P Factor

Recently, structural models of psychopathology, that address the diagnostic stability and comorbidity issues of the traditional nosological approach, have dominated much of the psychopathology literature. Structural approaches have given rise to the p-factor, which is claimed to reflect an individual’s propensity toward all common psychopathological symptoms. Neurocognitive abilities are argued to be important to the development and maintenance of a wide range of disorders, and have been suggested as an important driver of the p-factor. However, recent evidence argues against p being an interpretable substantive construct, limiting conclusions that can be drawn from associations between p, the specific factors of a psychopathology model, and neurocognitive abilities. Here, we argue for the use of the S-1 bifactor approach, where the general factor is defined by neurocognitive abilities, to explore the association between neurocognitive performance and a wide range of psychopathological symptoms. We use simulation techniques to give examples of how S-1 bifactor models can be used to examine this relationship, and how the results can be interpreted.

scholarly journals Misbegotten Methodologies and Forgotten Lessons from Tom Swift’s Electric Factor Analysis Machine: A Demonstration with Competing Structural Models of Psychopathology

2021 ◽  
Author(s):  
Ashley Lauren Greene ◽  
Ashley L. Watts ◽  
Miriam K. Forbes ◽  
Roman Kotov ◽  
Robert Krueger ◽  
...  
Keyword(s):  
Factor Analysis ◽  
Model Misspecification ◽  
Theory Development ◽  
Structural Models ◽  
General Factor ◽  
Psychological Constructs ◽  
Methodological Choices ◽  
Bifactor Models ◽  
Specific Factors ◽  
P Factor

Confirmatory factor analysis (CFA) and its bifactor models are popular in empirical investigations of the factor structure of psychological constructs. CFA offers straightforward hypothesis testing but has notable pitfalls, such as the imposition of strict assumptions (i.e., simple structure) that obscure unmodeled complexity. Due to the limitations of bifactor CFAs, they have yielded anomalous results across samples and studies that suggest model misspecification (e.g., evaporating specific factors and unexpected loadings). We propose the use of exploratory factor analysis (EFA) to evaluate the structural validity of CFA solutions—either before or after the estimation of more restrictive CFA models—to (1) identify model misspecifications that may drive anomalous estimates and (2) confirm CFA models by examining whether hypothesized structures emerge with limited researcher input. We evaluated the degree to which predominant factor structures were invariant across contexts along the exploratory-confirmatory continuum and demonstrate how poor methodological choices can distort results and impede theory development. All models fit well, but there were numerous differences in replicability and substantive interpretability. Several similarities emerged between bifactor CFA and EFA models, including evidence of overextraction, the collapse of specific factors onto the general factor, and subsequent shifts in how the general factor was defined. We situate these methodological shortcomings within the broader literature on structural models of psychopathology, articulate implications for theories (such as the p-factor) that are borne out of factor analysis, outline several remedies for problems encountered when performing exploratory bifactor analysis, and propose alternative specifications for confirmatory bifactor models.

Modeling General and Specific Abilities

Assessment ◽  
2016 ◽  
Vol 23 (6) ◽  
pp. 698-706 ◽  
Author(s):  
Dennis J. McFarland
Keyword(s):  
Test Performance ◽  
Cross Validation ◽  
Simulated Data ◽  
Independent Data ◽  
Fit Indices ◽  
Data Set ◽  
Bifactor Models ◽  
Specific Factors ◽  
Exact Amount ◽  
Woodcock Johnson

The present study examined issues related to structural modeling of abilities by the use of simulated data as well as analysis of the standardization data from the Woodcock–Johnson-III. In both cases, results were evaluated with cross-validation. Simulation results showed that cross-validation with an independent data set was more successful in identifying the model that was used to generate test scores than were several fit indices. Analysis of the Woodcock–Johnson-III standardization data with cross-validation showed that bifactor models provided better fit than hierarchical or correlated factor models. This was true considering both fit indices and cross-validation. General and specific factors shared a considerable amount of variance as evaluated by using the bifactor models to partition variance. The results of the present study suggest that there is a certain degree of ambiguity in determining the exact amount of covariance in test performance accounted for by general and specific factors. This calls in to question the practice of adjusting or controlling for general abilities when evaluating measures of specific abilities. Evidence for the validity of a construct should not be limited to factor analysis of tests purported to measure that construct.

Riskier Tests of the Validity of the Bifactor Model of Psychopathology

2019 ◽  
Vol 7 (6) ◽  
pp. 1285-1303 ◽  
Author(s):  
Ashley L. Watts ◽  
Holly E. Poore ◽  
Irwin D. Waldman
Keyword(s):  
Community Sample ◽  
General Factor ◽  
Symptom Dimensions ◽  
Bifactor Models ◽  
Specific Factors ◽  
Psychopathology Symptom ◽  
Using Data ◽  
P Factor ◽  
Correlated Factors ◽  
Additional Variance

We advanced several “riskier tests” of the validity of bifactor models of psychopathology, which included that the general and specific psychopathology factors should be reliable and well represented by their respective indicators and that including a general factor should improve on the correlated factor model’s external validity. We compared bifactor and correlated factors models of psychopathology using data from a community sample of youth ( N = 2,498) whose parents provided ratings on psychopathology and theoretically relevant external criteria (i.e., personality, aggression, antisociality). Bifactor models tended to yield either general or specific factors that were unstable and difficult to interpret. The general factor appeared to reflect a differentially weighted amalgam of psychopathology rather than a liability for psychopathology broadly construed. With rare exceptions, bifactor models did not explain additional variance in first-order psychopathology symptom dimensions or external criteria compared with correlated factors models. Together, our findings call into question the validity of bifactor models of psychopathology and the p factor more broadly.

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