Hierarchical dimensional models of psychopathology: yes, but…
Authors: Thomas M. Achenbach
Journal: World Psychiatry (2021)

I strongly concur with Lahey et al's advocacy of hierarchical dimensional models for psychopathology1. How could I do otherwise? I have been developing and advocating such models for over half a century2, 3. But God (or the devil, if you prefer) is in the details. Consequently, I address here some details of Lahey et al's paper that must be considered in order to advance our knowledge of psychopathology and ways of modeling it. First, although its title does not include the word "dimensional", the paper focuses mainly on hierarchies of dimensions based on factor analyses of associations between items that are rated in samples of individuals. The contents of the dimensions – i.e., the particular sets of items that are found to have substantial loadings on particular factors – are shaped by the nature of the items themselves (e.g., descriptive vs. inferential); the scales for rating the items (e.g., present/absent vs. 0-1-2); the content of the items (e.g., diagnostic criteria vs. colloquial descriptions); the periods spanned by the ratings (e.g., days vs. weeks, months or years); people who rate the sample of individuals (e.g., self vs. collaterals or clinicians); the age of assessed individuals (e.g., preschool vs. school age, adult or elderly); methods for computing associations between item ratings (e.g., Pearson r vs. tetrachoric); methods of factor analysis (e.g., principal factor vs. principal component); sample size (e.g., N=100 vs. 1,000); criteria for retaining factors (e.g., Kaiser's criterion vs. scree plot); criteria for retaining items on each factor (e.g., loadings that are statistically significant vs. ≥.30); methods for applying factors to the scoring of individuals (e.g., factor scores vs. unit weighting of items), and so forth. The diverse results obtainable with factor-analytic methods argue against expecting a single model to validly represent all psychopathology for all ages, genders, cultural groups, sources of data, and degrees of severity. Instead, statistical tools such as factor analysis organize large quantities of data into models whose value depends on judgments and criteria external to the statistical tools. Consequently, rather than seeking a single model for all psychopathology, we need to compare the value of different models for different purposes. As our methods and knowledge advance, we may find that different models are valid and useful for different purposes. Second, Lahey et al focus on the relative merits of second-order versus bifactor models for representing psychopathology hierarchically. Second-order factor analysis derives higher-order, broad-spectrum factors by analyzing associations between scores obtained in samples of individuals on first-order, narrow-spectrum factors, often called syndromes. As an example, Lahey et al repeatedly cite second-order factors designated as internalizing and externalizing, which are found so often that the constructs they represent have been used in over 75,000 published studies2, 4. Second-order factor analysis takes first-order factors (syndromes) at face value and then analyzes associations among scores obtained in large samples of individuals on the syndromes to derive groupings of syndromes. Second-order internalizing factors often include first-order syndromes comprising problems such as depression, anxiety, social withdrawal, and somatic complaints without apparent medical cause. Second-order externalizing factors, by contrast, often include first-order syndromes comprising problems such as aggressive and rule-breaking behavior. Bifactor analysis partitions the variance in ratings of each problem item into variance unique to the problem itself and variance in the problem's ratings that is shared by a general psychopathology (p) factor. Because second-order factor analysis retains first-order syndromes as constructs operationally defined as the aggregated scores of their constituent problems, it maps more closely onto clinical practice than bifactor analysis, which focuses on components of variance in the ratings of each problem. Neither bifactor analysis nor second-order factor analysis is necessarily optimal for all applications, and each has many methodological variations. The essential point is that we can usefully view psychopathology in terms of hierarchies that start at the "bottom" (the most molecular level) with specific problems. Associations among the problems are then analyzed to yield narrow-spectrum syndromes roughly analogous to DSM and ICD diagnoses. Associations among the syndromes are analyzed to yield broad-spectrum groupings such as those designated as internalizing and externalizing. Third, the p factor can be conceptualized as the apex of hierarchies that range from specific problems at the bottom, through narrow-spectrum syndromes, broad-spectrum groupings such as internalizing and externalizing, and culminate in a dimension comprising all the problems. General psychopathology dimensions can be obtained with both second-order and bifactor methods. Measures based on diverse problems – such as p – are likely to be especially good prognosticators, just as aggregations of diverse measures of ability are better indices of general intelligence (g) and better prognosticators than are narrow-spectrum measures of ability. There are multiple biological and environmental reasons for this, but neither p nor g have single gold-standard operational definitions. Lahey et al argue for the superiority of p factors derived from bifactor analyses that weight individual problems on the basis of residual variance (i.e., the variance remaining after lower-order variance is extracted). However, loadings of problems on the first principal factor can also be used to weight items on p. Item weights are affected by the factor-analytic method, the procedures for assessing problems, the samples from which the data are obtained, and so forth. Moreover, because the precise value of each problem's weight may fail to replicate in new samples, unit weighting of problems is often more robust. Fourth, Lahey et al argue for a "dimensional measure of psychopathology that includes all symptoms". Unfortunately, this is unrealistic, because it implies that the same measure of "all symptoms" would suffice for people of all ages, genders, cultures, and degrees of impairment. Regarding age, for example, the relevant "symptoms" and methods for assessing them differ greatly between such ages as 1, 9, 18, 50 and 80 years. It is also unrealistic to expect that "all symptoms" can be identified before research yields operational definitions of disorders in people of each age, assessed by multiple methods, such as self-reports, collateral reports, clinicians' observations, tests, and biomedical procedures. And the term "symptom" assumes that all phenotypic problems are clinical manifestations of underlying diseases, which is a problematic assumption. Finally, at the end of the paper, Lahey et al allude to the need for "replications in a variety of cultures and languages". Nearly all of their references are based on Anglophone samples. Rather than being added as an afterthought, multicultural studies of the structure, prevalence, and other aspects of psychopathology should be fundamental components of ongoing research on hierarchical models5, 6. To inspire confidence, hierarchical models need to be continually tested via methods such as confirmatory factor analysis of data from samples differing from those on which the models were based, rather than accepting the results of exploratory analyses at face value. Despite the growing popularity of hierarchical dimensional models, their value may be undercut if researchers fail to deal scientifically with the many details to be mastered in properly constructing, testing, and applying such models.