The p factor is the sum of its parts, for now
Authors: Eiko I. Fried, Ashley L. Greene, Nicholas R. Eaton
Journal: World Psychiatry (2021)

The general factor of psychopathology, or p factor, has received increasing attention over the last half decade, but questions remain about how to best conceptualize it1, 2. Here, we use data from a large-scale sur­vey (National Epidemiologic Survey on Alcohol and Related Conditions, NESARC), conducted in a nationally representative US sample, to demonstrate that, statistically, p is nearly identical to the sum of diagnoses it is estimated upon. The same holds for specific factors such as internalizing and externalizing, and our results are robust to various estimation methods. We discuss implications of this finding for the nature of these factors, and raise the question whether the sole reliance on reflective latent variable models used in the p factor literature is justified, given that nearly identical scores can be obtained by a much simpler statistical procedure that has fewer parameters and imposes fewer assumptions on the data. Questions about the interpretation of p are important, because this factor carries at least two meanings. Statistically, p refers to a latent variable estimated on a covariance matrix of psychopathology symptoms or diagnoses in a given dataset. The field has utilized one specific class of models, the reflective latent variable model, in several flavors, such as the bifactor and second-order factor models, that decompose variance somewhat differently3. No matter the specific model, general factors such as p necessarily emerge when data feature a positive manifold4. Statistically speaking, p is just a different way of stating that observed items are positively related. The p factor’s second meaning is conceptual: what p represents. Conceptualizations of p vary widely, including severity/dysfunction and a general liability for psychopathology through non-specific genetic and environmental influences, disordered thought processes, and/or trait-like attributes (e.g., negative emotionality)1, 2. It is an open question how these conceptualizations of p fit the data and methods used in the field. If p represents liability, for example, it is unclear why models are estimated on data on symptoms and diagnoses rath­er than data on risk factors and etiology, such as early adversity, mentalization/reflective functioning, and attachment insecurity5, 6. To shed light on the relation between the statistical and the conceptual p factor, we estimated two types of general factor models: the bifactor model (M1) and the higher-order factor model (M2). We repeated analyses for these general factor models’ specific factors (distress, fear and externalizing), as well as the correlated 3-factor (M3: distress, fear, externalizing) and correlated 2-factor (M4: internalizing, externalizing) models. The rationale for estimating numerous models was to investigate the degree to which latent variables are generally more than the sum of their indicators and to rule out that results are due to one particular parameterization. We utilized two waves of the NESARC dataset (W1: N=43,093, W2 follow-up: N=34,653; see https://osf.io/yrpw8 for details), which has commonly been used in the p factor literature7. Our main findings are as follows. First, in both waves, we identified high correlations between sum scores of all diagnoses and p, approaching unity for both M1 (range: 0.87-0.99) and M2 (range: 0.87-1.00). Second, domain-specific factors and their respective sum scores (e.g., externalizing factor with sum of externalizing diagnoses) were also highly related across all models: 0.82-0.94 for M1, 0.87-0.96 for M2, 0.78-1.00 for M3, and 0.82-0.96 for M4. Third, correlations between W1 and W2 latent variables were strikingly similar to those between W1 and W2 sum scores (e.g., M1 p factor vs. total sum score: 0.40 vs. 0.44). These findings hold regardless of whether the relations between latent factors and sum scores were estimated using factor scores or a single structural equation model. In sum, we show that the p factor as well as domain-specific factors are identical or nearly identical with the sum of diagnoses that go into these respective factors, and that results hold in both general factor and correlated factor models. We see three main implications of our findings. First, we compare two types of models: a simple sum of indicators vs. a class of highly sophisticated structural equation models that estimate a large number of parameters and impose considerable assumptions on the data, such as hierarchies in which factors are organized, or relations among factors that are constrained to zero3. Both models produce nearly identical scores for participants. If replicated in other studies, this finding suggests that the use of reflective la­tent variable models should be considered more carefully: what are the specific ben­efits of this modeling framework for the p factor literature, and do they outweigh the potential costs, such as over-parameterization and stringent assumptions imposed on the data3, 4? Such deliberations will ben­efit from explicit goals to determine wheth­er specific statistical models are adequate in the context of a given research question. In general, scientific progress is often ham­pered by overreliance on any particular type of model8, and thinking more clearly about conceptualizations of p may offer ­opportunities to diversify methodology. Second, we provide evidence that p is simply a re-expression of the sum of diagnoses that individuals experience. This is not surprising: about 70 years ago, Cattell9 described scores on the general factor as “essentially the sum of the scores”, and Lahey et al1 acknowledge the p factor is a “weighted average” of items. Our results imply that p represents severity or comorbidity, not liability, much in the same way as the sum of flu symptoms provides a rough index for severity, not liability. Whether competing accounts of p offer better explanations, such as the idea that it represents liability, requires that models be estimated on variables that actually denote liability, rather than variables denoting severity and comorbidity. Third, if p is a mere index of the data, this suggests that the meaning of p will only be invariant across studies inasmuch as the data that go into our models are invariant across studies. Overall, data can be brought to bear on theories when statistical models impose assumptions on the data that are in line with the theories. The p factor literature has been largely atheoretical and primarily concerned with description of data – a crucial first step to establish phenomena that can then be explained. But let us not lose sight of the fact that p is an effect that needs to be explained (i.e., explanandum), not something that does the explaining (i.e., explanans). It necessarily emerges from a positive manifold, and tells us nothing about the mechanisms that generated the data4, 6. Further, if the goal is the description of data, it is unclear why the reflective latent variable model that is solely relied upon in the literature should be the only model suited for this goal. Thinking more clearly about theories of p1, 2, and spelling out these theories precisely, will help adjudicate between different conceptual accounts of p. Criticizing and modifying theories requires that we know exactly where they start and end. Clearer theories will then facilitate choosing appropriate statistical models that can in turn guide theory reform.