An empirical examination of distributional assumptions underlying the relationship between personality disorder symptoms and personality traits

Personality disorder (PD) researchers have called for an integration of normal and pathological personality functioning within comprehensive dimensional models of personality (e.g., Depue & Lenzenweger, 2005; Widiger Livesley, & Clark, 2009). It has been argued that normal personality exists on a continuum of functioning with PDs (Widiger & Trull, 2007). A large empirical literature examining the relationship between traits and PDs contributed to the seminal decision to use a dimensional trait system to conceptualize phenotypic variation in PD in DSM-5 (Skodol et al., 2011). This research relies primarily on cross-sectional correlations and linear regression to model the relationship between personality traits and PD symptoms. However, these analytic tools suffer from limitations when the underlying distribution of the variables is severely non-normal, as is the case with PD symptoms in the population. Alternative approaches that more accurately model the observed PD symptom distribution may provide better estimates of the relationship between personality and its disorder, and may offer new insights into the nature of that relationship. The extant nosology of PDs represents personality pathology as a collection of “distinct clinical syndromes” (p. 689; APA, 2000) that differ categorically from normative functioning and each other. These distinctions have been criticized as arbitrary and lacking in robust scientific support (Widiger & Trull, 2007), and diagnostic criteria treated as dimensional markers for disorders perform better by empirical standards (Morey et al., 2007). However, measuring disorders dimensionally cannot confirm their continuity with normal functioning (Lenzenweger & Clarkin, 2005), and the accumulated research presents a mixed picture related to this issue. Meta-analyses (Samuel & Widiger, 2008, Saulsman & Page, 2004) demonstrate that basic personality traits exhibit significant and replicable relationships to PD, but the association between traits and PDs are generally only modest in size (Mdn |r| = .15; Range = .02–.54; Samuel & Widiger, 2008). Furthermore, in regression models, the five-factor domains and facets generally only explain a minority of the variance in PDs (e.g., Bagby, Costa, Widiger, Ryder, & Marshall, 2005). Thus, normal personality traits and PD are not interchangeable representations of functioning, despite clearly recognizable shared content (Krueger et al., 2011). Other researchers and theorists have highlighted the general impairment associated with PDs (Kernberg, 1984; Livesley & Jang, 2005; Pincus, 2005). Relatedly, a number of investigators have found that PD is primarily characterized by higher Neuroticism, lower Conscientiousness, and lower Agreeableness, with less in the way of distinction beyond this core trait profile (Hopwood et al., 2011; Morey et al., 2002; Saulsman & Page, 2004). Thus, it may be that a particular combination of traits reflects personality pathology generally, with further differentiation occurring in the presence of this profile. The question of continuity in personality and its pathology has taken center stage in the development of the DSM-5 which will shift to a dimensional model based on the robust empirical findings suggesting that PD is fundamentally dimensional in nature (Skodol et al., 2011). However, in part due to issues raised here, DSM-5 will distinguish between personality dysfunction, and the description of that dysfunction using pathological traits (Hopwood et al., 2011; Krueger et al., 2011). Indeed, the sum of the empirical literature leaves an unclear picture of how PD and personality traits are related to each other. It may be that PD is dimensionally continuous with basic personality traits (e.g., Depue & Lenzenweger, 2005). Alternatively, continuities and discontinuities may exist in these relationships, with some driven by the presence of PD and others, perhaps more subtle, driven by the severity of PD beyond its presence (see Lenzenweger & Clarkin, 2005). What is clear is that the theoretical goal of integrating normative personality traits and PD remains elusive. The key theoretical questions of how personality and PD relate to one another are also inherently questions of methodology. Dimensional approaches can make varied distributional assumptions that may have relevance for advancing the understanding of the relationship between normal and abnormal personality. Research examining this question relies almost exclusively on standard correlation and linear regression. These approaches make several important assumptions (i.e., normality of residuals, homoscedasticity, linearity of relationship, independence), that, when violated, can bias estimation (Cohen, Cohen, West, & Aiken, 2003). Less serious are biased standard errors, which can produce incorrect significance tests for parameters. More serious violations occur when the actual effect of a relationship is misestimated. A major contributing source to the violation of these assumptions is the distribution of the variables being modeled. In the population, the actual distribution of PD symptoms is highly positively skewed with a majority of individuals suffering from no symptoms. Figure 1 provides an example of such a distribution using the narcissistic personality disorder (NPD) features in the first wave of the Longitudinal Study of Personality Disorders (LSPD; Lenzenweger, 1999), the dataset used here. This histogram is characteristic of a count distribution. Modeling techniques for counts are primarily based on the Poisson and Negative-Binomial (NB) distributions and can be used for regression when appropriate (Cameron & Trivedi, 1998; Long, 1997). Of note is the large number of zeros in the distribution, which has important implications for modeling the relationship between the symptoms and other variables of interest. These zeros carry important information about who does and does not possess symptoms of PD. With large numbers of zeros in the data, two potential modifications to basic count models are recommended: zero-inflated and hurdle models (Atkins & Gallop, 2007; Cameron & Trivedi, 1998; Long, 1997). Zero-inflated models estimate a group of individuals based on the excess of zeros beyond a standard Poisson or NB model, which are treated as individuals who can only take on a zero value. Hurdle models make a binary distinction between those who have a zero value vs. those who have a non-zero value. Despite this distinction in the treatment of zero-values, both models estimate separate regression coefficients for the zero vs. non-zero (e.g., absence vs. presence of PD) and the count (e.g., severity of PD) portion of the models. These models are ideal for evaluating whether the traits that give rise to any symptoms of PDs are the same as those that predict the number of symptoms once present. Figure 1 Observed LSPD Narcissistic Personality Disorder Features. The current study explores the relationship of personality traits to PD symptoms using regression models capable of appropriately modeling the distribution of symptoms in the population. We use the LSPD sample, which is made up of participants recruited both with and without significant pathology, unlike samples selected based on shared diagnostic status or for high levels of pathology. As a result, the distributions of PD symptoms closely matches those found in epidemiological samples (Lenzenweger, 2008). The LSPD dataset is ideal for the types of investigations pursued here because it captures the boundary between those individuals whose personalities function well and those who evidence dysfunction. Our first aim was to evaluate whether the assumptions of linear regression are violated when predicting PD symptoms and to compare Poisson, ZIP, PH, NB, ZINB, and NBH regression models that predict PD symptoms from personality trait scores. Our second and more substantive aim involves comparing the patterns of significant regression coefficients to determine the effect of varying distributional assumptions on the relationship between traits and PDs. Attention is also given to differences in patterns in the prediction of presence vs. severity of PD features in the zero-inflated/hurdle models.