Taxometric analysis as a general strategy for distinguishing categorical from dimensional latent structure

Statistical analyses investigating latent structure can be divided into those that estimate structural model parameters and those that detect the structural model type. The most basic distinction among structure types is between categorical (discrete) and dimensional (continuous) models. It is a common, and potentially misleading, practice to apply some method for estimating a latent structural model such as factor analysis without first verifying that the latent structure type assumed by that method applies to the data. The taxometric method was developed specifically to distinguish between dimensional and 2-class models. This study evaluated the taxometric method as a means of identifying categorical structures in general. We assessed the ability of the taxometric method to distinguish between dimensional (1-class) and categorical (2-5 classes) latent structures and to estimate the number of classes in categorical datasets. Based on 50,000 Monte Carlo datasets (10,000 per structure type), and using the comparison curve fit index averaged across 3 taxometric procedures (Mean Above Minus Below A Cut, Maximum Covariance, and Latent Mode Factor Analysis) as the criterion for latent structure, the taxometric method was found superior to finite mixture modeling for distinguishing between dimensional and categorical models. A multistep iterative process of applying taxometric procedures to the data often failed to identify the number of classes in the categorical datasets accurately, however. It is concluded that the taxometric method may be an effective approach to distinguishing between dimensional and categorical structure but that other latent modeling procedures may be more effective for specifying the model.     

Type or dimension? A taxometric investigation of flashbulb memories

Flashbulb memories (FBMs) have been defined as vivid and detailed memory of a reception context under which one first heard of a public and unexpected emotional event. One of the issues still open for research on FBMs is to understand whether this latent construct has to be conceptualised as a continuum with other autobiographical memories, or whether it represents a special cluster of memories. This theoretical distinction has some implications for the measurement of the phenomenon, that could be assessed by a dimensional or categorical (taxonic) model. The current study attempted to provide an empirical answer to the problem of FBM measurement, by adopting a taxometric analysis. The main strength of these analyses is to treat taxonic and dimensional models as two competing hypotheses and to evaluate the relative support for each of them. Taxometric analyses were applied to FBM data for the Pope's death, and results supported the taxonic structure of FBMs.     

Type or dimension? A taxometric investigation of flashbulb memories

Flashbulb memories (FBMs) have been defined as vivid and detailed memory of a reception context under which one first heard of a public and unexpected emotional event. One of the issues still open for research on FBMs is to understand whether this latent construct has to be conceptualised as a continuum with other autobiographical memories, or whether it represents a special cluster of memories. This theoretical distinction has some implications for the measurement of the phenomenon, that could be assessed by a dimensional or categorical (taxonic) model. The current study attempted to provide an empirical answer to the problem of FBM measurement, by adopting a taxometric analysis. The main strength of these analyses is to treat taxonic and dimensional models as two competing hypotheses and to evaluate the relative support for each of them. Taxometric analyses were applied to FBM data for the Pope's death, and results supported the taxonic structure of FBMs.     

Is schizotypy taxonic? Response to

Beauchaine, Lenzenweger, and Waller (2008) criticize our taxometric study of schizotypy (Rawlings, Williams, Haslam, & Claridge, in press) on a variety of methodological and philosophical grounds. We argue that their critique selectively applies more stringent standards to our work than to studies supporting their view that schizotypy is taxonic (i.e., categorical). Many of their criticisms apply at least equally to existing studies that offer support for a schizotypy taxon, and these studies are vulnerable to biases favouring taxonic conclusions that were controlled for in our study. Contrary to their criticisms, we did not claim to have disconfirmed previous taxonic findings about schizotypy, and our findings positively support dimensional models of schizotypy rather than merely being null results. Similarly, our findings are not artefacts of the sampling or measurement decisions that they question. Even well-replicated taxometric findings are not immune to empirical challenge, and evaluation of such challenges must be even-handed.     

Assigning cases to groups using taxometric results: an empirical comparison of classification techniques

Determining whether individuals belong to different latent classes (taxa) or vary along one or more latent factors (dimensions) has implications for assessment. For example, no instrument can simultaneously maximize the efficiency of categorical and continuous measurement. Methods such as taxometric analysis can test the relative fit of taxonic and dimensional models, but it is not clear how best to assign individuals to groups using taxometric results. The present study compares the performance of two classification techniques-Bayes' theorem and a base-rate technique--across a wide range of data conditions. The base-rate technique achieves greater classification accuracy and a more even balance between sensitivity and specificity. In addition, the base-rate classification technique is easier to implement than Bayes' theorem and is more versatile in that it can be used when the context of assessment requires that cases be classified despite the absence of latent classes.     

Applying the Bootstrap to Taxometric Analysis: Generating Empirical Sampling Distributions to Help Interpret Results

Meehl's taxometric method was developed to distinguish categorical and continuous constructs. However, taxometric output can be difficult to interpret because expected results for realistic data conditions and differing procedural implementations have not been derived analytically or studied through rigorous simulations. By applying bootstrap methodology, one can generate empirical sampling distributions of taxometric results using data–based estimates of relevant population parameters. We present iterative algorithms for creating bootstrap samples of taxonic and dimensional comparison data that reproduce important features of the research data with good precision and negligible bias. In a series of studies, we demonstrate the utility of these comparison data as an interpretive aid in taxometric research. Strengths and limitations of the approach are discussed along with directions for future research.     

Taxometric analysis of fuzzy categories: a Monte Carlo study

A small Monte Carlo study examined the performance of a form of taxometric analysis (the MAXCOV procedure) with fuzzy data sets. These combine taxonic (categorical) and nontaxonic (continuous) features, containing a subset of casts with intermediate degrees of category membership. Fuzzy data sets tended to yield taxonic findings on plot inspection and two popular consistency tests, even when the degree of fuzziness, i.e., the proportion of intermediate cases, was large. These results suggest that fuzzy categories represent a source of pseudotaxonic inferences, if on is understood in the usual binary, "either-or" fashion. This in turn implies that dichotomous causes cannot be confidently inferred when taxometric analyses yield apparently taxonic findings.     

Inferential errors in taxometric analyses of ordered three-class constructs

Taxometric analysis (Waller & Meehl, 1998) has become a popular tool for investigating whether personality and psychopathology constructs are better modeled as dimensional or categorical. Monte Carlo evidence for the validity of taxometric methods, however, has been restricted to data that are derived either from latent dimensional or dichotomous models. There are various circumstances in which the correct model for a psychosocial construct could involve three or more ordered classes. It was demonstrated both mathematically and empirically that under these circumstances, the results of taxometric analyses can lead to incorrect conclusions about the population structure. Recommendations are provided for future studies intended to distinguish between categorical and dimensional structures.     

Is perfectionism categorical or dimensional? A taxometric analysis

Considerable debate exists within the perfectionism literature regarding whether perfectionism is most accurately conceptualized as a dimensional or categorical construct. Specifically, some researchers have viewed perfectionism as a continuous construct, with extreme scores being associated with negative psychological outcomes (e.g., obsessive-compulsive disorder, eating disorders, etc.). In contrast, others have argued that two distinct forms of perfectionism exist (i.e., adaptive vs. maladaptive perfectionism) that are associated with both positive and negative outcomes. The purpose of this study was to examine the latent structure of perfectionism using taxometric procedures to determine whether perfectionism is most accurately conceptualized as taxonic (categorical) or dimensional (continuous). We applied four taxometric procedures (maximum eigenvalue [Waller & Meehl, 1998], maximum covariance [Meehl & Yonce, 1996], mean above minus below a cut [Meehl & Yonce, 1994], and latent-mode factor analysis [Waller & Meehl, 1998]) to perfectionism data collected from 2 large nonclinical samples. Results provided convergent evidence for a dimensional conceptualization of perfectionism across samples, perfectionism measures, and statistical procedures. We discuss the implications of these findings for the theory, assessment, and investigation of perfectionism are discussed.     

Using taxometric analysis to distinguish a small latent taxon from a latent dimension with positively skewed indicators: the case of involuntary defeat syndrome

Joining the debate on the structure of depression, S. R. H. Bearh and N. Amir (2003) analyzed college students' responses to 6 Beck Depression Inventory (BDI) items with predominantly somatic content and concluded that they identified a small latent taxon corresponding to involuntary defeat syndrome. An exact replication of these analyses yielded virtually identical taxometric results, but parallel analyses of simulated taxonic and dimensional comparison data matching the intercorrelations and skewed distributions of the BDI items showed the results to be more consistent with dimensional than with taxonic latent structure. Analyses in a clinical sample with nonskewed indicators further supported a dimensional interpretation. The authors discuss methodological strategies for conducting and interpreting taxometric analyses under the adverse conditions commonly encountered in psychopathology research, including skewed indicators and small putative taxa.     

Somatic symptom reporting has a dimensional latent structure: Results from taxometric analyses

Medically unexplained symptoms (MUS) are one of the key features of somatoform disorders. Although MUS are currently treated as both categorical (in terms of the diagnosis of somatoform disorders) and dimensional (in terms of quantitative measures of somatization/somatic symptom reporting), little is known about the empirical latent structure of MUS. Using taxometric analyses, the latent structure of somatic symptom reporting was analyzed with the Patient Health Questionnaire (PHQ)-15 in two student samples (N = 782 and N = 2,577) and a primary care sample (N = 519). We applied three popular taxometric methods: Maximum Eigenvalue (MAXEIG), Mean Above Minus Below a Cut (MAMBAC) and Latent-Mode (L-Mode). Simulation data were created to evaluate the appropriateness of the data for our analyses and to create the comparison curve fit index (CCFI) as an objective outcome measure. The results of all taxometric methods in any of the three data sets were in favor of a dimensional solution (CCFI < .50). Simulated taxonic and dimensional datasets differed substantially and the samples were appropriate for taxometric analysis. Accordingly, the latent structure of somatization/somatic symptom reporting as assessed by the PHQ-15 is dimensional in both primary care and student samples. Implications regarding the practical application as well as models of etiology and pathogenesis of somatic symptom reporting are discussed. (PsycINFO Database Record (c) 2012 APA, all rights reserved).     

Differentiating categorical and dimensional data with taxometric analysis: are two variables better than none?

Taxometric analyses have proven helpful for distinguishing categorical and dimensional data. Many taxometric procedures require at least 3 variables for analysis. What if a construct is defined by only 2 conceptually nonredundant characteristics or a data set contains only 2 empirically nonredundant variables? In Study 1, we performed extensive simulations to determine whether informative results can be obtained when only 2 variables are available for taxometric analysis. The mean above minus below a cut (MAMBAC) and maximum slope (MAXSLOPE) procedures, used with parallel analyses of comparison data, successfully differentiated categorical and dimensional structure. With just 2 variables, it seems especially important that indicators vary across as many distinct values as possible and that investigators obtain as large a sample as possible. Additional findings address questions about the most effective way to implement taxometric analyses. In Study 2, the potential utility of 2-variable taxometric analysis is illustrated using data on proactive and reactive childhood aggression, where the results provided strong support for dimensional structure. As long as high-quality data are available, it appears that one can have confidence in the results of taxometric analyses performed with only 2 variables.     

Subtyping obsessive-compulsive disorder: A taxometric analysis

Obsessive-compulsive disorder (OCD) is a heterogeneous condition comprising multiple symptoms. Researchers have identified OCD subtypes using a range of symptom-based research methods, including factor and cluster analyses and examination of differential treatment response. These methods can be challenged on the grounds that they fail to demonstrate the existence of discrete taxonomic entities. Furthermore, no study has examined subtyping on the basis of cognitive characteristics. In the present study, the categorical vs. dimensional status of 6 possible subtypes of OCD was examined using taxometric methods. Three potential cognitive subtypes (based on high levels of responsibility/threat estimation, perfectionism/certainty, and importance/control of thoughts) and 3 potential symptomatic subtypes (based on elevated levels of contamination obsessions and cleaning compulsions, checking, and obsessionality) were examined using the MAXEIG and MAMBAC procedures in a sample of 404 diagnosed cases of OCD. Findings favored dimensional models of the potential responsibility, perfectionism, checking, and contamination subtypes, but offered qualified support for taxonic models of the importance/control of thoughts and obsessional subtypes. Implications for the subclassification of OCD are discussed.     

Taxometric analysis supports a dimensional latent structure for schizotypy

The existence of a discrete class of people vulnerable to schizophrenia spectrum disorders is the most replicated finding of taxometric research. Evidence for such a “taxon” has been obtained with diverse measures of schizotypy in clinical, high-risk, and normal samples. However, recent demonstrations that skewed indicators of a latent dimension can yield a spuriously taxonic pattern of results may call some of these findings into question. Normal adults (N = 1073) completed measures of positive (perceptual aberration, magical ideation) and negative (physical and social anhedonia) components of schizotypy. Taxometric curves resembled those obtained previously, but when a simulation procedure took skew into account, dimensional models of schizotypy received stronger support than taxonic models for most schizotypy components, with findings for magical thinking inconclusive. A re-evaluation of previous taxonic conclusions regarding the latent structure of schizotypy is indicated.     

Does attention-deficit/hyperactivity disorder have a dimensional latent structure? A taxometric analysis

An understanding of the latent structure of attention-deficit/hyperactivity disorder (ADHD) is essential for developing causal models of this disorder. Although some researchers have presumed that ADHD is dimensional and others have assumed that it is taxonic, there has been relatively little research directly examining the latent structure of ADHD. The authors conducted a set of taxometric analyses using data from the NICHD Study of Early Child Care and Youth Development (ns between 667 and 1,078). The results revealed a dimensional latent structure across a variety of different analyses and sets of indicators for inattention, hyperactivity/impulsivity, and ADHD. Furthermore, analyses of correlations with associated features indicated that dimensional models demonstrated stronger validity coefficients with these criterion measures than dichotomous models. These findings jibe with recent research on the genetic basis of ADHD and with contemporary models of ADHD.     

A structure-based approach to psychological assessment: matching measurement models to latent structure

The present article sets forth the argument that psychological assessment should be based on a construct's latent structure. The authors differentiate dimensional (continuous) and taxonic (categorical) structures at the latentand manifest levels and describe the advantages of matching the assessment approach to the latent structure of a construct. A proper match will decrease measurement error, increase statistical power, clarify statistical relationships, and facilitate the location of an efficient cutting score when applicable. Thus, individuals will be placed along a continuum or assigned to classes more accurately. The authors briefly review the methods by which latent structure can be determined and outline a structure-based approach to assessment that builds on dimensional scaling models, such as item response theory, while incorporating classification methods as appropriate. Finally, the authors empirically demonstrate the utility of their approach and discuss its compatibility with traditional assessment methods and with computerized adaptive testing.     

Taxometric and factor analytic models of anxiety sensitivity: integrating approaches to latent structural research

This study represents an effort to better understand the latent structure of anxiety sensitivity (AS), as indexed by the 16-item Anxiety Sensitivity Index (ASI; S. Reiss, R. A. Peterson, M. Gursky, & R. J. McNally, 1986), by using taxometric and factor-analytic approaches in an integrative manner. Taxometric analyses indicated that AS has a taxonic latent class structure (i.e., a dichotomous latent class structure) in a large sample of North American adults (N=2,515). As predicted, confirmatory factor analyses indicated that a multidimensional 3-factor model of AS provided a good fit for the AS complement class (normative or low-risk form) but not the AS taxon class (high-risk form). Exploratory factor analytic results suggested that the AS taxon may demonstrate a unique, unidimensional factor solution, though there are alternative indications that it may be characterized by a 2-factor solution. Findings suggest that the latent structural nature of AS can be conceptualized as a taxonic latent class structure composed of 2 types or forms of AS, each of these forms characterized by its own unique latent continuity and dimensional structure.     

Malingering as a categorical or dimensional construct: the latent structure of feigned psychopathology as measured by the SIRS and MMPI-2

The 6 nonoverlapping primary scales of the Structured Interview of Reported Symptoms (SIRS) were subjected to taxometric analysis in a group of 1,211 criminal and civil examinees in order to investigate the latent structure of feigned psychopathology. Both taxometric procedures used in this study, mean above minus below a cut (MAMBAC) and maximum covariance (MAXCOV), produced dimensional results. A subgroup of participants (n = 711) with valid Minnesota Multiphasic Personality Inventory-2 (MMPI-2) protocols were included in a second round of analyses in which the 6 nonoverlapping primary scales of the SIRS and the Infrequency (F), Infrequency-Psychopathology (Fp), and Dissimulation (Ds) scales of the MMPI-2 served as indicators. Again, the results were more consistent with dimensional latent structure than with taxonic latent structure. On the basis of these findings, it is concluded that feigned psychopathology forms a dimension (levels of fabrication or exaggeration) rather than a taxon (malingering-honest dichotomy) and that malingering is a quantitative distinction rather than a qualitative one. The theoretical and clinical practice implications of these findings are discussed.     

Differentiating Categories and Dimensions: Evaluating the Robustness of Taxometric Analyses

Interest in modeling the structure of latent variables is gaining momentum, and many simulation studies suggest that taxometric analysis can validly assess the relative fit of categorical and dimensional models. The generation and parallel analysis of categorical and dimensional comparison data sets reduces the subjectivity required to interpret results by providing an objective Comparison Curve Fit Index (CCFI). This study takes advantage of developments in the generation of comparison data to examine the robustness of taxometric analyses to unfavorable data conditions. Very large comparison data sets are treated as populations from which many samples are drawn randomly, placing the method on a firmer statistical foundation and increasing its run-time efficiency. The impressive accuracy of the CCFI was consistent with prior findings and robust across novel manipulations of asymmetry, tail weight, and heterogeneous variances. Analyses, an empirical illustration using Minnesota Multiphasic Personality Inventory (MMPI) hypochondriasis data, and discussion focus on the practical implications for differentiating categories and dimensions.     

The latent structure and coincidence of hypohedonia and schizotypy and their validity as indices of psychometric risk for schizophrenia

Recent exchanges on the place of hypohedonia within Meehl's theory of schizotaxia, schizotypy, and schizophrenia focus on evidence of the taxonicity of asociality, not hedonic capacity per se. Two hypotheses were contrasted, one that hypohedonia is a nonpathological individual difference variable independent of schizotypy, the other that schizotypy and hypohedonia tap independent taxonic processes that predict the emergence of positive and negative signs of schizophrenia, respectively. Undergraduates (n = 1,543) completed a multifaceted measure of schizotypy and hypohedonia. A consecutive subsample of these (n = 284) also completed a continuous performance test and the Symptom Checklist 90-Revised. Independent taxometric analyses (maximum covariance and maximum eigenvalue) indicated schizotypy was taxonic and hypohedonia was dimensional. Their coincidence was no greater than chance. Schizotypy was associated with impaired attention and significant psychological distress, whereas hypohedonia was not. Hypohedonia does not behave like a core component of schizotypy.