Toward a Model-Based Approach to the Clinical Assessment of Personality Psychopathology

Recent years have witnessed tremendous growth in the scope and sophistication of statistical methods available to explore the latent structure of psychopathology, involving continuous, discrete, and hybrid latent variables. The availability of such methods has fostered optimism that they can facilitate movement from classification primarily crafted through expert consensus to classification derived from empirically based models of psychopathological variation. The explication of diagnostic constructs with empirically supported structures can then facilitate the development of assessment tools that appropriately characterize these constructs. Our goal in this article is to illustrate how new statistical methods can inform conceptualization of personality psychopathology and therefore its assessment. We use magical thinking as an example, because both theory and earlier empirical work suggested the possibility of discrete aspects to the latent structure of personality psychopathology, particularly forms of psychopathology involving distortions of reality testing, yet other data suggest that personality psychopathology is generally continuous in nature. We directly compared the fit of a variety of latent variable models to magical thinking data from a sample enriched with clinically significant variation in psychotic symptomatology for explanatory purposes. Findings generally suggested a continuous latent variable model best represented magical thinking, but results varied somewhat depending on different indexes of model fit. We discuss the implications of the findings for classification and applied personality assessment. We also highlight some limitations of this type of approach that are illustrated by these data, including the importance of substantive interpretation, in addition to use of model fit indexes, when evaluating competing structural models.     

Factor copula models for mixed data

We develop factor copula models to analyse the dependence among mixed continuous and discrete responses. Factor copula models are canonical vine copulas that involve both observed and latent variables, hence they allow tail, asymmetric and nonlinear dependence. They can be explained as conditional independence models with latent variables that do not necessarily have an additive latent structure. We focus on important issues of interest to the social data analyst, such as model selection and goodness of fit. Our general methodology is demonstrated with an extensive simulation study and illustrated by reanalysing three mixed response data sets. Our studies suggest that there can be a substantial improvement over the standard factor model for mixed data and make the argument for moving to factor copula models.     

Information-theoretic latent distribution modeling: distinguishing discrete and continuous latent variable models

Distinguishing between discrete and continuous latent variable distributions has become increasingly important in numerous domains of behavioral science. Here, the authors explore an information-theoretic approach to latent distribution modeling, in which the ability of latent distribution models to represent statistical information in observed data is emphasized. The authors conclude that loss of statistical information with a decrease in the number of latent values provides an attractive basis for comparing discrete and continuous latent variable models. Theoretical considerations as well as the results of 2 Monte Carlo simulations indicate that information theory provides a sound basis for modeling latent distributions and distinguishing between discrete and continuous latent variable models in particular.     

Models with discrete latent variables for analysis of categorical data: A framework and a MATLAB MDLV toolbox

Studies in the social and behavioral sciences often involve categorical data, such as ratings, and define latent constructs underlying the research issues as being discrete. In this article, models with discrete latent variables (MDLV) for the analysis of categorical data are grouped into four families, defined in terms of two dimensions (time and sampling) of the data structure. A MATLAB toolbox (referred to as the “MDLV toolbox”) was developed for applying these models in practical studies. For each family of models, model representations and the statistical assumptions underlying the models are discussed. The functions of the toolbox are demonstrated by fitting these models to empirical data from the European Values Study. The purpose of this article is to offer a framework of discrete latent variable models for data analysis, and to develop the MDLV toolbox for use in estimating each model under this framework. With this accessible tool, the application of data modeling with discrete latent variables becomes feasible for a broad range of empirical studies.     

Latent partition analysis

Latent partition analysis has been formulated to study the relationships between two or more partitions of the same set of items. The major structural hypothesis is that a latent partition underlies the manifest partitions; that is, it is assumed that each item belongs to a latent category and that the manifest categories are derived by dividing and combining the latent categories. We have found that by examining manifest categories it is possible to reconstruct information about the latent partition and about its relation to the manifest partitions.The research reported herein was originally supported through the U. S. O. E. Cooperative Research Project 5-1005-2-12-1, directed by Donald M. Miller, at the Instructional Research Laboratory, University of Wisconsin. Further work has been supported by the National Science Foundation Grant No. GS-1025 at The University of Chicago. The author wishes to acknowledge the invaluable assistance of Richard G. Wolfe in the final statement of the theory and the assistance of Robert M. Pruzek in certain early formulations.     

The relation of perception and motor action: ideomotor compatibility and interference in divided attention

Ideomotor theory is one variation of the general position that perception and motor action are related. According to this theory, a perceptual representation of the goal of a response must be generated prior to response initiation. Ideomotor theory can be extended by assuming that generation of this representation, which usually is required prior to motor action, is not needed if the stimulus itself corresponds to the response goal, that is, if the stimulus and response are ideomotor compatible. Because processing to generate the response representation is not needed with ideomotor compatibility, it should be possible to control two responses simultaneously without mutual interference if at least one stimulus-response relation is ideomotor compatible. Although supported in previous work involving discrete responses, this prediction of perfect time-sharing was found not to hold in the experiments reported here. These experiments, unlike those showing perfect time-sharing, involved continuous responses. We propose an alternative version of ideomotor compatibility, in which perfect time-sharing can occur if an integrated stimulus is provided to match the continuous and integrated response.     

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.     

Taxometric Investigation of PTSD: data from two nationally representative samples

Current psychiatric nosology depicts posttraumatic stress disorder (PTSD) as a discrete diagnostic category. However, only one study has examined the latent structure of PTSD, and this study suggested that PTSD may be more accurately conceptualized as an extreme reaction to traumatic life events rather than a discrete clinical syndrome. To build on the existing literature base, the present research examined the latent structure of posttraumatic stress reactions by applying three taxometric procedures (MAXEIG, MAMBAC, and L-Mode) to data collected from large nationally representative samples of women (ns = 2684 and 3033) and adolescents (n = 3775). Results consistently provided evidence for a dimensional PTSD solution across samples and statistical procedures. These findings have important implications for the theory, assessment, and investigation of posttraumatic stress reactions.     

A Latent Structure Analysis of Cognitive Vulnerability to Depression in Adolescence

Whether cognitive vulnerability to depression exists along a continuum of severity or as a qualitatively discrete phenomenological entity has direct bearing on theoretical formulations of risk for depression and clinical risk assessment. This question is of particular relevance to adolescence, given that cognitive vulnerability appears to coalesce and rates of depression begin to rise markedly during this period of development. Although a dimensional view is often assumed, it is necessary to submit this assumption to direct empirical evaluation. Taxometric analysis is a family of statistical techniques developed directly to test such assumptions. The present study applied taxometric methods to address this question in a community sample of early adolescents (n = 485), drawing on three indices of cognitive vulnerability to depression (i.e., negative inferential style, ruminative response style, self-referent information processing). The results of three taxometric analyses (i.e., mean above minus below a cut [MAMBAC], maximum eigenvalue [MAXEIG], and latent mode [L-Mode]) were consistent in unambiguously supporting a dimensional conceptualization of this construct. The latent structure of the tested indices of cognitive vulnerability to depression in adolescence appears to exist along a continuum of severity rather than as a discrete clinical entity.     

Theoretical and empirical review of multinomial process tree modeling

We review a current and popular class of cognitive models calledmultinomial processing tree (MPT) models. MPT models are simple, substantively motivated statistical models that can be applied to categorical data. They are useful as data-analysis tools for measuring underlying or latent cognitive capacities and as simple models for representing and testing competing psychological theories. We formally describe the cognitive structure and parametric properties of the class of MPT models and provide an inferential statistical analysis for the entire class. Following this, we provide a comprehensive review of over 80 applications of MPT models to a variety of substantive areas in cognitive psychology, including various types of human memory, visual and auditory perception, and logical reasoning. We then address a number of theoretical issues relevant to the creation and evaluation of MPT models, including model development, model validity, discrete-state assumptions, statistical issues, and the relation between MPT models and other mathematical models. In the conclusion, we consider the current role of MPT models in psychological research and possible future directions.     

The Dimensional Nature of Externalizing Behaviors in Adolescence: Evidence from a Direct Comparison of Categorical,Dimensional, and Hybrid Models

Researchers have recognized the importance of developing an accurate classification system for externalizing disorders, though much of this work has been framed by a priori preferences for categorical vs. dimensional constructs. Newer statistical technologies now allow categorical and dimensional models of psychopathology to be compared empirically. In this study, we directly compared the fit of categorical and dimensional models of externalizing behaviors in a large and representative community sample of adolescents at two time points separated by nearly 2.5 years (N = 2027; mean age at Time 1 = 11.09 years; 50.8% female). Delinquent and aggressive behaviors were assessed with child and parent Child Behavior Checklist reports. Latent trait, latent class, and factor mixture models were fit to the data, and at both time points, the latent trait model provided the best fit to the data. The item parameters were inspected and interpreted, and it was determined that the items were differentially sensitive across all regions of the dimension. We conclude that classification models can be based on empirical evidence rather than a priori preferences, and while current classification systems conceptualize externalizing problems in terms of discrete groups, they can be better conceptualized as dimensions.     

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.     

A New Zero-Inflated Negative Binomial Methodology for Latent Category Identification

We introduce a new statistical procedure for the identification of unobserved categories that vary between individuals and in which objects may span multiple categories. This procedure can be used to analyze data from a proposed sorting task in which individuals may simultaneously assign objects to multiple piles. The results of a synthetic example and a consumer psychology study involving categories of restaurant brands illustrate how the application of the proposed methodology to the new sorting task can account for a variety of categorization phenomena including multiple category memberships and for heterogeneity through individual differences in the saliency of latent category structures.     

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.     

A latent class distance association model for cross‐classified data with a categorical response variable

In this paper we propose a latent class distance association model for clustering in the predictor space of large contingency tables with a categorical response variable. The rows of such a table are characterized as profiles of a set of explanatory variables, while the columns represent a single outcome variable. In many cases such tables are sparse, with many zero entries, which makes traditional models problematic. By clustering the row profiles into a few specific classes and representing these together with the categories of the response variable in a low‐dimensional Euclidean space using a distance association model, a parsimonious prediction model can be obtained. A generalized EM algorithm is proposed to estimate the model parameters and the adjusted Bayesian information criterion statistic is employed to test the number of mixture components and the dimensionality of the representation. An empirical example highlighting the advantages of the new approach and comparing it with traditional approaches is presented.     

Is risky sexual behavior continuous or categorical? A taxometric analysis of the Sexual Risk Survey

Risky sexual behaviors are behaviors that involve the possibility of an adverse outcome, such as contracting a sexually transmitted infection or unwanted pregnancy. The question of whether risky sexual behavior exists as a discrete class (i.e., taxon) or as a dimensional construct has not previously been explored. The authors performed a set of taxometric analyses on 4 factor scales derived from the Sexual Risk Survey (Turchik & Garske, 2009) with data from 1,103 college students. The results provided consistent support for a dimensional latent structure in which variations in reported risky sexual behavior reflect differences in degree and not differences in kind. The implications of these findings for the assessment of risky sexual behavior are discussed.     

Loglinear multidimensional IRT models for polytomously scored items

A loglinear IRT model is proposed that relates polytomously scored item responses to a multidimensional latent space. The analyst may specify a response function for each response, indicating which latent abilities are necessary to arrive at that response. Each item may have a different number of response categories, so that free response items are more easily analyzed. Conditional maximum likelihood estimates are derived and the models may be tested generally or against alternative loglinear IRT models.Hank Kelderman is currently affiliated with Vrije Universiteit, Amsterdam.We thank Linda Vodegel-Matzen of the Division of Developmental Psychology of the University of Amsterdam for making available the data used in the example in this article.     

Dimensionality of the Latent Structure and Item Selection Via Latent Class Multidimensional IRT Models

With reference to a questionnaire aimed at assessing the performance of Italian nursing homes on the basis of the health conditions of their patients, we investigate two relevant issues: dimensionality of the latent structure and discriminating power of the items composing the questionnaire. The approach is based on a multidimensional item response theory model, which assumes a two-parameter logistic parameterization for the response probabilities. This model represents the health status of a patient by latent variables having a discrete distribution and, therefore, it may be seen as a constrained version of the latent class model. On the basis of the adopted model, we implement a hierarchical clustering algorithm aimed at assessing the actual number of dimensions measured by the questionnaire. These dimensions correspond to disjoint groups of items. Once the number of dimensions is selected, we also study the discriminating power of every item, so that it is possible to select the subset of these items which is able to provide an amount of information close to that of the full set. We illustrate the proposed approach on the basis of the data collected on 1,051 elderly people hosted in a sample of Italian nursing homes.     

Loglinear Rasch models for the analysis of stability and change

Loglinear unidimensional and multidimensional Rasch models are considered for the analysis of repeated observations of polytomous indicators with ordered response categories. Reparameterizations and parameter restrictions are provided which facilitate specification of a variety of hypotheses about latent processes of change. Models of purely quantitative change in latent traits are proposed as well as models including structural change. A conditional likelihood ratio test is presented for the comparison of unidimensional and multiple scales Rasch models. In the context of longitudinal research, this renders possible the statistical test of homogeneity of change against subject-specific change in latent traits. Applications to two empirical data sets illustrate the use of the models.The author is greatly indebted to Ulf Böckenholt, Rolf Langeheine, and several anonymous reviewers for many helpful suggestions.     

Log-Multiplicative Association Models as Item Response Models

Log-multiplicative association (LMA) models, which are special cases of log-linear models, have interpretations in terms of latent continuous variables. Two theoretical derivations of LMA models based on item response theory (IRT) arguments are presented. First, we show that Anderson and colleagues (Anderson &; Vermunt, 2000; Anderson &; Böckenholt, 2000; Anderson, 2002), who derived LMA models from statistical graphical models, made the equivalent assumptions as Holland (1990) when deriving models for the manifest probabilities of response patterns based on an IRT approach. We also present a second derivation of LMA models where item response functions are specified as functions of rest-scores. These various connections provide insights into the behavior of LMA models as item response models and point out philosophical issues with the use of LMA models as item response models. We show that even for short tests, LMA and standard IRT models yield very similar to nearly identical results when data arise from standard IRT models. Log-multiplicative association models can be used as item response models and do not require numerical integration for estimation.