Comparing the relative fit of categorical and dimensional latent variable models using consistency tests.

A number of recent studies have used Meehl’s (1995) taxometric method to determine empirically whether one should model assessment-related constructs as categories or dimensions. The taxometric method includes multiple data-analytic procedures designed to check the consistency of results. The goal is to differentiate between strong evidence of categorical structure, strong evidence of dimensional structure, and ambiguous evidence that suggests withholding judgment. Many taxometric consistency tests have been proposed, but their use has not been operationalized and studied rigorously. What tests should be performed, how should results be combined, and what thresholds should be applied? We present an approach to consistency testing that builds on prior work demonstrating that parallel analyses of categorical and dimensional comparison data provide an accurate index of the relative fit of competing structural models. Using a large simulation study spanning a wide range of data conditions, we examine many critical elements of this approach. The results provide empirical support for what marks the first rigorous operationalization of consistency testing. We discuss and empirically illustrate guidelines for implementing this approach and suggest avenues for future research to extend the practice of consistency testing to other techniques for modeling latent variables in the realm of psychological assessment. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Testing the degree of cross-sectional and longitudinal dependence between two discrete dynamic processes.

Developmental research often involves studying change across 2 or more processes or constructs simultaneously. A natural question in this work is whether change in these 2 processes is related or independent. Associative latent transition analysis (ALTA) was designed to test hypotheses about the degree to which change in 2 discrete latent variables is related. The ALTA model is a type of latent class model, which is a categorical latent variable model based on categorical indicators. In the ALTA approach, level and change on 1 variable is predicted by level and change in another. Two types of hypotheses are discussed: (a) broad hypotheses of dependence between the 2 discrete latent variables and (b) targeted hypotheses comparing specific patterns of change between levels of the discrete variables. Both types of hypotheses are tested via nested model comparisons. Analyses of relations between psychological state and substance use illustrate the model. Recent psychological state and recent substance use were found to be associated cross-sectionally and longitudinally, implying that change in recent substance use was related to change in recent psychological state. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Psychometric approaches for developing commensurate measures across independent studies: Traditional and new models.

[Correction Notice: An erratum for this article was reported in Vol 14(4) of Psychological Methods (see record 2009-22665-007). In this article, the authors wrote, "To our knowledge, the multisample framework is the only available option within these [latent variable] programs that allows for the moderation of all types of parameters, and this approach requires a single categorical moderator variable to define the samples.” Bengt Muthén has clarified for the authors that some programs, including Mplus and Mx, can allow for continuous moderation through the implementation of nonlinear constraints involving observed variables, further enlarging the class of MNLFA models that can be fit with these programs.] When conducting an integrative analysis of data obtained from multiple independent studies, a fundamental problem is to establish commensurate measures for the constructs of interest. Fortunately, procedures for evaluating and establishing measurement equivalence across samples are well developed for the linear factor model and commonly used item response theory models. A newly proposed moderated nonlinear factor analysis model generalizes these models and procedures, allowing for items of different scale types (continuous or discrete) and differential item functioning across levels of categorical and/or continuous variables. The potential of this new model to resolve the problem of measurement in integrative data analysis is shown via an empirical example examining changes in alcohol involvement from ages 10 to 22 years across 2 longitudinal studies. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

"Psychometric approaches for developing commensurate measures across independent studies: Traditional and new models": Clarification to Bauer and Hussong (2009).

Reports a clarification to "Psychometric approaches for developing commensurate measures across independent studies: Traditional and new models" by Daniel J. Bauer and Andrea M. Hussong (Psychological Methods, 2009[Jun], Vol 14[2], 101-125). In this article, the authors wrote, "To our knowledge, the multisample framework is the only available option within these [latent variable] programs that allows for the moderation of all types of parameters, and this approach requires a single categorical moderator variable to define the samples.” Bengt Muthén has clarified for the authors that some programs, including Mplus and Mx, can allow for continuous moderation through the implementation of nonlinear constraints involving observed variables, further enlarging the class of MNLFA models that can be fit with these programs. (The following abstract of the original article appeared in record 2009-08072-001.) When conducting an integrative analysis of data obtained from multiple independent studies, a fundamental problem is to establish commensurate measures for the constructs of interest. Fortunately, procedures for evaluating and establishing measurement equivalence across samples are well developed for the linear factor model and commonly used item response theory models. A newly proposed moderated nonlinear factor analysis model generalizes these models and procedures, allowing for items of different scale types (continuous or discrete) and differential item functioning across levels of categorical and/or continuous variables. The potential of this new model to resolve the problem of measurement in integrative data analysis is shown via an empirical example examining changes in alcohol involvement from ages 10 to 22 years across 2 longitudinal studies. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Pseudotaxonicity in MAMBAC and MAXCOV analyses of rating-scale data: Turning continua into classes by manipulating observer's expectations.

Taxometric procedures such as mean above minus below a cut and maximum covariance can determine whether a trait is distributed as a discrete latent class. These methods have been used to infer taxonic structure in several personality and psychopathology constructs, often from analyses of rating scale data. This is problematic given (a) well established biases in ratings, (b) the human tendency to think categorically, and (c) implicit typological models of personality and psychopathology among expert raters. Using an experimental method in which the cognitive sets of raters were manipulated as dimensional versus categorical, it is demonstrated that pseudotaxonicity can be created readily with rating scale measures. This suggests that researchers avoid an exclusive reliance on rating scales when conducting taxometrics investigations. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Detecting small taxa using simulated comparison data: A reanalysis of Beach, Amir, and Bau's (2005) data.

On the basis of taxometric analyses of data sets that they created to pose interpretive challenges, S. R. H. Beach, N. Amir, and J. J. Bau (2005) cautioned that using comparison data simulated by J. Ruscio's programs can lead to inaccurate conclusions. Careful examination of S. R. H. Beach et al.'s methods and results plus reanalysis of their data fails to substantiate this concern: Using comparison data identified the taxonic structure of S. R. H. Beach et al.'s data sets, even when the taxon base rate was very low. The authors show that J. Ruscio's simulation programs generate comparison data appropriately and that analyzing these data provides a useful interpretive aid. Additionally, the authors discuss and illustrate the effective use of the inchworm consistency test to disambiguate taxometric results for small taxa and dimensional constructs with positively skewed indicators. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

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. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

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. (PsycINFO Database Record (c) 2011 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. (PsycINFO Database Record (c) 2011 APA, all rights reserved)     

Item factor analysis: Current approaches and future directions.

The rationale underlying factor analysis applies to continuous and categorical variables alike; however, the models and estimation methods for continuous (i.e., interval or ratio scale) data are not appropriate for item-level data that are categorical in nature. The authors provide a targeted review and synthesis of the item factor analysis (IFA) estimation literature for ordered-categorical data (e.g., Likert-type response scales) with specific attention paid to the problems of estimating models with many items and many factors. Popular IFA models and estimation methods found in the structural equation modeling and item response theory literatures are presented. Following this presentation, recent developments in the estimation of IFA parameters (e.g., Markov chain Monte Carlo) are discussed. The authors conclude with considerations for future research on IFA, simulated examples, and advice for applied researchers. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Is Depression Best Viewed as a Continuum or Discrete Category? A Taxometric Analysis of Childhood and Adolescent Depression in a Population-Based Sample.

The authors examined the latent structure of depression in a population-based sample of children and adolescents. Youth's self-reports and parents' reports of the youth's Diagnostic and Statistical Manual of Mental Disorders (4th ed.; DSM-IV; American Psychiatric Association, 1994) major depressive symptoms were assessed via a structured clinical interview. The authors used Meehl's (1995) taxometric procedures to discern whether youth depression is dimensional or categorical. Taxometric analyses that explicitly took into account the skewness of depressive symptoms suggested that depression is a dimensional, not categorical, construct. The dimensional structure of depression was obtained for all of the DSM-IV major depressive symptoms as well as for different domains of depression (emotional distress symptoms and vegetative, involuntary defeat symptoms), youth and parent reports, and different subsamples (i.e., boys vs. girls and younger vs. older youth). (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Taxometrics, polytomous constructs, and the comparison curve fit index: A Monte Carlo analysis.

The taxometric method effectively distinguishes between dimensional (1-class) and taxonic (2-class) latent structure, but there is virtually no information on how it responds to polytomous (3-class) latent structure. A Monte Carlo analysis showed that the mean comparison curve fit index (CCFI; Ruscio, Haslam, & Ruscio, 2006) obtained with 3 taxometric procedures—mean above minus below a cut (MAMBAC), maximum covariance (MAXCOV), and latent mode factor analysis (L-Mode)—accurately identified 1-class (dimensional) and 2-class (taxonic) samples and produced taxonic results when applied to 3-class (polytomous) samples. From these results it is concluded that using the simulated data curve approach and averaging across procedures is an effective way of distinguishing between dimensional (1-class) and categorical (2 or more classes) latent structure. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

An array of qualitative data analysis tools: A call for data analysis triangulation.

One of the most important steps in the qualitative research process is analysis of data. The purpose of this article is to provide elements for understanding multiple types of qualitative data analysis techniques available and the importance of utilizing more than one type of analysis, thus utilizing data analysis triangulation, in order to understand phenomenon more fully for school psychology research and beyond. The authors describe seven qualitative analysis tools: methods of constant comparison, keywords-in-context, word count, classical content analysis, domain analysis, taxonomic analysis, and componential analysis. Then, the authors outline when to use each type of analysis. In so doing, the authors use real qualitative data to help distinguish the various types of analyses. Furthermore, flowcharts and tables are provided to help delineate when to choose each type of analysis. Finally, the role of computer-assisted software in the qualitative data-analytic process is discussed. As such, use of the analyses outlined in this article should help to promote rigor in qualitative research. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

To sum or not to sum: Taxometric analysis with ordered categorical assessment items.

Meehl's taxometric method has been shown to differentiate between categorical and dimensional data, but there are many ways to implement taxometric procedures. When analyzing the ordered categorical data typically provided by assessment instruments, summing items to form input indicators has been a popular practice for more than 20 years. A Monte Carlo study compared the accuracy of taxometric analyses implemented in the traditional way (without summing items) and taxometric analyses implemented with the summed-input method. These analyses generated no support for the summed-input method, which substantially reduced discriminating power for 2 of the 3 procedures studied. Accuracy was highest when 5 or more indicators and 4 or more ordered categories were used. Findings from the simulation study were then used to help interpret the results for taxometric analyses of antisocial personality disorder criteria with real research data. In this example, the traditional method yielded clearer results than the summed-input method. Implications for the use and further study of the taxometric method in assessment research are discussed. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

The four-factor model of depressive symptoms in dementia caregivers: A structural equation model of ethnic differences.

Previous studies have suggested that 4 latent constructs (depressed affect, well-being, interpersonal problems, somatic symptoms) underlie the item responses on the Center for Epidemiological Studies Depression (CES-D) Scale. This instrument has been widely used in dementia caregiving research, but the fit of this multifactor model and the explanatory contributions of multifactor models have not been sufficiently examined for caregiving samples. The authors subjected CES-D data (N = 1,183) from the initial Resources for Enhancing Alzheimer's Caregiver Health Study to confirmatory factor analysis methods and found that the 4-factor model provided excellent fit to the observed data. Invariance analyses suggested only minimal item-loading differences across race subgroups and supported the validity of race comparisons on the latent factors. Significant race differences were found on 3 of the 4 latent factors both before and after controlling for demographic covariates. African Americans reported less depressed affect and better well-being than White caregivers, who reported better well-being and fewer interpersonal problems than Hispanic caregivers. These findings clarify and extend previous studies of race differences in depression among diverse samples of dementia caregivers. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

New approaches to studying problem behaviors: A comparison of methods for modeling longitudinal, categorical adolescent drinking data.

Analyzing problem-behavior trajectories can be difficult. The data are generally categorical and often quite skewed, violating distributional assumptions of standard normal-theory statistical models. In this article, the authors present several currently available modeling options, all of which make appropriate distributional assumptions for the observed categorical data. Three are based on the generalized linear model: a hierarchical generalized linear model, a growth mixture model, and a latent class growth analysis. They also describe a longitudinal latent class analysis, which requires fewer assumptions than the first 3. Finally, they illustrate all of the models using actual longitudinal adolescent alcohol-use data. They guide the reader through the model-selection process, comparing the results in terms of convergence properties, fit and residuals, parsimony, and interpretability. Advances in computing and statistical software have made the tools for these types of analyses readily accessible to most researchers. Using appropriate models for categorical data will lead to more accurate and reliable results, and their application in real data settings could contribute to substantive advancements in the field of development and the science of prevention. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Factor analysis in the development and refinement of clinical assessment instruments.

The goals of both exploratory and confirmatory factor analysis are described and procedural guidelines for each approach are summarized, emphasizing the use of factor analysis in developing and refining clinical measures. For exploratory factor analysis, a rationale is presented for selecting between principal components analysis and common factor analysis depending on whether the research goal involves either identification of latent constructs or data reduction. Confirmatory factor analysis using structural equation modeling is described for use in validating the dimensional structure of a measure. Additionally, the uses of confirmatory factor analysis for assessing the invariance of measures across samples and for evaluating multitrait-multimethod data are also briefly described. Suggestions are offered for handling common problems with item-level data, and examples illustrating potential difficulties with confirming dimensional structures from initial exploratory analyses are reviewed. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Are infant attachment patterns continuously or categorically distributed? A taxometric analysis of strange situation behavior.

Contemporary attachment research is based on the assumption that at least three types of infant attachment patterns exist: secure, avoidant, and resistant. It is not known, however, whether individual differences in attachment organization are more consistent with a continuous or a categorical model. The authors addressed this issue by applying P. E. Meehl's (1973, 1992) taxometric techniques for distinguishing latent types (i.e., classes, natural kinds) from latent continua (i.e., dimensions) to Strange Situation data on 1,139 fifteen-month-old children from the NICHD Study of Early Child Care. The results indicate that variation in attachment patterns is largely continuous, not categorical. The discussion focuses on the implications of dimensional models of individual differences for attachment theory and research. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Paranoid personality has a dimensional latent structure: Taxometric analyses of community and clinical samples.

Although paranoid personality is one of the most commonly diagnosed personality disorders and is associated with numerous negative life consequences, relatively little is known about the structural properties of this condition. This study examines whether paranoid personality traits represent a latent dimension or a discrete class (i.e., taxon). In Study 1, the authors conducted taxometric analyses of paranoid personality disorder criteria in a sample of 731 patients participating in the Collaborative Longitudinal Study of Personality Disorders project (Gunderson et al., 2000) who had been administered a semistructured diagnostic interview for personality disorders according to criteria of the Diagnostic and Statistical Manual of Mental Disorders (4th ed.; American Psychiatric Association, 1994). In Study 2, the authors conducted parallel analyses of the Paranoia scale of the Personality Assessment Inventory (PAI; L. C. Morey, 2007), using data from the PAI community and clinical normative databases. Analyses across both self-report and interview-based indicators offered compelling support for a dimensional structure. Additionally, analyses of external correlates in these data sets suggested that dimensional models demonstrated stronger validity coefficients with criterion measures than did dichotomous models. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Clarifying Boundary Issues in Psychopathology: The Role of Taxometrics in a Comprehensive Program of Structural Research.

Despite decades of debate, important questions about the boundaries that separate psychological disorder from normality and that distinguish 1 disorder from another remain largely unanswered. These issues pose empirical questions that may be addressed by assessing the latent structure of psychopathological constructs. Because these constructs are likely to be structurally complex, and no single statistical tool addresses all structural questions, it is proposed in this article that boundary issues be examined through programmatic research grounded in the taxometric method and elaborated by complementary analyses. The authors describe how such a program could delimit the structure of disorders and test competing explanations of diagnostic co-occurrence, emphasizing the potential to enhance the reliability and validity of assessment, maximize the power of research designs, and improve diagnostic classification. (PsycINFO Database Record (c) 2010 APA, all rights reserved)