Factor Mixture Modeling Research Articles

Development of sense of coherence in adulthood: a person-centered approach. The population-based HeSSup cohort study

We sought to identify the most typical patterns of change in sense of coherence (SOC) in adulthood. This prospective population-based Health and Social Support (HeSSup) study was based on four age cohorts including men and women initially aged 20-24 years (n = 4,682), 30-34 years (n = 4,248), 40-44 years (n = 4,598), and 50-54 years (n = 4,997). SOC was assessed at baseline and at the 5-year follow-up point. Factor Mixture Modeling was used to identify the latent classes of persons whose mean changes in SOC were similar over time. Three development classes were supported by the data. In all age cohorts, the largest class consisted of those people whose SOC was high at baseline and increased thereafter (46-58% of participants depending on the age group). A class of high SOC with a decreasing trend and that of low SOC with an increasing trend were also found. In all age groups, the rank-order stability was high in the first development class (0.84-0.98) but low in other classes (0.35-0.44). This analysis shows continuous increase in the level of SOC over time to be common in adulthood, irrespective of age. High SOC, rather than higher age, seems to determine a stable development of the SOC.

Dimensional, Categorical, or Dimensional-Categories: Testing the Latent Structure of Anxiety Sensitivity Among Adults Using Factor-Mixture Modeling

The present study tested multiple, competing latent structural models of anxiety sensitivity (AS), as measured by the Anxiety Sensitivity Index-3 (ASI-3; Taylor et al., 2007). Data were collected from 3 sites in North America ( N = 634). Participants were predominantly university students ( M = 21.3 years, SD = 5.4). ASI-3 data were evaluated using an integration of mixture modeling and confirmatory factor analysis—factor mixture modeling (FMM; Muthén, 2008). Results supported a 2-class 3-factor partially invariant model of AS. Specifically, the FMM analyses indicated that AS is a taxonic (two-class) variable, and that each categorical class has a unique multidimensional factor structure. Consistent with the specific point-prediction regarding the hypothesized parameters of the putative latent class variable, FMM indicated that the putatively “high-risk” subgroup of cases or latent form of AS composed approximately 12% of the studied sample whereas the putatively “normative” subgroup of cases or latent form of AS composed 88% of the sample. In addition, the AS Physical and Psychological Concerns subscales, but not the Social Concerns subscale, most strongly discriminated between the two latent classes. Finally, comparison of continuous levels of AS Physical and Psychological Concerns between FMM-derived AS latent classes and independent clinical samples of patients with anxiety disorders provided empirical support for the theorized taxonic-dimensional model of AS and anxiety psychopathology vulnerability. Findings are discussed in regard to the implications of this and related research into the nature of AS and anxiety psychopathology vulnerability.

Exploring the Latent Structures of Psychological Constructs in Social Development Using the Dimensional–Categorical Spectrum

This paper provides an introduction to a recently developed conceptual framework-the dimensional-categorical spectrum-for utilizing general factor mixture models to explore the latent structures of psychological constructs. This framework offers advantages over traditional latent variable models that usually employ either continuous latent factors or categorical latent class variables to characterize the latent structure and require an a priori assumption about the underlying nature of the construct as either purely dimension or purely categorical. The modeling process is discussed in detail and then illustrated with data on the delinquency items of Achenbach's child behavior checklist from a sample of children in the National Adolescent and Child Treatment Study.

Abuse and dependence on prescription opioids in adults: a mixture categorical and dimensional approach to diagnostic classification

For the emerging DSM-V, it has been recommended that dimensional and categorical methods be used simultaneously in diagnostic classification; however, little is known about this combined approach for abuse and dependence. Using data (n=37 708) from the 2007 National Survey on Drug Use and Health (NSDUH), DSM-IV criteria for prescription opioid abuse and dependence among non-prescribed opioid users (n=3037) were examined using factor analysis (FA), latent class analysis (LCA, categorical), item response theory (IRT, dimensional), and factor mixture (hybrid) approaches. A two-class factor mixture model (FMM) combining features of categorical latent classes and dimensional IRT estimates empirically fitted more parsimoniously to abuse and dependence criteria data than models from FA, LCA and IRT procedures respectively. This mixture model included a severely affected group (7%) with a comparatively moderate to high probability (0.32-0.88) of endorsing all abuse and dependence criteria items, and a less severely affected group (93%) with a low probability (0.003-0.16) of endorsing all criteria. The two empirically defined groups differed significantly in the pattern of non-prescribed opioid use, co-morbid major depression, and substance abuse treatment use. A factor mixture model integrating categorical and dimensional features of classification fits better to DSM-IV criteria for prescription opioid abuse and dependence in adults than a categorical or dimensional approach. Research is needed to examine the utility of this mixture classification for substance use disorders and treatment response.

ADHD Across Cultures: Is There Evidence for a Bidimensional Organization of Symptoms?

We examined the phenotypic expression of attention-deficit/hyperactivity disorder (ADHD) across cultures by assessing the factor/latent class structure of its core symptoms. We conducted a systematic review of the literature published from January 1987 to November 2008 using Medline and PsycINFO. We systematically reviewed 2,511 article abstracts, and 48 of these abstracts were included in this review. Research with school-age children from 15 countries including different samples, informants, and rating instruments supported a two-factor ADHD model consisting of inattention and combined hyperactivity and impulsivity. This model was not supported for preschool children. Cross-cultural equivalence for the two-factor model was suggested in some studies. Latent class analyses using parental data and more recent approaches like factor mixture modeling are generally consistent with factor analyses. These findings argue in favor of a cross-cultural validity of the syndrome. The implications of these findings for further research and classificatory systems in mental health like the Diagnostic and Statistical Manual of Mental Disorders (5th ed.) are discussed.

Detecting Social Desirability Bias Using Factor Mixture Models

Based on the conceptualization that social desirable bias (SDB) is a discrete event resulting from an interaction between a scale's items, the testing situation, and the respondent's latent trait on a social desirability factor, we present a method that makes use of factor mixture models to identify which examinees are most likely to provide biased responses, which items elicit the most socially desirable responses, and which external variables predict SDB. Problems associated with the common use of correlation coefficients based on scales' total scores to diagnose SDB and partial correlations to correct for SDB are discussed. The method is demonstrated with an analysis of SDB in the Attitude toward Interprofessional Service-Learning scale with a sample of students from health-related fields.

Use of factor mixture modeling to capture Spearman's law of diminishing returns

Spearman's law of diminishing returns (SLODR) posits that at higher levels of general cognitive ability the general factor ( g) performs less well in explaining individual differences in cognitive test performance. Research has generally supported SLODR, but previous research has required the a priori division of respondents into separate ability or IQ groups. The present study sought to obviate this limitation through the use of factor mixture modeling to investigate SLODR in the Kaufman Assessment Battery for Children-Second Edition (KABC-II). A second-order confirmatory factor model was modeled as a within-class factor structure. The fit and parameter estimates of several models with varying number of classes and factorial invariance restrictions were compared. Given SLODR, a predictable pattern of findings should emerge when factor mixture modeling is applied. Our results were consistent with these SLODR-based predictions, most notably the g factor variance was less in higher g mean classes. Use of factor mixture modeling was found to provide support for SLODR while improving the model used to investigate SLODR.

Globalization and the Growth of International Educational Testing and National Assessment

Education has long been characterized as a central requirement for national economic development and political democratization in the contemporary world. Moreover, international benchmarking has been identified as the “basis for improvement. . . . It is only through such benchmarking that countries can understand relative strengths and weaknesses of their education systems and identify best practices and ways forward” (OECD 2006, 18). Statements such as this example signal an international consensus that has emerged— at least among “developed” countries—about the legitimacy and, even more so, the necessity of international testing and national assessment. As David P. Baker and Gerald K. LeTendre (2005) observe, both international testing and national assessment are linked to efforts to reform educational systems and are often themselves stimuli for further cycles of reform. The results of international testing, they note, will fuel further interest in national assessment. Here we develop an argument about the global forces that have led to the explosive growth of national educational assessment and international testing. In particular, we argue that the international acceptance of testing comes from key ideological forces in the world polity that are associated with the accelerating globalization of national and international cultural, economic, and political structures. As we develop and warrant this argument, we also qualify it by pointing out that national adaptations to this larger world culture may vary depending on the presence and capacities of international organizations and regional associations that act to mediate and adapt these changes to conditions in individual countries. In addition, we consider the effects of subnational movements in introducing pressures for change that may favor more national assessment.

Empirical evidence regarding relations among a model of epistemic and ontological cognition, academic performance, and educational level.

Models of personal epistemology have not been sufficiently integrated despite conceptual similarities. We attempted to model both dimensional and positional aspects of personal epistemology, as well as examine the domain specificity of these phenomena. The conceptual framework for this study was a new model of epistemic and ontological cognitive development that addresses numerous concerns in the literature. A model-based quantitative instrument was created and administered to 740 students ranging from middle-school through graduate school. Results of confirmatory factor and factor-mixture model analyses provided evidence for the construct validity and reliability of scores from the instrument as well as support for many aspects of the underlying conceptual model. Implications for further model development and research are discussed.

Body image disturbance in 1000 male appearance and performance enhancing drug users

Body image disturbance (BID) among men has only recently become a phenomenon of clinical significance with noted heterogeneity in the behavioral consequences of these disturbances. The degree of heterogeneity among appearance and performance enhancing drug (APED) users is unknown and an empirically derived framework for studying BID is necessary. APED users ( N = 1000) were recruited via the Internet and they completed a comprehensive online assessment APED use patterns, motivations, consequences, and BID. Data were evaluated using latent trait, latent class, and factor mixture models. Model results were validated using a range of covariates including cycle characteristics, age, APED history, and APED risk. A 1-Factor, 4-Class model provided the best fit to the data with Class 1 scoring the highest on all measures of BID and Class 4 the lowest on all measures. Class 2 differed in their preference for being lean over muscular and Class 3 preferred adding mass and size. Each class was associated with unique risks, APED history, and training identity. Not all APED users suffer from significant BID and there are unique profiles for those with elevated BID. Future research on male BID should account for this structure in order to better define relevant diagnostic categories and evaluate the clinical significance of BID.

Predictors of Computer Anxiety: A Factor Mixture Model Analysis

A mixture modeling approach was used to assess the existence of latent classes in terms of the perceptions of individuals toward computer anxiety and subsequently predictors of the identified latent classes were examined. The perceptions of individuals were measured using the Computer Anxiety Scale. Mixture models are ideally suited to represent subpopulations or classes of respondents with common patterns of responses. Using data from a sample of Turkish college students, two classes of respondents were identified and designated as occasionally uncomfortable users and as anxious computerphobic users. Results indicated that the best predictors of the identified classes were variables dealing with past computer experiences.

Maternal Ratings of Attention Problems in ADHD: Evidence for the Existence of a Continuum

ObjectiveTo investigate whether items assessing attention problems provide evidence of quantitative differences or categorically distinct subtypes of attention problems (APs) and to investigate the relation of empirically derived latent classes to DSM-IV diagnoses of subtypes of attention-deficit/hyperactivity disorder (ADHD), for example, combined subtype, predominantly inattentive type, and predominantly hyperactive/impulsive type. MethodData on attention problems were obtained from maternal ratings on the Child Behavior Check List (CBCL). Latent class models, which assume categorically different subtypes, and factor mixture models, which permit severity differences, are fitted to data obtained from Dutch boys at age 7 (N = 8,079), 10 (N = 5,278), and 12 years (N = 3,139). The fit of the different models to the data is compared to decide which model, and hence, which corresponding interpretation of AP, is most appropriate. Next, ADHD diagnoses are regressed on latent class membership in a subsample of children. ResultsAt all the three ages, models that distinguish between three mainly quantitatively different classes (e.g., mild, moderate, and severe attention problems) provide the best fit to the data. Within each class, the CBCL items measure three correlated continuous factors that can be interpreted in terms of hyperactivity/impulsivity, inattentiveness/dreaminess, and nervous behavior. The AP severe class contains all of the subjects diagnosed with ADHD–combined subtype. Some subjects diagnosed with ADHD–predominantly inattentive type are in the moderate AP class. ConclusionsFactor mixture analyses provide evidence that the CBCL AP syndrome varies along a severity continuum of mild to moderate to severe attention problems. Children affected with ADHD are at the extreme of the continuum. These data are important for clinicians, research scholars, and the framers of the DSM-V as they provide evidence that ADHD diagnoses exist on a continuum rather than as discrete categories. J. Am. Acad. Child Adolesc. Psychiatry, 2009;48(11):1085–1093.

Two-Part Factor Mixture Modeling: Application to an Aggressive Behavior Measurement Instrument

This study introduces a two-part factor mixture model as an alternative analysis approach to modeling data where strong floor effects and unobserved population heterogeneity exist in the measured items. As the names suggests, a two-part factor mixture model combines a two-part model, which addresses the problem of strong floor effects by decomposing the data into dichotomous and continuous response components, with a factor mixture model, which explores unobserved heterogeneity in a population by establishing latent classes. Two-part factor mixture modeling can be an important tool for situations in which ordinary factor analysis produces distorted results and can allow researchers to better understand population heterogeneity within groups. Building a two-part factor mixture model involves a consecutive model building strategy that explores latent classes in the data for each part as well as a combination of the two-part. This model building strategy was applied to data from a randomized preventive intervention trial in Baltimore public schools administered by the Johns Hopkins Center for Early Intervention. The proposed model revealed otherwise unobserved subpopulations among the children in the study in terms of both their tendency toward and their level of aggression. Furthermore, the modeling approach was examined using a Monte Carlo simulation.

Discrete-Time Survival Factor Mixture Analysis for Low-Frequency Recurrent Event Histories

In this article, the latent class analysis framework for modeling single event discrete-time survival data is extended to low-frequency recurrent event histories. A partial gap time model, parameterized as a restricted factor mixture model, is presented and illustrated using juvenile offending data. This model accommodates event-specific baseline hazard probabilities and covariate effects; event recurrences within a single time period; and accounts for within- and between-subject correlations of event times. This approach expands the family of latent variable survival models in a way that allows researchers to explicitly address questions about unobserved heterogeneity in the timing of events across the lifespan.

Distinguishing Between Latent Classes and Continuous Factors with Categorical Outcomes: Class Invariance of Parameters of Factor Mixture Models

Factor mixture models are latent variable models with categorical and continuous latent variables that can be used as a model-based approach to clustering. A previous article covered the results of a simulation study showing that in the absence of model violations, it is usually possible to choose the correct model when fitting a series of models with different numbers of classes and factors within class. The response format in the first study was limited to normally distributed outcomes. This article has 2 main goals, first, to replicate parts of the first study with 5-point Likert scale and binary outcomes, and second, to address the issue of testing class invariance of thresholds and loadings. Testing for class invariance of parameters is important in the context of measurement invariance and when using mixture models to approximate nonnormal distributions. Results show that it is possible to discriminate between latent class models and factor models even if responses are categorical. Comparing models with and without class-specific parameters can lead to incorrectly accepting parameter invariance if the compared models differ substantially with respect to the number of estimated parameters. The simulation study is complemented with an illustration of a factor mixture analysis of 10 binary depression items obtained from a female subsample of the Virginia Twin Registry.

Abstract: A Comparison of the Factor Mixture Model and Taxometric Procedures

Taxometric procedures and the Factor Mixture Model (FMM) have a complimentary set of strengths and weaknesses. Both approaches purport to detect evidence of a latent class structure. Taxometric procedures, popular in psychiatric and psychopathology literature, make no assumptions beyond those needed to compute means and covariances. However, Taxometric procedures assume that observed items are uncorrelated within a class or taxon. This assumption is violated when there are individual differences in the trait underlying the items (i.e., severity differences within class). FMMs can model within-class covariance structures ranging from local independence to multidimensional within-class factor models and permits the specification of more than two classes. FMMs typically rely on normality assumptions for within-class factors and error terms. FMMs are highly parameterized and susceptible to misspecifications of the within-class covariance structure. The current study compared the Taxometric procedures MAXEIG and the Base-Rate Classification Technique to the FMM in their respective abilities to (1) correctly detect the two-class structure in simulated data, and to (2) correctly assign subjects to classes. Two class data were simulated under conditions of balanced and imbalanced relative class size, high and low class separation, and 1-factor and 2-factor within-class covariance structures. For the 2-factor data, simple and cross-loaded factor loading structures, and positive and negative factor correlations were considered. For the FMM, both correct and incorrect within-class factor structures were fit to the data. FMMs generally outperformed Taxometric procedures in terms of both class detection and in assigning subjects to classes. Imbalanced relative class size (e.g., a small minority class and a large majority class) negatively impacted both FMM and Taxometric performance while low class separation was much more problematic for Taxometric procedures than the FMM. Comparisons of alterative FMMs based on information criteria generally resulted in correct model choice but deteriorated when small class separation was combined with imbalanced relative class size.

Refining the tobacco dependence phenotype using the Wisconsin Inventory of Smoking Dependence Motives.

The construct of tobacco dependence is important from both scientific and public health perspectives, but it is poorly understood. The current research integrates person-centered analyses (e.g., latent profile analysis) and variable-centered analyses (e.g., exploratory factor analysis) to clarify the latent structure of nicotine dependence and to guide distillation of the phenotype. Using data from 4 samples of smokers, latent profiles were derived using the Wisconsin Inventory of Smoking Dependence Motives subscale scores. Across all 4 samples, results revealed a unique latent profile that had relative elevations on 4 subscales (Automaticity, Craving, Loss of Control, and Tolerance). Variable-centered analyses supported the uniqueness of these 4 subscales as they constituted a distinct common factor and were the strongest predictors of relapse and other dependence criteria. Conversely, the remaining 9 motives carried little unique predictive validity regarding dependence. Applications of a factor mixture model further supported the presence of a unique class of smokers in relation to a common factor underlying the 4 subscales. The results suggest that a pattern of smoking that is heavy, pervasive, automatic, and relatively unresponsive to instrumental contingencies is a necessary and sufficient condition for severe nicotine dependence.

Using a factor mixture modeling approach in alcohol dependence in a general population sample

Alcohol dependence (AD) is a complex and heterogeneous disorder. The identification of more homogeneous subgroups of individuals with drinking problems and the refinement of the diagnostic criteria are inter-related research goals. They have the potential to improve our knowledge of etiology and treatment effects, and to assist in the identification of risk factors or specific genetic factors. Mixture modeling has advantages over traditional modeling that focuses on either the dimensional or categorical latent structure. The mixture modeling combines both latent class and latent trait models, but has not been widely applied in substance use research. The goal of the present study is to assess whether the AD criteria in the population could be better characterized by a continuous dimension, a few discrete subgroups, or a combination of the two. More than seven thousand participants were recruited from the population-based Virginia Twin Registry, and were interviewed to obtain DSM-IV (Diagnostic and Statistical Manual of Mental Disorder, version IV) symptoms and diagnosis of AD. We applied factor analysis, latent class analysis, and factor mixture models for symptom items based on the DSM-IV criteria. Our results showed that a mixture model with 1 factor and 3 classes for both genders fit well. The 3 classes were a non-problem drinking group and severe and moderate drinking problem groups. By contrast, models constrained to conform to DSM-IV diagnostic criteria were rejected by model fitting indices providing empirical evidence for heterogeneity in the AD diagnosis. Classification analysis showed different characteristics across subgroups, including alcohol-caused behavioral problems, comorbid disorders, age at onset for alcohol-related milestones, and personality. Clinically, the expanded classification of AD may aid in identifying suitable treatments, interventions and additional sources of comorbidity based on these more homogenous subgroups of alcohol use problems.

Subtypes Versus Severity Differences in Attention-Deficit/Hyperactivity Disorder in the Northern Finnish Birth Cohort

To investigate whether behaviors of inattention, hyperactivity, and impulsivity among adolescents in Northern Finland reflect qualitatively distinct subtypes of ADHD, variants along a single continuum of severity, or of severity differences within subtypes. Latent class models, exploratory factor models, and factor mixture models were applied to questionnaire data of ADHD behaviors obtained from the Northern Finland Birth Cohort (NFBC). Latent class models correspond to qualitatively distinct subtypes, factor analysis corresponds to severity differences, and factor mixture analysis allows for both subtypes and severity differences within subtypes. A comparison of the different models shows that models that distinguish between a low scoring majority class (unaffecteds) and a high scoring minority class (affecteds), and allow for two factors (inattentive, hyperactive-impulsive) with severity differences provide the best fit. The analysis provides support that a high-scoring minority group (8.8% of males and 6.8% of females) likely reflects an ADHD group in the Northern Finland Birth Cohort, whereas the majority of the population falls into a low-scoring group of unaffecteds. Distinct factors composed of items of inattention and hyperactivity-impulsivity are evident for both sexes with considerable variability in severity within each class.

Introduction: ADHD in an Adolescent Finnish Population

Attention-deficit/hyperactivity disorder (ADHD) is a common, chronic behavioral disorder characterized by inattention, hyperactivity, and impulsivity. A substantial amount of controversy still surrounds ADHD as questions regarding its diagnostic validity continue, and others concerning medication treatment of the syndrome are voiced. The current special section brings to light several new findings that may provide new insight into thinking about ADHD. First and foremost, ADHD is a clearly recognizable condition with a relatively stable prevalence throughout the world. Using DSM-IV diagnostic criteria in a population-based birth cohort of adolescents (ages 16Y18) in northern Finland, the estimated prevalence of ADHD is 8.5%. The clinical characteristics of ADHD in this population isolate in Finland are remarkably comparable to that found in other adolescent samples drawn from around the world with more males than females affected, persistence into adolescence (from childhood) in some two thirds of cases, comparable subtype distributions, and strong associations with other psychiatric disorders, including anxiety, depression, substance abuse and dependence, and conduct and oppositional disorders. Smalley et al. (2007) describe these findings along with a detailed description of the birth cohort and sampling methods. The second major point to be highlighted by the articles in this special section is that an analysis of ADHD symptomatology at a population level, although varied in level of impairment, comorbidity, and other features, reveals ADHD to be best described as a unitary construct rather than being composed of multiple subtypes. Previous studies suggesting that numerous latent classes were necessary to capture symptom data may have been limited because of the statistical methodologies used. The development of a robust statistical procedure that incorporates both factor analysis and latent class analysis (factor mixture modeling) enables a more rigorous evaluation of putative classes or groups (subtypes) in ADHD. At least by the time of adolescence, there appears to be only a need for two classes (affected and unaffected) at a population level based on behaviors reported using the Strengths and Weaknesses of ADHD-Symptoms and Normal-Behavior (SWAN) survey, and no need for specific subtypes based on inattentive or hyperactiveimpulsive symptoms, a crucial distinction for genetic studies. These data presented by Lubke and colleagues (2007) demonstrate the powerful role newly developed statistical approaches can have on interpreting data. The third major point revealed in this series of articles is the striking evidence that executive function deficits are by no means ubiquitous in ADHD and that although they occur with greater frequency (~50%) in that sample than among normal controls (~8%), they are not evident for about half of the adolescents with ADHD. These data, presented by Loo and colleagues (2007), highlight the need for further research on the cognitive endophenotypes in ADHD and highlight the