Factor Analysis of Scales Composed of Binary Items: Illustration with the Maudsley Obsessional Compulsive Inventory

It is well known that traditional factor analytic methods are designed for use with continuous data, and suboptimal for items with 2 response options (i.e., binary items). Nevertheless, traditional methods have been employed in all previous assessment of the dimensionality of the Maudsley Obsessional Compulsive Inventory (MOCI), a true/false measure of obsessive–compulsive symptoms ( R. J. Hodgson &; S. Rachman, 1977). The aim of this paper is to illustrate 2 techniques that are more suitable for factor-analyzing binary items than traditional methods, through application to the MOCI (n = 1,080). Computer files for use with the TESTFACT (D. Wilson, R. L. Wood, &; R. Gibbons, 1991 ) and Mplus (Muthén &; Muthén, 1998) computer programs are provided. Results from an inappropriately applied principal axis factor analysis are presented for comparison, and factor structures, loadings, and interfactor correlations are compared across methods.     

On muthén’s maximum likelihood for two-level covariance structure models

Data in social and behavioral sciences are often hierarchically organized. Special statistical procedures that take into account the dependence of such observations have been developed. Among procedures for 2-level covariance structure analysis, Muthén’s maximum likelihood (MUML) has the advantage of easier computation and faster convergence. When data are balanced, MUML is equivalent to the maximum likelihood procedure. Simulation results in the literature endorse the MUML procedure also for unbalanced data. This paper studies the analytical properties of the MUML procedure in general. The results indicate that the MUML procedure leads to correct model inference asymptotically when level-2 sample size goes to infinity and the coefficient of variation of the level-1 sample sizes goes to zero. The study clearly identifies the impact of level-1 and level-2 sample sizes on the standard errors and test statistic of the MUML procedure. Analytical results explain previous simulation results and will guide the design or data collection for the future applications of MUML.This research was supported by NSF Grant DMS04-37167.We thank Dr.Bengt Muthén for providing key references. We are also grateful to three expert reviewers for their constructive comments that have led the paper to an improvement over the previous version.This revised article was published online in August 2005 with the PDF paginated correctly.     

A general structural equation model with dichotomous,ordered categorical,and continuous latent variable indicators

A structural equation model is proposed with a generalized measurement part, allowing for dichotomous and ordered categorical variables (indicators) in addition to continuous ones. A computationally feasible three-stage estimator is proposed for any combination of observed variable types. This approach provides large-sample chi-square tests of fit and standard errors of estimates for situations not previously covered. Two multiple-indicator modeling examples are given. One is a simultaneous analysis of two groups with a structural equation model underlying skewed Likert variables. The second is a longitudinal model with a structural model for multivariate probit regressions.This research was supported by Grant No. 81-IJ-CX-0015 from the National Institute of Justice, by Grant No. DA 01070 from the U.S. Public Health Service, and by Grant No. SES-8312583 from the National Science Foundation. I thank Julie Honig for drawing the figures. Requests for reprints should be sent to Bengt Muthén, Graduate School of Education, University of California, Los Angeles, California 90024.     

Finite mixtures in confirmatory factor-analysis models

In this paper, various types of finite mixtures of confirmatory factor-analysis models are proposed for handling data heterogeneity. Under the proposed mixture approach, observations are assumed to be drawn from mixtures of distinct confirmatory factor-analysis models. But each observation does not need to be identified to a particular model prior to model fitting. Several classes of mixture models are proposed. These models differ by their unique representations of data heterogeneity. Three different sampling schemes for these mixture models are distinguished. A mixed type of the these three sampling schemes is considered throughout this article. The proposed mixture approach reduces to regular multiple-group confirmatory factor-analysis under a restrictive sampling scheme, in which the structural equation model for each observation is assumed to be known. By assuming a mixture of multivariate normals for the data, maximum likelihood estimation using the EM (Expectation-Maximization) algorithm and the AS (Approximate-Scoring) method are developed, respectively. Some mixture models were fitted to a real data set for illustrating the application of the theory. Although the EM algorithm and the AS method gave similar sets of parameter estimates, the AS method was found computationally more efficient than the EM algorithm. Some comments on applying the mixture approach to structural equation modeling are made.Note: This paper is one of the Psychometric Society's 1995 Dissertation Award papers.—EditorThis article is based on the dissertation of the author. The author would like to thank Peter Bentler, who was the dissertation chair, for guidance and encouragement of this work. Eric Holman, Robert Jennrich, Bengt Muthén, and Thomas Wickens, who served as the committee members for the dissertation, had been very supportive and helpful. Michael Browne is appreciated for discussing some important points about the use of the approximate information in the dissertation. Thanks also go to an anonymous associate editor, whose comments were very useful for the revision of an earlier version of this article.     

Latent variable modeling in heterogeneous populations

Common applications of latent variable analysis fail to recognize that data may be obtained from several populations with different sets of parameter values. This article describes the problem and gives an overview of methodology that can address heterogeneity. Artificial examples of mixtures are given, where if the mixture is not recognized, strongly distorted results occur. MIMIC structural modeling is shown to be a useful method for detecting and describing heterogeneity that cannot be handled in regular multiple-group analysis. Other useful methods instead take a random effects approach, describing heterogeneity in terms of random parameter variation across groups. These random effects models connect with emerging methodology for multilevel structural equation modeling of hierarchical data. Examples are drawn from educational achievement testing, psychopathology, and sociology of education. Estimation is carried out by the LISCOMP program.Presidential address delivered at the Psychometric Society meetings in Los Angeles, USA and Leuven, Belgium, July 1989. The research was supported by Grant No. SES-8821668 from the National Science Foundation and by Grant No. OERI-G-86-003 from the Office for Educational Research and Improvement, Department of Education. I thank Leigh Burstein, Mike Hollis, Linda Muthén, and Albert Satorra for helpful discussions and Tammy Tam, Jin-Wen Yang, Suk-Woo Kim, and Lynn Short for computational assistance. Designs were created by Arlette Collier, Rita Ling and Jennifer Edic-Bryant.     

Limited information estimation and testing of Thurstonian models for paired comparison data under multiple judgment sampling

We relate Thurstonian models for paired comparisons data to Thurstonian models for ranking data, which assign zero probabilities to all intransitive patterns. We also propose an intermediate model for paired comparisons data that assigns nonzero probabilities to all transitive patterns and to some but not all intransitive patterns.There is a close correspondence between the multidimensional normal ogive model employed in educational testing and Thurstone's model for paired comparisons data under multiple judgment sampling with minimal identification restrictions. Alike the normal ogive model, Thurstonian models have two formulations, a factor analytic and an IRT formulation. We use the factor analytic formulation to estimate this model from the first and second order marginals of the contingency table using estimators proposed by Muthén. We also propose a statistic to assess the fit of these models to the first and second order marginals of the contingency table. This is important, as a model may reproduce well the estimated thresholds and tetrachoric correlations, yet fail to reproduce the marginals of the contingency table if the assumption of multivariate normality is incorrect.A simulation study is performed to investigate the performance of three alternative limited information estimators which differ in the procedure used in their final stage: unweighted least squares (ULS), diagonally weighted least squares (DWLS), and full weighted least squares (WLS). Both the ULS and DWLS show a good performance with medium size problems and small samples, with a slight better performance of the ULS estimator.This paper is based on the author's doctoral dissertation; Ulf Böckenholt, advisor. The final stages of this research took place while the author was at the Department of Statistics and Econometrics, Universidad Carlos III de Madrid. The author is indebted to Adolfo Hernández for stimulating discussions that helped improve this paper, and to Ulf Böckenholt and the Associate Editor for a number of helpfulsuggestions to a previous draft.     

Anchor Point Selection: Scale Alignment Based on an Inequality Criterion

For detecting differential item functioning (DIF) between two or more groups of test takers in the Rasch model, their item parameters need to be placed on the same scale. Typically this is done by means of choosing a set of so-called anchor items based on statistical tests or heuristics. Here the authors suggest an alternative strategy: By means of an inequality criterion from economics, the Gini Index, the item parameters are shifted to an optimal position where the item parameter estimates of the groups best overlap. Several toy examples, extensive simulation studies, and two empirical application examples are presented to illustrate the properties of the Gini Index as an anchor point selection criterion and compare its properties to those of the criterion used in the alignment approach of Asparouhov and Muthén. In particular, the authors show that—in addition to the globally optimal position for the anchor point—the criterion plot contains valuable additional information and may help discover unaccounted DIF-inducing multidimensionality. They further provide mathematical results that enable an efficient sparse grid optimization and make it feasible to extend the approach, for example, to multiple group scenarios.     

Simultaneous factor analysis of dichotomous variables in several groups

A new method is proposed for a simultaneous factor analysis of dichotomous responses from several groups of individuals. The method makes it possible to compare factor loading pattern, factor variances and covariances, and factor means over groups. The method uses information from first and second order proportions and estimates the model by generalized least-squares. Hypotheses regarding different degrees of invariance over groups may be evaluated by a large-sample chi-square test.The research of the first author was supported partly by the Bank of Sweden Tercentenary Foundation under project Structural Equation Models in the Social Sciences, project director Karl G. Jöreskog, and partly by the Swedish Research Council in the Humanistic and Social Sciences under project Analysis of Contingency Tables, project director Bengt Muthén.     

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.     

Impact of a prevention program on aggressive children's friendships and social adjustment

A group of 46 aggressive boys aged 8 to 9 years participated in a prevention program aimed at reducing their externalizing problems in the short term and at preventing delinquency in the long term. Outcome measures were collected during the 3-year period following the prevention program. At that time, the boys were 10, 11, and 12 years old. Outcome measures included teacher ratings of aggressiveness and self-reports of delinquent behaviors. The boys' friends were rated on disruptive behaviors by their classmates. The experimental boys' outcome measures were compared to the measures obtained from 58 aggressive boys in a control group. The disruptive ratings of the experimental and control subjects' best friends were also compared. Differences in teacher-rated aggressiveness between the two groups increased from one year to the next for the 3-year followup period. Similarly, the friends' disruptive scores differed increasingly between the two groups over the 3-year period. The effect of the prevention program on the subjects' friendships and the mediating impact of friends with regard to social adjustment were stressed.This study was funded by the following agencies: National Welfare Grants Program of the Canadian Ministry of Health and Welfare, Conseil Québécois de la Recherche Sociale, Conseil de la Santé et des Services Sociaux Régional du Montréal Métropolitain, Fondation Cité des Prairies, Fonds FCAR-Centre et Equipes, Institut de la Recherche en Psycho-Education de Montréal, Centre d'Accueil le Mainbourg. Lucie Bertrand, Rita Béland, Michel Bouillon, Raymond Labelle, Hélène O'Reilly, and Daniel Reclus-Prince supervised or administered the intervention.     

A note on verisimilitude and relativization to problems

This note aims at critically assessing a little-noticed proposal made by Popper in the second edition ofObjective Knowledge to the effect that verisimilitude of scientific theories should be made relative to the problems they deal with. Using a simple propositional calculus formalism, it is shown that the relativized definition fails for the very same reason why Popper's original concept of verisimilitude collapsed-only if one of two theories is true can they be compared in terms of the suggested definition of versimilitude.This note was written when the author was visiting the Groupe de Recherche en Épistémologie Comparative (Université du Québec à Montréal).     

Protégés’ and mentors’ reactions to participating in formal mentoring programs: A qualitative investigation

Mentors and protégés from two formal mentoring programs were interviewed about the benefits associated with program participation, problems encountered in the program, and recommendations for program improvements. The most commonly reported benefits for protégés included learning, coaching, career planning, and psychosocial support. Mentors most frequently reported learning, developing a personal relationship, personal gratification, and enhanced managerial skills. Both groups identified a range of problems including mentor-protégé mismatches, scheduling difficulties, and geographic distance. Unique problems were also identified, including mentor neglect (by protégés), unmet expectations (by protégés), structural separation from the mentor (by protégés), and feelings of personal inadequacy (by mentors). Finally, suggestions for program improvement were identified such as clearer communication of program objectives, better matching, targeted participation in the program, and better program monitoring. Findings are discussed in terms of what we currently know about informal mentoring and implications for mentoring theory. Suggestions for mentoring practice are also discussed.     

Behavioral assessment of methylphenidate in a child with frontal lobe damage

The assessment and management of inattentive, hyperactive, and impulsive behavior in a 6-year-old girl who experienced frontal lobe damage are described. A multimodel approach combining medical, educational, and behavioral techniques to assess hyperactive behavior, optimal medication level, and medication and psychotherapeutic effectiveness is described. The results of the study suggest that in similar cases, children and adolescents manifesting these behaviors should be given a trial of stimulant medication in a controlled environment to assess if such therapy is indicated. Additional support is given for the increasing need for detanté and cooperation with health-care professionals.     

Protégé selection by mentors: Contributing individual and organizational factors

Protégé selection was examined in a laboratory experiment and a field study of experienced mentors. The results from both studies indicated that protégé willingness to learn was a critical component of protégé selection. Results of the field study also revealed that organizational rewards for developing others related to the influence protégé ability and willingness to learn had on protégé selection. Finally, the field study indicated that mentor motives for mentoring others differentially related to the importance protégé ability and willingness to learn had on protégé selection. Specifically, mentors motivated by self-enhancement were more likely to indicate that protégé ability was important in their selection of protégé, whereas mentors motivated by intrinsic satisfaction were more likely to indicate that protégé willingness to learn was important in their selection of protégé.     

Using mixture models with known class membership to address incomplete covariance structures in multiple‐group growth models

Multi‐group latent growth modelling in the structural equation modelling framework has been widely utilized for examining differences in growth trajectories across multiple manifest groups. Despite its usefulness, the traditional maximum likelihood estimation for multi‐group latent growth modelling is not feasible when one of the groups has no response at any given data collection point, or when all participants within a group have the same response at one of the time points. In other words, multi‐group latent growth modelling requires a complete covariance structure for each observed group. The primary purpose of the present study is to show how to circumvent these data problems by developing a simple but creative approach using an existing estimation procedure for growth mixture modelling. A Monte Carlo simulation study was carried out to see whether the modified estimation approach provided tangible results and to see how these results were comparable to the standard multi‐group results. The proposed approach produced results that were valid and reliable under the mentioned problematic data conditions. We also present a real data example and demonstrate that the proposed estimation approach can be used for the chi‐square difference test to check various types of measurement invariance as conducted in a standard multi‐group analysis.     

Body size estimation in early adolescence: factors associated with perceptual accuracy in a nonclinical sample

This study investigated body size estimation in Norwegian adolescents (aged 12-15; N=406) using a distorting photograph technique. The percentage of over- or underestimation was calculated for pictures of the subject, other persons and a neutral object. The Eating Disorders Inventory for Children (EDI-C) was also completed. Among adolescents at risk of eating problems, girls tended to overestimate their own body size while boys showed a pattern of underestimation, compared to a relatively accurate body perception for low-risk subjects. The groups did not differ in the perception of the neutral object. Important predictors of perceived body size included the size estimation of other children, preoccupation with weight and shape, self-esteem, and emotional instability. The results support the predictive value of body size estimation. Gender differences in judgement bias can be interpreted within present aesthetic ideals and their relation to self perception, body image, and eating problems in adolescence.     

Impulsive and premeditated subtypes of aggression in conduct disorder: differences in time estimation

Research aimed at identifying and studying subtypes of aggression have historically dichotomized aggressive subtypes, although specific nomenclature has varied; one approach has been to classify aggressive behavior as predominantly impulsive or predominantly premeditated. There are a number of behavioral and cognitive differences between those exhibiting these different forms of aggression. This study was designed to extend understanding of the impulsive/premeditated aggression dichotomy by comparing time estimation among adolescents exhibiting predominantly impulsive or predominantly premeditated forms of physical aggression who have a psychiatric diagnosis of conduct disorder (CD). Time estimation has previously been shown to be disrupted in impulsive and some aggressive individuals. Time estimation was compared between healthy Controls (n = 37) and two groups of adolescents with CD, those with histories of either predominantly impulsive (CD-Impulsive, n = 26) or predominantly premeditated (CD-Premeditated, n = 38) aggressive behaviors. Participants completed five computerized trials during which they estimated when 1 min had passed. Among aggressive adolescents with CD, the misperception of time was specific to those with histories of impulsive aggression, although time estimates improved with repeated testing and performance feedback. This study confirms the importance of considering the role and type of physical aggression when studying heterogeneous diagnostic groups like CD and supports the relevance of time estimation to certain subgroups of adolescents with CD.     

Perceived support for mentoring: A multiple perspectives approach

Two studies were conducted to examine how perceptions of support for mentoring relate to mentoring attitudes and outcomes for both protégés and mentors, over and above established predictors. In study 1, protégés provided information on their perceptions of support for mentoring and mentoring received. As expected, perceived management support for mentoring was positively related to career-related and psychosocial support; and perceived mentor accountability for mentoring was negatively related to mentoring problems. In study 2, we examined mentors’ perceptions of support for mentoring in relation to their willingness to mentor others in the future and the extent to which they viewed their current relationship as complementary. Mentors’ perceptions of management support for mentoring were positively related to their belief that mentoring relationships were mutually beneficial. However, consistent with theories of self-determination, as mentors’ perceptions of their own accountability in the relationship increased their willingness to mentor others in the future decreased. Implications for mentoring theory, future research, and applied practice are discussed.     

Mentor and protégé predictors and outcomes of mentoring in a formal mentoring program

This study examines the predictors and outcomes of mentoring received by participants of a 12-month formal mentoring program. Based on relationship theory, we examined how the personality of the individuals in the mentoring dyad, their perceived similarity, and mentor perceived support for mentoring contributed to relationship outcomes. The study includes data from both mentors and protégés at the program launch, midway through the program, and at program close. Mentor proactivity was related to more career and psychosocial mentoring; protégé’s perceptions of similarity to the mentor was related to more psychosocial mentoring. More mentoring was related to positive protégé and mentor outcomes, including improved protégé career clarity over the duration of the study.     

The Role of Formal Mentoring on Business Success and Self-Esteem in Participants of a New Business Start-Up Program

The current study investigated the relationship between career-related mentoring, psychosocial mentoring, business success, and self-esteem in participants of a program that was designed to assist in the establishment of a new business. Seventy-seven protégés and their matched mentors were included in the study. A comparison of mentor and protégé perceptions revealed that mentors considered themselves to provide higher levels of psychosocial support than did the protégés. Protégé perceptions of business success were predicted by the frequency of mentor contact and the level of career-related support provided by their mentor.