Uniqueness of real-valued hierarchical classes models

Two novel uniqueness theorems are derived for the family of hierarchical classes (HICLAS) models, a family of structural decomposition models for N-way N-mode data that imply simultaneous hierarchically organized classifications of all modes involved in the data. The theorems generalize earlier results on binary HICLAS models to the integer- and real-valued cases. In addition, they allow for a shorter and insightful proof of a result on Boolean matrix invertibility that goes back to earlier work of Luce (1952) and Rutherford (1963).     

Hierarchical Classes Modeling of Rating Data

Hierarchical classes (HICLAS) models constitute a distinct family of structural models for N-way N-mode data. All members of the family include N simultaneous and linked classifications of the elements of the N modes implied by the data; those classifications are organized in terms of hierarchical, if–then-type relations. Moreover, the models are accompanied by comprehensive, insightful graphical representations. Up to now, the hierarchical classes family has been limited to dichotomous or dichotomized data. In the present paper we propose a novel extension of the family to two-way two-mode rating data (HICLAS-R). The HICLAS-R model preserves the representation of simultaneous and linked classifications as well as of generalized if–then-type relations, and keeps being accompanied by a comprehensive graphical representation. It is shown to bear interesting relationships with classical real-valued two-way component analysis and with methods of optimal scaling. The research reported in this paper was supported by the Research Fund of the University of Leuven (GOA/00/02 and GOA/05/04) and by the Fund for Scientific Research-Flanders (project G.0146.06). Eva Ceulemans is a Post-doctoral Researcher supported by the Fund for Scientific Research, Flanders. The authors gratefully acknowledge the help of Gert Quintiens and Kaatje Bollaerts in collecting the data used in Section 4 and of Jan Schepers in additional analyses of these data.     

Bayesian Hierarchical Classes Analysis

Hierarchical classes models are models for N-way N-mode data that represent the association among the N modes and simultaneously yield, for each mode, a hierarchical classification of its elements. In this paper we present a stochastic extension of the hierarchical classes model for two-way two-mode binary data. In line with the original model, the new probabilistic extension still represents both the association among the two modes and the hierarchical classifications. A fully Bayesian method for fitting the new model is presented and evaluated in a simulation study. Furthermore, we propose tools for model selection and model checking based on Bayes factors and posterior predictive checks. We illustrate the advantages of the new approach with applications in the domain of the psychology of choice and psychiatric diagnosis. Iwin Leenen is now at the Instituto Mexicano de Investigación de Familia y Población (IMIFAP), Mexico. The research reported in this paper was partially supported by the Spanish Ministerio de Educación y Ciencia (programa Ramón y Cajal) and by the Research Council of K.U.Leuven (PDM/99/037, GOA/2000/02, and GOA/2005/04). The authors are grateful to Johannes Berkhof for fruitful discussions.     

The Local Minima Problem in Hierarchical Classes Analysis: An Evaluation of a Simulated Annealing Algorithm and Various Multistart Procedures

Hierarchical classes models are quasi-order retaining Boolean decomposition models for N-way N-mode binary data. To fit these models to data, rationally started alternating least squares (or, equivalently, alternating least absolute deviations) algorithms have been proposed. Extensive simulation studies showed that these algorithms succeed quite well in recovering the underlying truth but frequently end in a local minimum. In this paper we evaluate whether or not this local minimum problem can be mitigated by means of two common strategies for avoiding local minima in combinatorial data analysis: simulated annealing (SA) and use of a multistart procedure. In particular, we propose a generic SA algorithm for hierarchical classes analysis and three different types of random starts. The effectiveness of the SA algorithm and the random starts is evaluated by reanalyzing data sets of previous simulation studies. The reported results support the use of the proposed SA algorithm in combination with a random multistart procedure, regardless of the properties of the data set under study. Eva Ceulemans is a post-doctoral fellow of the Fund for Scientific Research Flanders (Belgium). Iwin Leenen is a post-doctoral researcher of the Spanish Ministerio de Educación y Ciencia (programa Ramón y Cajal). The research reported in this paper was partially supported by the Research Council of K.U. Leuven (GOA/05/04).     

The analysis of three-way contingency tables by three-mode association models

TheRC(M) association model (Goodman, 1979, 1985, 1986, 1991) is useful for analyzing the relationship between the variables of a 2-way cross-classification. The models presented here are generalizations of theRC(M) association model for 3-way tables. The family of models proposed here, 3-mode association models, use Tucker's 3-mode components model (Tucker, 1964, 1966; Kroonenberg, 1983) to represent either the three factor interaction or the combined effects of two and three factor interactions. An example from a study in developmental psychology (Kramer & Gottman, 1992) is provided to illustrate the usefulness of the proposed models.I thank Stanley Wasserman, Laurie Kramer, Ulf Böckenholt, Larwence Hubert, Jeffrey Tanaka, and five anonymous reviewers for valuable comments.     

The CHIC Model: A Global Model for Coupled Binary Data

Often problems result in the collection of coupled data, which consist of different N-way N-mode data blocks that have one or more modes in common. To reveal the structure underlying such data, an integrated modeling strategy, with a single set of parameters for the common mode(s), that is estimated based on the information in all data blocks, may be most appropriate. Such a strategy implies a global model, consisting of different N-way N-mode submodels, and a global loss function that is a (weighted) sum of the partial loss functions associated with the different submodels. In this paper, such a global model for an integrated analysis of a three-way three-mode binary data array and a two-way two-mode binary data matrix that have one mode in common is presented. A simulated annealing algorithm to estimate the model parameters is described and evaluated in a simulation study. An application of the model to real psychological data is discussed. T. Wilderjans is a Research Assistant of the Fund for Scientific Research—Flanders (Belgium). The research reported in this paper was partially supported by the Research Council of K.U. Leuven (GOA/2005/04). We are grateful to Kristof Vansteelandt for providing us with an interesting data set. We also thank three anonymous reviewers for their useful comments.     

Family Allocentrism and Adolescent Depressive Symptoms: The Role of Self-Identity Style

Recent research has found that a strong family allocentrism relates to reduced adolescent depressive symptoms. Besides providing continuous support for this relation, this research extended the scope by exploring whether there was a U-shaped association between family allocentrism and depressive symptoms and testing the mediation effect of identity style among Italian adolescents (N?=?387, 183 boys, 204 girls, M_age?=?16.38 years). Result of hierarchical regression model showed that the association between family allocentrism and depressive symptoms was linear rather than U-shaped. More importantly, this linear relation was mediated by normative and diffuse-avoidant style. In sum, the current findings suggest that adolescents who are allocentric toward family tend to follow family members’ expectations to establish self-identity and deal with identity issues more proactively, and thus they are less likely to experience depressive symptoms. Moreover, there is no significant evidence that too much family allocentrism would lead to elevated depressive symptoms.     

Communal Responsiveness in Relationships with Female versus Male Family Members

Two studies of college students in the US utilized a new methodological approach in which participants arranged their multiple family members (i.e. parents, siblings, aunts, and uncles) within a series of relationship network grids. These grids measured participants’ own feelings of communal responsiveness toward and perceived feelings of communal responsiveness from each family member relative to one another. The results of Study 1 (N = 86) and Study 2 (N = 111) supported the hypotheses that (1) people perceive more responsiveness from female family members than from male family members and (2) people feel more responsive toward female than toward male family members. Study 2 provided evidence that these associations were mediated by felt and perceived intimacy, dependence, and obligation, but not liking.     

Can teacher-child relationships alter the effects of early socioeconomic status on achievement in middle childhood?

Using data from the NICHD SECCYD (N = 1053), we used two-level hierarchical linear models with site fixed effects to examine whether teacher-child closeness and conflict moderated associations between two indicators of early socioeconomic status (maternal education and family income) and standardized measures of children's math and reading achievement at 54 months, 1st, 3rd, and 5th grades. Children whose mothers had lower levels of education and conflictual relationships with teachers exhibited lower reading achievement, on average, across elementary school. At the same time, children with less educated mothers who experienced increases in teacher-child closeness and decreases in teacher-child conflict exhibited improvements in reading achievement across elementary school. Finally, low teacher-child closeness elevated the risk for poor math achievement posed by low family income. Implications for intervention design and development are discussed.     

A constrained optimization model of risky decisions

A decision model is formulated for individual choices between gambles whose probabilities and payoffs are explicitly stated. The decision situation is characterized as R_N = (X, P, Z, T, α) where X is a payoff matrix, P is the objective probability distribution over the states of nature, Z is a class of objective functions, T is tolerable regret and 1 ? α is the maximum probability for accepting regrets greater than T. Given R_N, the problem of selecting a strategy is the solution of a chance constrained optimization problem. The solutions for choice situations having two alternatives and n states of nature are developed in a series of theorems. Some implications for experimentation and possible applications are discussed.     

Psychometric analysis of the Empathy Quotient (EQ)

This study assessed the dimensionality of the Empathy Quotient (EQ) using two statistical approaches: Rasch and Confirmatory Factor Analysis (CFA). Participants included N = 658 with an autism spectrum condition diagnosis (ASC), N = 1375 family members of this group, and N = 3344 typical controls. Data were applied to the Rasch model (Rating Scale) using WINSTEPS. The Rasch model explained 83% of the variance. Reliability estimates were greater than .90. Analysis of differential item functioning (DIF) demonstrated item invariance between the sexes. Principal Components Analysis (PCA) of the residual factor showed separation into Agree and Disagree response subgroups. CFA suggested that 26-item model with response factors had the best fit statistics (RMSEA.05, CFI .93). A shorter 15-item three-factor model had an omega (ω) of .779, suggesting a hierarchical factor of empathy underlies these sub-factors. The EQ is an appropriate measure of the construct of empathy and can be measured along a single dimension.     

Body size dissatisfaction and avoidance behavior: How gender,age, ethnicity,and relative clothing size predict what some won’t try

Sixty-eight percent of U.S. adults are overweight/obese, and this epidemic has physical, psychosocial, and behavioral consequences. An internet sample of adults (N = 2997) perceiving themselves as larger than ideal in clothing size reported their body mass index (BMI), relative clothing size (RS; discrepancy between current and ideal size), and avoidance behaviors. Exploratory factor analysis of 10 avoidance items produced social avoidance and body display avoidance factors. A relative importance analysis revealed RS as a better predictor than BMI for avoidance. A hierarchical multivariate analysis of covariance found RS to predict both avoidance constructs. The relationship between RS and both avoidance constructs was stronger for women than men, and for younger as compared to older participants. Caucasians reported more body display avoidance than African Americans. This suggests that personal dissatisfaction with body size may deter involvement in varied life events and that women are especially avoidant of activities that entail displaying their bodies.     

Utility-uncertainty trade-off structures

A qualitative axiomatization of a generalization of expected utility theory is given in which the expected value of simple gambles is not necessarily the product of subjective probability and utility. Representation and uniqueness theorems for these generalized structures are derived for both Archimedean and nonarchimedean cases. It is also shown that a simple condition called distributivity is necessary and sufficient in the case of simple gambles for one of these generalized expected utility structures to have simultaneously an additive subjective probability function and a multiplicative combining rule for expected values.     

Motor vehicle accidents and adolescents: An empirical study on their emotional and behavioral profiles,defense strategies and parental support

Background: Research has limitedly focused on adolescents’ emotional–behavioral functioning preceding road collisions and on the role of family support. Objective: To verify whether the rates of motorbikes collisions among adolescents are associated with their emotional–behavioral functioning, their use of specific defense strategies and family support. Method: N = 150 adolescents who visited an emergency department for road accidents were selected and completed self-report questionnaires assessing emotional–behavioral functioning, difficulty in identifying and describing emotions, use of defense strategies and perceived family support. Results: Higher rates of motorbike collisions are associated with more maladaptive emotional–behavioral functioning. Higher perceived family support is associated with lower rates of collisions. Conclusions: Recidivism of motor vehicle collision among adolescents can be considered as a form of acting-out caused by their psychological difficulties.     

The Factor Structure of the Forms of Self-Criticising/Attacking & Self-Reassuring Scale in Thirteen Distinct Populations

There is considerable evidence that self-criticism plays a major role in the vulnerability to and recovery from psychopathology. Methods to measure this process, and its change over time, are therefore important for research in psychopathology and well-being. This study examined the factor structure of a widely used measure, the Forms of Self-Criticising/Attacking & Self-Reassuring Scale in thirteen nonclinical samples (N?=?7510) from twelve different countries: Australia (N?= 319), Canada (N?= 383), Switzerland (N?= 230), Israel (N?=?476), Italy (N?=?389), Japan (N?=?264), the Netherlands (N?=?360), Portugal (N?=?764), Slovakia (N?=?1326), Taiwan (N?=?417), the United Kingdom 1 (N?=?1570), the United Kingdom 2 (N?=?883), and USA (N?=?331). This study used more advanced analyses than prior reports: a bifactor item-response theory model, a two-tier item-response theory model, and a non-parametric item-response theory (Mokken) scale analysis. Although the original three-factor solution for the FSCRS (distinguishing between Inadequate-Self, Hated-Self, and Reassured-Self) had an acceptable fit, two-tier models, with two general factors (Self-criticism and Self-reassurance) demonstrated the best fit across all samples. This study provides preliminary evidence suggesting that this two-factor structure can be used in a range of nonclinical contexts across countries and cultures. Inadequate-Self and Hated-Self might not by distinct factors in nonclinical samples. Future work may benefit from distinguishing between self-correction versus shame-based self-criticism.     

The Relative Contribution of a Typological versus a Dimensional Approach for Understanding Obsessive-Compulsive Symptoms in Adolescents

In order to better understand the heterogeneous nature of Obsessive-Compulsive (OC) symptoms, a typological or a dimensional approach can be used to structure the variety of symptoms into a set of core components. However, there is still no consensus on which approach is the most robust to predict several OC-related criterion measures, especially in adolescents. From this perspective, the current study empirically identified OC classes (i.e., types), and explored whether types or dimensions are the strongest predictors of adolescent OC-related criterion variables. To identify OC classes, we conducted latent class analysis on the Youth Obsessive-Compulsive Symptoms Scale (YOCSS; De Caluwé and De Clercq 2014) that was completed by 682 community and referred adolescents (71.4 % girls, 12–18 years old, mean age = 15.67, SD = 1.53), and we also computed OC dimension scores as outlined in De Caluwé and De Clercq (2014). We subsequently used hierarchical regression analysis to examine the incremental validity of the OC classes beyond the OC domains, and vice versa, in predicting several OC-related criterion variables that were completed by the adolescents or their mothers (N = 325). The results indicated that the two identified OC classes only differed quantitatively but not qualitatively, hence reflecting severity classes, and also showed that OC domains have significant effects beyond the effects of the OC classes, whereas the reverse did not hold. The dimensional approach appears to have the strongest predictive value for OC symptomatology in adolescents, leading to clinical implications for conceptualization and assessment of obsessive and compulsive problems in younger age groups.     

Comparing hierarchical models of personality pathology

Two dimensional, hierarchical classification models of personality pathology have emerged as alternatives to traditional categorical systems: multi-tiered models with increasing numbers of factors and models that distinguish between a general factor of severity and specific factors reflecting style. Using a large sample (N = 840) with a range of psychopathology, we conducted exploratory factor analyses of individual personality disorder criteria to evaluate the validity of these conceptual structures. We estimated an oblique, “unfolding” hierarchy and a bifactor model, then examined correlations between these and multi-method functioning measures to enrich interpretation. Four-factor solutions for each model, reflecting rotations of each other, fit well and equivalently. The resulting structures are consistent with previous empirical work and provide support for each theoretical model.     

A latent transition analysis of the longitudinal stability of dual-factor mental health in adolescence

Dual-factor models of mental health are increasingly supported but little is known about longitudinal trends in dual-factor mental health. The current study used latent profile analysis (LPA) to empirically identify dual-factor mental health classes at each of Grades 9 through 12 and latent transition analysis (LTA) to examine stability of classes over four academic years. A sample of 875 adolescents from two cohorts reported on their social-emotional strengths and psychological distress. Cross-sectional LPAs for each grade year resulted in four mental health classes: complete mental health, moderately mentally healthy, symptomatic but content, and troubled. An LTA model indicated that the complete mental health class exhibited the most stability, followed by moderately mentally healthy and symptomatic but content classes. The troubled class exhibited the least stability. Less than 24% of participants remained in the same mental health class across all years. Findings support regular monitoring of students' dual-factor mental health to accurately inform mental health promotion, prevention, and intervention efforts.