Tucker3 hierarchical classes analysis

This paper presents a new model for binary three-way three-mode data, called Tucker3 hierarchical classes model (Tucker3-HICLAS). This new model generalizes Leenen, Van Mechelen, De Boeck, and Rosenberg's (1999) individual differences hierarchical classes model (INDCLAS). Like the INDCLAS model, the Tucker3-HICLAS model includes a hierarchical classification of the elements of each mode, and a linking structure among the three hierarchies. Unlike INDCLAS, Tucker3-HICLAS (a) does not restrict the hierarchical classifications of the three modes to have the same rank, and (b) allows for more complex linking structures among the three hierarchies. An algorithm to fit the Tucker3-HICLAS model is described and evaluated in an extensive simulation study. An application of the model to hostility data is discussed.The first author 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/2000/02). We are grateful to Kristof Vansteelandt for providing us with an interesting data set.     

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.     

Effects of a School‐Based Life Skills and HIV‐Prevention Program for Adolescents in Mexican High Schools1

A school‐based life skills and sexuality education HIV/AIDS program for adolescents was evaluated in Toluca, Mexico, through a quasi‐experimental pre–post design with 1,566 cases, divided over a control group and an experimental group. Based on a previously tested path model, 3 levels of variables were included as a guide for the contents of the program: personal variables (self‐knowledge, self‐efficacy regarding condom use, and decision making), intervening variables (subjective norms about, knowledge about HIV/AIDS, and attitudes toward condoms), and outcome variables (communication on sexuality and intentions to use condoms). Evaluation was conducted following these categories. Significant increases in all of these variables recognized as precursors of safer sex were found in the experimental group.     

Systematic Withdrawal

Although AGM theory contraction (Alchourrón et al., 1985; Alchourrón and Makinson, 1985) occupies a central position in the literature on belief change, there is one aspect about it that has created a fair amount of controversy. It involves the inclusion of the postulate known as Recovery. As a result, a number of alternatives to AGM theory contraction have been proposed that do not always satisfy the Recovery postulate (Levi, 1991, 1998; Hansson and Olsson, 1995; Fermé, 1998; Fermé and Rodriguez, 1998; Rott and Pagnucco, 1999). In this paper we present a new addition, systematic withdrawal, to the family of withdrawal operations, as they have become known. We define systematic withdrawal semantically, in terms of a set of preorders, and show that it can be characterised by a set of postulates. In a comparison of withdrawal operations we show that AGM contraction, systematic withdrawal and the severe withdrawal of Rott and Pagnucco (1999) are intimately connected by virtue of their definition in terms of sets of preorders. In a future paper it will be shown that this connection can be extended to include the epistemic entrenchment orderings of Gärdenfors (1988) and Gärdenfors and Makinson (1988) and the refined entrenchment orderings of Meyer et al. (2000).     

Longitudinal study of a school based HIV/AIDS early prevention program for Mexican adolescents

A quasi-experimental study is reported with four measurement occasions to evaluate longer-term effects of a life-skills and HIV/AIDS school-based prevention program. Trained teachers administered the program promoting precursors of safer sex behavior to 2064 Mexican high-school students at an age before most were sexually active. The variables included in the study (knowledge about HIV/AIDS prevention, attitudes towards use of condoms, subjective norms, intentions to use condoms and life skills as decision-making skills, partner communication and individual responsibility) have been reported as precursors of protective sexual behavior. The results demonstrate the stability of training effects and a positive impact on these precursors over 1 year of follow-up.     

Indclas: A three-way hierarchical classes model

A three-way three-mode extension of De Boeck and Rosenberg's (1988) two-way two-mode hierarchical classes model is presented for the analysis of individual differences in binary object × attribute arrays. In line with the two-way hierarchical classes model, the three-way extension represents both the association relation among the three modes and the set-theoretical relations among the elements of each model. An algorithm for fitting the model is presented and evaluated in a simulation study. The model is illustrated with data on psychiatric diagnosis. Finally, the relation between the model and extant models for three-way data is discussed.The research reported in this paper was partially supported by NATO (Grant CRG.921321 to Iven Van Mechelen and Seymour Rosenberg).     

A Generic Disjunctive/Conjunctive Decomposition Model for n-ary Relations

This paper discusses a generic decomposition model that represents an arbitrary n-ary relation as a disjunctive or conjunctive combination of a number of n-ary component relations of a prespecified type. An important subclass of order-preserving decompositions is defined and its properties are derived. The generic model is shown to subsume various known models as special cases, including the models of Boolean factor analysis, hierarchical classes analysis, and disjunctive/conjunctive nonmetric factor analysis. Moreover, it also subsumes a broad range of new models as exemplified with a novel model for multidimensional parallelogram analysis and novel three-way extensions of nonmetric factor analysis. Copyright 1999 Academic Press.     

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).     

Models for ordinal hierarchical classes analysis

This paper proposes an ordinal generalization of the hierarchical classes model originally proposed by De Boeck and Rosenberg (1998). Any hierarchical classes model implies a decomposition of a two-way two-mode binary arrayM into two component matrices, called bundle matrices, which represent the association relation and the set-theoretical relations among the elements of both modes inM. Whereas the original model restricts the bundle matrices to be binary, the ordinal hierarchical classes model assumes that the bundles are ordinal variables with a prespecified number of values. This generalization results in a classification model with classes ordered along ordinal dimensions. The ordinal hierarchical classes model is shown to subsume Coombs and Kao's (1955) model for nonmetric factor analysis. An algorithm is described to fit the model to a given data set and is subsequently evaluated in an extensive simulation study. An application of the model to student housing data is discussed.