Assessing the Factorial Validity of the Attitudes and Belief Scale 2-Abbreviated Version: A Call for the Development a Gold Standard Method of Measuring Rational and Irrational Beliefs

Rational Emotive Behaviour Therapy (REBT) does not possess a measure of rational and irrational beliefs that meets internationally recognised standards for acceptable psychometric properties. Without such a measure the theory/practice of REBT cannot be rigorously evaluated, thus undermining its scientific veracity. The current study investigates the validity and reliability of a recently developed measure of rational and irrational beliefs: the Attitudes and Belief Scale 2-Abbreviated Version (ABS-2-AV). University students from three countries completed the ABS-2-AV (N = 397). An alternative models framework using confirmatory factor analysis indicated that a theoretically consistent eight-factor model of the ABS-2-AV provided the best fit of the data. A number of post-hoc modifications were required in order to achieve acceptable model fit results, and these modifications revealed important methodological limitations with the ABS-2-AV. Results indicated that the validity of the ABS-2-AV was undermined due to items measuring both the psychological process of interest (rational and irrational beliefs) and the context in which these beliefs processes are presented. This is a serious methodological limitation of the ABS-2 and all questionnaires derived from it, including the ABS-2-AV. This methodological limitation resulted in the ABS-2-AV possessing poor internal reliability. These limitations are discussed in relation to the broader REBT literature and the impact such problems have on research and practice. A call is made for REBT researchers to come together to develop a “gold standard” method of assessing rational and irrational beliefs that meets international standard for psychometric excellence

The k-means algorithm for 3D shapes with an application to apparel design

Clustering of objects according to shapes is of key importance in many scientific fields. In this paper we focus on the case where the shape of an object is represented by a configuration matrix of landmarks. It is well known that this shape space has a finite-dimensional Riemannian manifold structure (non-Euclidean) which makes it difficult to work with. Papers about clustering on this space are scarce in the literature. The basic foundation of the -means algorithm is the fact that the sample mean is the value that minimizes the Euclidean distance from each point to the centroid of the cluster to which it belongs, so, our idea is integrating the Procrustes type distances and Procrustes mean into the -means algorithm to adapt it to the shape analysis context. As far as we know, there have been just two attempts in that way. In this paper we propose to adapt the classical -means Lloyd algorithm to the context of Shape Analysis, focusing on the three dimensional case. We present a study comparing its performance with the Hartigan-Wong -means algorithm, one that was previously adapted to the field of Statistical Shape Analysis. We demonstrate the better performance of the Lloyd version and, finally, we propose to add a trimmed procedure. We apply both to a 3D database obtained from an anthropometric survey of the Spanish female population conducted in this country in 2006. The algorithms presented in this paper are available in the Anthropometry R package, whose most current version is always available from the Comprehensive R Archive Network.Vinue, G.; Simo, A.; Alemany Mut, MS. (2016). The k-means algorithm for 3D shapes with an application to apparel design. Advances in Data Analysis and Classification. 10(1):103-132. doi:10.1007/s11634-014-0187-1S103132101Alemany S, González JC, Nácher B, Soriano C, Arnáiz C, Heras H (2010) Anthropometric survey of the spanish female population aimed at the apparel industry. 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