Linear programming techniques for multidimensional analysis of preferences

This paper offers a new methodology for analyzing individual differences in preference judgments with regard to a set of stimuli prespecified in a multidimensional attribute space. The individual is modelled as possessing an ideal point denoting his most preferred stimulus location in this space and a set of weights which reveal the relative saliences of the attributes. He prefers those stimuli which are closer to his ideal point (in terms of a weighted Euclidean distance measure). A linear programming model is proposed for external analysisi.e., estimation of the coordinates of his ideal point and the weights (involved in the Euclidean distance measure) by analyzing his paired comparison preference judgments on a set of stimuli, prespecified by their coordinate locations in the multidimensional space. A measure of poorness of fit is developed and the linear programming model minimizes this measure overall possible solutions. The approach is fully nonmetric, extremely flexible, and uses paired comparison judgments directly. The weights can either be constrained nonnegative or left unconstrained. Generalizations of the model to consider ordinal or interval preference data and to allow an orthogonal transformation of the attribute space are discussed. The methodology is extended to perform internal analysis,i.e., to determine the stimuli locations in addition to weights and ideal points by analyzing the preference judgments of all subjects simultaneously. Computational results show that the methodology for external analysis is unbiased—i.e., on an average it recovers the true ideal point and weights. These studies also indicate that the technique performs satisfactorily even when about 20 percent of the paired comparison judgments are incorrectly specified.The authors wish to express their deep appreciation to J. Douglas Carroll and Joseph B. Kruskal for their most valuable comments on an earlier version of this paper.     

Ethnic differences in subclinical paranoia: an expansion of norms of the paranoia scale

The Paranoia Scale (PS) was designed to assess subclinical paranoid ideation (A. Fenigstein & P. A. Vanable, 1992). Despite its established validity, the PS has several problems that need to be addressed. There are no normative data on ethnic minority groups such as African Americans, making it difficult to interpret this group's performance on the PS. Data from the present research revealed that African Americans scored higher on the PS than non-Hispanic Whites. However, interpretation of these findings should be tempered as they may reflect other contextual factors such as discrimination and the impact of racism. Implications for using the PS with African Americans and possible explanations for the observed results were discussed.     

The association between gender, coping style and whiplash related symptoms in sufferers of whiplash associated disorder

The aim of the present study was to examine specifically whether the relationship between coping style and symptoms of whiplash injury change as a function of gender. A total of 1709 sufferers of whiplash associated disorder (1349 women, 360 men) belonging to the Danish Society for Polio, Traffic and Accident Victims completed questionnaires measuring demographic and psychological factors (including coping style), and symptoms of whiplash trauma (including pain). Men and women were not found to differ significantly in their use of coping strategies, however emotion focused coping strategies were related significantly more strongly to whiplash related symptoms in men compared to women. Women were found to display more symptoms related to whiplash injury compared to men. Possible reasons for the present findings are discussed in light of related research indicating mood as a potential moderating variable in the relationship between maladaptive coping style and degree of symptoms related to injury in men.