A note on the use of directional statistics in weighted euclidean distances multidimensional scaling models

Autonomic physiological response patterns related to intelligence

“…ALSCAL provides analyses with a minimum of two and a maximum of six dimensions. Although there is some controversy on the use of conventional, or linear, statistics (operating on scalars, as opposed to directional statistics operating on vectors) on dimensional weights (e.g., Rodgers, 1985;Schiffman et al, 1981), we followed the suggestion made by Jones (1983) that linear statistical analyses involving dimensional weights should be corrected by their corresponding goodness-of-fit measure R 2 .…”

Computer assisted text analysis in the social sciences

“…In addition to descriptive statistics-the resultant lengths, standard deviations and mean directions (in dimension coordinates)-an approximate analysis of angular variation can be made. It seems unlikely that the distributional assumptions of the null-hypothesis test originally proposed are met by directional data from weighted multidimensional models as the individual weights are constrained to being nonnegative (Jones 1983). In addition, an F-test for ANAVA assumes that angular variation within groups is homogeneous, and the significance level is accurate only when the observations (i.e.…”

Points or vectors? A comment on Irwin et al. ‘Risk perception and victim perception: the judgment of HIV cases'

“…the weights are estimated in a way which constrains their sum of squares to vary in approximate proportion to the percentage of variance in a given individual's data that is accounted for by the group space. As such, it is the relative directionality of these vectors that is useful for exploring dierential cognition, rather than their absolute magnitude (see for example, Coxon, 1982;Coxon and C. L. Jones, 1980;C. L. Jones, 1983;MacCallum, 1977).…”

“…Fortunately, there are several alternative analytical strategies to be found in the extant literature on the theory and practice of multidimensional scaling which circumvent these problems (for a review see C. L. Jones, 1983). However, by far the most straightforward approach is to calculate the logarithms of the within-subject ratios of the source weights.…”

“…While the meaning and signi®cance of the group space is relatively straightforward and well understood, the question as to how applied researchers should interpret source weights in a three-way scaling analysis is far from uncontroversial (see, for example, Arabie et al, 1987;Schiman et al, 1981). In a recent paper in this journal, Irwin, L. E. Jones andMundo (1996) employed Pruzansky's (1975) SINDSCAL algorithm and associated computer programme for ®tting the INDSCAL model, in an eort to explore the ways in which research participants' perceptions of some 16 scenarios, depicting the circumstances in which HIV victims had contracted the infection, diered according to various demographic and attitudinal variables. In order to explore the hypothesis that political and religious aliations, gender, homophobic attitudes, and attitudes about extramarital sex and the like were related to individual dierences in perceptions of the various HIV/AIDS scenarios, Irwin et al computed the correlation coecients between the raw source weights associated with each of the four dimensions derived from their three-way MDS solution, on the one hand, and on the other, the various attitudinal and biographical variables employed in their study.…”