Random versus rational strategies for initial configurations in nonmetric multidimensional scaling

An examination is made concerning the utility and design of studies comparing nonmetric scaling algorithms and their initial configurations, as well as the agreement between the results of such studies. Various practical details of nonmetric scaling are also considered.This research was supported by NSF Grants SOC 76-24512 and SOC 76-24394.     

Some current models for the perception and judgment of risk

We survey some of the models more recently used to portray panelists' perceptions of risk, viewed as a complex psychological response. These models are compared (a) as continuous versus discrete, (b) with regard to type of data and tasks required of panelists, and (c) by facility for portraying different patterns of judgments among panelists. Substantive results from applying different models to the same risks and/or data are presented. Finally, we consider possible future directions for research in the perception of risk, oriented toward use of the models presented here.     

Positive psychology and war: an oxymoron

The author was deeply disturbed by the January 2011 issue of the American Psychologist, which engendered a series of emotions in the author: first dismay, then anger, and finally a sense of shame about the current state of the profession. This was ostensibly an exposition of "positive psychology" principles and how they are to be applied in a colossal experiment designed to support our military in their fight against the ideology of jihadist Islam. The author found it hard to see what was positive in the presentation. Not one of the authors in this special issue discussed applying positive psychology principles to the reduction of conflict between nations, to the prevention of war, or to the promotion of peace. How about a positive psychology that questions the wisdom of leaders who tell us that the use of force is unavoidable, and seeks instead to help them find alternative, peaceful solutions? A true positive psychology should be primarily addressed to eradicating the disease of war, not to supporting those who fight it.     

Understanding the family in multiple cultural contexts: Avoiding therapeutic traps

Developing a balanced picture of a family's functioning is difficult when the family is culturally different from the therapist. Open-minded family therapists often translate culturally different traits and behaviors as culturally appropriate and exclude them from clinical judgment, which can limit therapeutic range and effectiveness. The following case study about an Indian family with a mentally retarded child is especially illustrative of the dilemmas facing the therapist working with families of different backgrounds. Therapeutic traps were avoided by having the family assess its own differences, while the therapist held steadfast to social interconnectedness as essential to healthy family functioning.An earlier and somewhat different version of this material appeared under a different title in Families, published by the Family Institute of Philadelphia.     

An algorithm for clustering relational data with applications to social network analysis and comparison with multidimensional scaling

A method of hierarchical clustering for relational data is presented, which begins by forming a new square matrix of product-moment correlations between the columns (or rows) of the original data (represented as an n × m matrix). Iterative application of this simple procedure will in general converge to a matrix that may be permuted into the blocked form [_?1¹₁^?1]. This convergence property may be used as the basis of an algorithm (CONCOR) for hierarchical clustering. The CONCOR procedure is applied to several illustrative sets of social network data and is found to give results that are highly compatible with analyses and interpretations of the same data using the blockmodel approach of White (White, Boorman & Breiger, 1976). The results using CONCOR are then compared with results obtained using alternative methods of clustering and scaling (MDSCAL, INDSCAL, HICLUS, ADCLUS) on the same data sets.     

The menstrual taboo in the Judeo-Christian tradition

The menstrual taboo continues to be a primary reason why women in Judaism and Christianity are excluded from positions of authority. This is demonstrated by examining positions taken toward menstruation by religious leaders in past history and in the present day. Jesus and Gregory the Great are notable exceptions to the disdain expressed by male religionists toward menstruants. Only after the removal of this persistent taboo will religious bodies come to treat women as full participants.     

The approximation of two-mode proximity matrices by sums of order-constrained matrices

A least-squares strategy is proposed for representing a two-mode proximity matrix as an approximate sum of a small number of matrices that satisfy certain simple order constraints on their entries. The primary class of constraints considered define Q-forms (or anti-Q-forms) for a two-mode matrix, where after suitable and separate row and column reorderings, the entries within each row and within each column are nondecreasing (or nonincreasing) to a maximum (or minimum) and thereafter nonincreasing (or nondecreasing). Several other types of order constraints are also mentioned to show how alternative structures can be considered using the same computational strategy.     

Correspondence analysis and optimal structural representations

Many well-known measures for the comparison of distinct partitions of the same set ofn objects are based on the structure of class overlap presented in the form of a contingency table (e.g., Pearson's chi-square statistic, Rand's measure, or Goodman-Kruskal'sτ _b ), but they all can be rephrased through the use of a simple cross-product index defined between the corresponding entries from twon ×n proximity matrices that provide particular a priori (numerical) codings of the within- and between-class relationships for each of the partitions. We consider the task of optimally constructing the proximity matrices characterizing the partitions (under suitable restriction) so as to maximize the cross-product measure, or equivalently, the Pearson correlation between their entries. The major result presented states that within the broad classes of matrices that are either symmetric, skew-symmetric, or completely arbitrary, optimal representations are already derivable from what is given by a simple one-dimensional correspondence analysis solution. Besides severely limiting the type of structures that might be of interest to consider for representing the proximity matrices, this result also implies that correspondence analysis beyond one dimension must always be justified from logical bases other than the optimization of a single correlational relationship between the matrices representing the two partitions.