Least squares metric,unidimensional scaling of multivariate linear models

The squared error loss function for the unidimensional metric scaling problem has a special geometry. It is possible to efficiently find the global minimum for every coordinate conditioned on every other coordinate being held fixed. This approach is generalized to the case in which the coordinates are polynomial functions of exogenous variables. The algorithms shown in the paper are linear in the number of parameters. They always descend and, at convergence, every coefficient of every polynomial is at its global minimum conditioned on every other parameter being held fixed. Convergence is very rapid and Monte Carlo tests show the basic procedure almost always converges to the overall global minimum.The author thanks Ivo Molenaar, three anonymous referees, and Howard Rosenthal for their many helpful comments.     

A multivariate analysis of social dominance in children

The social dominance behavior of dyads of unacquainted, same-sex 31/2 year-olds was observed in a familiar laboratory playroom under two conditions: A free play situation and a situation where candy was introduced. In each of the two conditions, a principal components analysis was used to explore two issues: the usefulness of the multivariate approach in devising a definition of dominance, and the cross-situational stability of the construct. In the free play session, the first principal component that emerged was consistent with a theoretical definition of dominance. This picture was disrupted by the introduction of candy in the second condition. However, a high correlation was found between the dominance hierarchies established in each situation. It was concluded that the multivariate analysis is a useful method for the study of dominance. The generalizability of social dominance across settings was discussed as a possible explanation for the high cross-situational stability.     

A set theoretic analysis of group interactions

Prior to the statistical treatment of experimentally derived data the experimenter must obtain the data. In many studies in psychology, the content of group interactions is obtained by a data coding scheme. Coding schemes are shown to possess hierarchical structures and can be characterized by a hierarchy of fields. Three examples of coding schemes as hierarchies of fields are given. Techniques for extracting numbers from the set are presented. Problems associated with the improper assignment of elements of a data coding scheme to a theoretical structure are examined. The main result is that there will be errors in assignment of data to theory unless the structure of the data coding scheme is identical with that structure which is relevant to the theory being tested. Whenever the structures are not equal, the results are hard to interpret. In fact, any size of assignment error can be obtained. Since these errors precede the usual statistical treatment of data, it would appear that reported empirical findings are only valid when there exists no assignment errors.This research was sponsored by N.S.F. Grant GS-1944.     

A set of inequalities in factor analysis

Inequalities relating the communalities to the multiple-correlation coefficients are derived. They are stronger than the well-known inequalities which have played an important role in factor analysis for the past thirty years. Necessary and sufficient conditions for equality are obtained.     

Toward a complete analysis of GSR data

A critique of amplitude analyses in GSR conditioning is discussed. It was pointed out that, when amplitudes are properly analyzed with all Ss contributing equally to each repeated measures point, the concern of latency interval, definition of response probability, and distribution of GSR amplitudes are concerns which apply to analyses of magnitude, probability, and latency, as well as of amplitude. It was concluded that nothing is lost in separating magnitude into its amplitude and probability components, particularly when magnitude, as well, is included in the statistical analyses, and that, to the contrary, we stand to learn something by such a partitioning which could not be learned without it.     

Suicide risk among dentists: A multivariate analysis

Dentists are recognized as an occupational group with a high incidence of suicide. Past work, however, has focused only on the bivariate dentist‐suicide relationship. It is not clear whether this risk of suicide is because of occupational stress or sociodemographic factors, such as gender and divorce, which are covariates of dentist status. The present study reassesses the link between dentistry and suicide by controlling for dentistry's covariates. Controlling for sociodemographic factors, dentists still have a significantly higher risk of suicide, indicating that occupational stress may be a source of their high suicidality.     

A cognitive multivariate time series and its analysis

The method of analyzing a multivariate time series, by factoring a matrix polynomial of linear transfer function coefficients, is briefly outlined and shown to be potentially applicable to cognitive experiments where the inputs are numerically predictable and the outputs suitably quantified. An experiment on sequences of 90 figures, judged in terms of similarity and of the probability of exceeding or not exceeding some size, was analyzed individually for 12 subjects and their dynamic characteristics expressed in pole zero diagrams. Some dynamic components neglected by classical time-independent psychological methods are identified.     

A multivariate analysis of adolescents' orientations toward physician use

Health professionals know surprisingly little about the origins of the health beliefs and orientations they often seek to change, and they do not know about when, or if, changes in these orientations are likely to occur. This study is aimed at increasing our understanding of the origins and development of health beliefs and attitudes by focusing on the impact of parents' orientations toward physician utilization (inclination to consult a doctor when experiencing somatic symptoms) on the comparable orientations of their adolescent children. Hypotheses regarding direct parent-adolescent links are examined within a multivariate structural equations model relating demographics, adolescents' interpersonal competencies, and parental variables to adolescents' orientations toward physician utilization. Evidence for the development of these orientations is obtained by comparing influences across two groups of adolescents: 12- to 13-year-olds and 16- to 18-year-olds. Findings indicate that adolescents' orientations toward physician use are associated with those of their parents and that this link is generally stronger and more specific during late adolescence. The model also suggests that these orientations conform to social and cultural variables related to differences in social stratification.     

A method of determining unbiased distribution in the latin square

The paper describes a method of constructing Latin-square designs in which treatment sequences are unbiased with regard to serial order as well as position of treatment. The procedure is useful for those Latin squares in which the number of cells in each column (or row) is an even number, which, when written in ascending and descending series, contain corresponding ordered numbers prime to each other. Such numbers are 2, 4, 6, 10, 12, 16, 18, 22, 28, 30, 36, etc.     

The drawing of squares and diamonds: a perceptual-motor task analysis

The aim of the present study was to establish the role of perceptual-motor factors in copying an equilateral four-sided figure. Children, 5 to 12 years, and adults, were asked to copy the figure presented in either "square" or "diamond" orientation under five conditions: control; large model presentation; neutral picture frame surround; partial visual information reduction; and total visual information loss. The model was present at all times. Scores were orientation and angular variability. Developmental trends were found for both figures; the diamond was less well performed than the square at all ages tested. Three perceptual-motor factors were found to be important: formulation of the movement plan; movement programming, and sensory feedback. The difficulty of the diamond is thought to be due to the high programming and hence planning demands in drawing oblique lines. Both kinaesthesis and sequential vision are important factors in drawing; and only from 12 years of age are environmental cues used efficiently to orient the figure.