Restricted multidimensional scaling models

A class of multidimensional scaling models are developed wherein certain parameters may be fixed as known constants, or proportional to one another. Traditional multidimensional scaling can be obtained as a special case by fixing only the orientation and origin of a configuration. Methods of obtaining least-square estimates of the parameters via nonlinear programming are discussed, and an effective computer program is developed to implement application of the models to data. Several well-known data sets are reanalyzed under various restricted models, and the results demonstrate the possibility of achieving insight not attainable under the traditional approach. The potential distortion arising from inadequate model specification is discussed, and the importance of substantive theory to multidimensional scaling research is emphasized.     

Improving the efficiency and effectiveness of interactively selected MDS data designs

Two revisions of interactive MDS data selection procedures are presented. One revision improves the estimates of the MDS parameters by adding an analysis of the volume of the spatial coordinates of stimuli. Frames of stimuli augmented by an analysis of volume should more nearly surround the swarm of stimulus points. The second revision, based on randomly ordering the list of stimuli, permits more efficient data designs to be selected by reducing the number of judgments collected but never analyzed.This investigation was supported in part by a Research Scientist Development Award (KO2-DA00017), research grants (DA01070 and MH24149) from the U.S. Public Health Service, and a research and instruction award (IUC 2-47622-1990) from the University of California.     

A study of male and female soldiers' beliefs about the “appropriateness” of various jobs for women in the army

The purpose of this paper is to document the often discussed (e.g., Goldman, 1973) and recently initiated expansion of women's role in the U.S. Army and to present evidence regarding one aspect of soldiers' probable reaction to this expansion — viz., the extent to which soldiers believe certain military jobs are appropriate for women and, in particular, the extent to which these beliefs are related to respondent sex, rank, and expectation of leaving the Army before retirement.     

The Houdini Transformation: True,but Illusory

Molenaar (2003, 2011) showed that a common factor model could be transformed into an equivalent model without factors, involving only observed variables and residual errors. He called this invertible transformation the Houdini transformation. His derivation involved concepts from time series and state space theory. This article verifies the Houdini transformation on a general latent variable model using algebraic methods. The results show that the Houdini transformation is illusory in the sense that the Houdini-transformed model remains a latent variable model. Contrary to common knowledge, a model that is a path model with only observed variables and residual errors may, in fact, be a latent variable model.     

Ridge structural equation modelling with correlation matrices for ordinal and continuous data

This paper develops a ridge procedure for structural equation modelling (SEM) with ordinal and continuous data by modelling the polychoric/polyserial/product‐moment correlation matrix R . Rather than directly fitting R , the procedure fits a structural model to R _a= R +a I by minimizing the normal distribution‐based discrepancy function, where a > 0. Statistical properties of the parameter estimates are obtained. Four statistics for overall model evaluation are proposed. Empirical results indicate that the ridge procedure for SEM with ordinal data has better convergence rate, smaller bias, smaller mean square error, and better overall model evaluation than the widely used maximum likelihood procedure.     

Structural equation models with continuous and polytomous variables

A two-stage procedure is developed for analyzing structural equation models with continuous and polytomous variables. At the first stage, the maximum likelihood estimates of the thresholds, polychoric covariances and variances, and polyserial covariances are simultaneously obtained with the help of an appropriate transformation that significantly simplifies the computation. An asymptotic covariance matrix of the estiates is also computed. At the second stage, the parameters in the structural covariance model are obtained via the generalized least squares approach. Basic statistical properties of the estimates are derived and some illustrative examples and a small simulation study are reported.This research was supported in part by a research grant DA01070 from the U. S. Public Health Service. We are indebted to several referees and the editor for very valuable comments and suggestions for improvement of this paper. The computing assistance of King-Hong Leung and Man-Lai Tang is also gratefully acknowledged.     

Personality, problem drinking, and drunk driving: mediating, moderating, and direct-effect models

Three different general explanations of the effect of personality on problems from drinking alcohol were investigated. One general explanation involved mediating effects. The 2nd explanation involved direct effects of personality. The 3rd general personality process held that alcohol consumption and personality interact as moderating effects on drinking problems. Results provided support for each of the 3 general explanations of personality effects, although certain effects were found primarily for only 2 of the 6 personality constructs investigated (sensation seeking and cognitive motivation). These findings helped delimit the personality processes associated with drinking problems and demonstrated the viability of several specific processes that go beyond traditional assumptions about personality and problem drinking.     

Human figure drawings of gender-problem and school-problem boys

In this study 19 boys aged 4 through 13 years referred for gender problems were compared with 35 similar-aged boys referred for school problems on variables derived from sets of human figure drawings. The results indicated that gender-problem boys, relative to school-problem boys, were more likely to draw female figures in response to a Draw-a-Person (DAP) instruction, were more likely to draw figures with good rather than average body proportion, tended to draw more articles of clothing on their figures, and tended to draw their female figures larger than their male figures. There were no differences between the groups in the frequency of emotional disturbance indicators, frequency of age-expected or age-exceptional figure details, and total number of body features. These results are discussed in terms of their implications for the validation of the DAP procedure, their contribution to an understanding of boyhood effeminacy, and their implications for the role of the DAP test as a clinical assessment procedure only in conjunction with other sources of information.     

Application of optimal sign-vectors to reliability and cluster analysis

Expressions involving optimal sign vectors are derived so as to yield two new applications. First, coefficient alpha for the sign-weighted composite is maximized in analogy to Lord's scale-independent solution with differential weights. Second, optimal sign vectors are used to define two groups of objects that are maximally distinct in terms of a function of the squared euclidean distances between groups. An efficient computing algorithm is described along with several examples.This research was supported in part by a research grant (DA 01070) from the U. S. Public Health Service.