Simulating multivariate nonnormal distributions

A method for generating multivariate nonnormal distributions with specified intercorrelations and marginal means, variances, skews, and kurtoses is proposed. As an example, the method is applied to the generation of simulated scores on three psychological tests administered to a single group of individuals.     

Classification by multivariate analysis

The problem considered is the use of a set of measurements on an individual to decide from which of several populations he has been drawn. It is assumed that in each population there is a probability distribution of the measurements. Principles for choosing the rule of classification are based on costs of misclassification. Optimum procedures are derived in general terms. If the measurements are normally distributed, the procedures use one discriminant function in the case of two populations and several discriminant functions in the cases of more populations. The numerical example given involves three normal populations.Sponsored in part by the Office of Naval Research.     

Some developments in multivariate generalizability

This article is concerned with estimation of components of maximum generalizability in multifacet experimental designs involving multiple dependent measures. Within a Type II multivariate analysis of variance framework, components of maximum generalizability are defined as those composites of the dependent measures that maximize universe score variance for persons relative to observed score variance. The coefficient of maximum generalizability, expressed as a function of variance component matrices, is shown to equal the squared canonical correlation between true and observed scores. Emphasis is placed on estimation of variance component matrices, on the distinction between generalizability- and decision-studies, and on extension to multifacet designs involving crossed and nested facets. An example of a two-facet partially nested design is provided.Appreciation is expressed to the Office of Research in Medical Education, University of Texas Medical Branch, for permitting use of their data.     

Two-sample multivariate similarity permutation comparison

A multivariate permutation test of similarity between two populations with corresponding unordered disjoint categories is described. The test statistic, resampling probability value, and measure of effect size are described.     

A multivariate model for discrimination methods

We describe a multivariate model for a certain class of discrimination methods in this paper and discuss a multivariate Euclidean model for a particular method, the triangular method. The methods of interest involve the selection or grouping of stimuli drawn from two stimulus sets on the basis of attributes invoked by the subject. These methods are commonly used for estimation and hypothesis testing concerning possible differences between foods, beverages, odorants, tastants and visual stimuli.Mathematical formulation of the bivariate model for the triangular method is provided as well as extensive Monte Carlo results for up to 10-dimensional cases. The effect of correlation structure and variance inequality are discussed. Results from these methods (as probability of a correct response) are not monotonically related to the distance between the means of the stimulus sets from which the stimuli are drawn but depend in a particular way on dimensionality, correlation structure, and the relative orientation of the momentary sensory values in a multidimensional space. The importance of these results to the validity of these methods as currently employed is discussed and the possibility of developing a new approach to multidimensional scaling on the basis of this new theory is considered.     

Graphing multivariate data with Chernoff''s faces

Chernoff's faces is one of several icon graphics routines accessible through the SYGRAPH module available through SYSTAT Inc. SYSTAT is a very sophisticated statistics package that has been previously reviewed in the Journal of School Psychology (Roberts, D. M. JSP 25, 313–318, 1987). SYSTAT and SYGRAPH are available for both the IBM PC and the Apple Macintosh computers. The output from this example was produced with SYSTAT 5.1 on a Macintosh computer.     

Loglinear representations of multivariate Bernoulli Rasch models

In this paper, the extended Rasch model for dichotomously scored items is derived from the general multivariate Bernoulli distribution. The necessary and sufficient conditions for the multivariate Bernoulli distribution to be equal to the extended Rasch model provide a new loglinear representation of the extended Rasch model. Conditions are also given under which the extended Rasch model is equal to the random effects Rasch model, and it is shown under what conditions the extended Rasch model is equal to a random effects Rasch model in which the underlying variable has a normal distribution. In addition, alternative models for the construction of likelihood ratio tests are proposed. One of these alternative models is Haberman's extended interaction model. Furthermore, it is shown how both the SPSS and SAS programs can be used to estimate and test loglinear representations of extended Rasch models.     

Multidimensional scale types and invariant multivariate statistics

This paper proposes an extension of the definition of one‐dimensional ordinal, interval, ratio, difference and absolute scales to the multidimensional case. The connection between measurement structures and statistical structures suggested in a previous paper is also extended to the multivariate case, and examples of invariance properties of multivariate functions and statistics are discussed.     

Applications of multivariate visualization to behavioral sciences

The complexity of psychological science often requires the collection and analysis of multidimensional data. Such data bring about a corresponding cognitive load that has led scientists to develop techniques of scientific visualization to ease the burden. This paper provides an introduction to scientific visualization techniques, a framework for understanding those techniques, and an assessment of the suitability of this approach for psychology. The framework employed builds on the notion of balancingnoise andsmooth in statistical analysis.     

Implementation of nonparametric multivariate statistics with S

Multivariate nonparametric statistical methods have not been widely used by psychologists. One reason for this may have been that the usual general-purpose packages do not provide easy implementation of these methods. In this article, we briefly describe the multivariate extensions of the sign, signed-rank, and rank-sum tests and use S, a programming environment for data analysis, to implement these statistical procedures. Three numerical examples are used to illustrate the flexibility and efficiency of these computations in S.     

On the geometric approach to multivariate selection

Multivariate selection can be represented as a linear transformation in a geometric framework. This approach has led to considerable simplification in the study of the effects of selection on factor analysis. In this note this approach is extended to describe the effects of selection on regression analysis and to adjust for the effects of selection using the inverse of the linear transformation.     

Visualization of multivariate data: Human-factors considerations

Recent software provides new tools for visualizing multivariate data that facilitate data analysis. We focus on (1) the learnability and use of visualization systems, and (2) the perceptual and cognitive processes involved in viewing visualizations. Effective visualization systems support a broad range of user tasks and abilities, are easy to learn, and provide powerful and flexible output formatting. Effective visualizations incorporate Gestalt and other perceptual and cognitive principles that encourage more rapid, automatic processing, and less slow, controlled processing.     

The comprehensive approach to analyzing multivariate constructs

Many psychological constructs of interest to personality psychologists, such as personality, behavior, and emotions, are made up of many variables. Moreover, similarity metrics, such as self-other agreement, profile similarity, or behavioral consistency, result from calculations conducted across many variables. When analyzed using a comprehensive approach, such multivariate constructs present unique analytic challenges. Such challenges are not well addressed in standard graduate statistics textbooks or presently available in standard commercial software. This article introduces the ‘multicon’ package, freely available in the R statistical package, designed to aid researchers interested in taking a comprehensive approach to analyzing multivariate constructs. Realistic examples from personality psychology are provided to demonstrate the utility of this package.     

Models for multivariate paired comparison experiments with ties

Three models for multivariate paired comparison experiments are developed using the Farlie-Gumbel-Morgenstern approach to constructing multivariate distributions. Model 3 is a direct extension of the multivariate paired comparison model with no ties due to Davidson and Bradley.     

Recognition and source memory as multivariate decision processes

Recognition memory, source memory, and exclusion performance are three important domains of study in memory, each with its own findings, its specific theoretical developments, and its separate research literature. It is proposed here that results from all three domains can be treated with a single analytic model. This article shows how to generate a comprehensive memory representation based on multidimensional signal detection theory and how to make predictions for each of these paradigms using decision axes drawn through the space. The detection model is simpler than the comparable multinomial model, it is more easily generalizable, and it does not make threshold assumptions. An experiment using the same memory set for all three tasks demonstrates the analysis and tests the model. The results show that some seemingly complex relations between the paradigms derive from an underlying simplicity of structure.     

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.