The rank of reduced dispersion matrices

Psychometricians working in factor analysis and econometricians working in regression with measurement error in all variables are both interested in the rank of dispersion matrices under variation of the diagonal elements. Psychometricians concentrate on cases in which low rank can be attained, preferably rank one, the Spearman case. Econometricians cocentrate on cases in which the rank cannot be reduced below the number of variables minus one, the Frisch case. In this paper we give an extensive historial discussion of both fields, we prove the two key results in a more satisfactory and uniform way, we point out various small errors and misunderstandings, and we present a methodological comparison of factor analysis and regression on the basis of our results.Financial support by the Netherlands Organization for the Advancement of Pure Research (ZWO) is gratefully acknowledged.     

Retrospective questions and correlations

In survey research it is not uncommon to ask questions of the following type: “How many times did you undertake actiona in reference periodT of length τ?.” The relationship is established between τ and the correlation of the number of reported actions with some background variable. To this end it is assumed that the process of actions satisfies a renewal model with individual heterogeneity. Also a model has to be formulated for possible recall effects. Applications are given in the field of medical consumption.     

Relationships between the Beck Depression Inventory and the Hamilton Psychiatric Rating Scale for Depression in depressed outpatients

The Beck Depression Inventory (BDI) and the Hamilton Psychiatric Rating Scale for Depression (HRSD) were used with 300 outpatients diagnosed with DSM-III major depression disorders. A principal-components analysis was performed on the intercorrelations among the 21 BDI and 24 HRSD symptoms. Three orthogonal components were found and interpreted as reflecting differences in self-report and clinical rating methods for measuring the severity of depression. The importance of using both self-reports and clinical ratings for evaluating depression in psychiatric outpatients was discussed.     

A stochastic growth model applied to repeated tests of academic knowledge

In the course of the medical program at the University of Limburg, students complete a total of 24 progress tests, consisting of items drawn from a constant itembank. A model is presented for the growth of knowledge reflected by these results. The Rasch model is used as a starting point, but both ability and difficulty parameters are taken to be random, and moreover the logistic distribution is replaced by the normal. Both individual and group abilities are estimated and explained through simple linear regression. Application to real data shows that the model fits very well.     

On the use of bisection procedures in animal psychophysical scaling

The ability of bisection procedures to specify the form of the psychophysical scale depends upon the precision of the technique. It is demonstrated that the precision of bisection techniques is a function of the stimulus interval bisected. Consequently, the choice of stimuli in a bisection experiment may predispose the ability of the experiment to distinguish between alternative psychophysical scales. The testing of interval scale properties of derived scales and the assessment of context effects in bisection experiments was also discussed.This material has been reviewed by the Walter Reed Army Institute of Research, and there is no objection to its presentation and/or publication. The opinions or assertions contained herein are the private views of the author and are not to be construed as official or as reflecting the view of the Department of the Army or the Department of Defense.     

Comparing latent distributions

We consider the problem of comparingm latent population distributions when the observed values are scores on a test battery with binary items. The latent densities are assumed to be normal densities, and we consider a test for equality of the means as well as a test equality of the variances. In addition, we consider a longitudinal model, where the test battery has been applied to the same individuals at different points in time. This model allows for correlations between the latent variable at different time points, and methods are discussed for estimating the correlation coefficient.This work was supported in part by a grant from the Danish Social Science Research Council.     

Assessing structure building in college classrooms at scale

Structure building refers to the way in which people construct meaning from incoming information by creating a foundation of mental nodes, mapping incoming information to the foundational structure, and shifting to a new structure when necessary. Structure building ability has been shown to moderate learning both in laboratory-based and classroom-based research (e.g., use of outlines for effective note-taking and course final grades, respectively). However, measurement of structure building can be resource intensive. The purpose of the present study was to evaluate a shortened, scalable measure of structure building (developed by a textbook publisher) in a real-world context. The results are consistent with the hypothesis that this tool, embedded in the online ancillary materials accompanying a textbook, can be used to measure a variable that is relevant to students' learning in introductory psychology courses.