Principals versus osmod: A comment on saito and otsu

Saito and Otsu (1988) compared their OSMOD method of nonmetric principal-component analysis to an early and incorrect implementation of the PRINCIPALS algorithm of Young, Takane, and de Leeuw (1978). In this comment we present results from the current, correct implementations of the algorithm.     

Joint consistency of nonparametric item characteristic curve and ability estimation

The simultaneous and nonparametric estimation of latent abilities and item characteristic curves is considered. The asymptotic properties of ordinal ability estimation and kernel smoothed nonparametric item characteristic curve estimation are investigated under very general assumptions on the underlying item response theory model as both the test length and the sample size increase. A large deviation probability inequality is stated for ordinal ability estimation. The mean squared error of kernel smoothed item characteristic curve estimates is studied and a strong consistency result is obtained showing that the worst case error in the item characteristic curve estimates over all items and ability levels converges to zero with probability equal to one.     

Uniqueness proof for a family of models sharing features of Tucker's three-mode factor analysis and PARAFAC/candecomp

Some existing three-way factor analysis and MDS models incorporate Cattell's “Principle of Parallel Proportional Profiles”. These models can—with appropriate data—empirically determine a unique best fitting axis orientation without the need for a separate factor rotation stage, but they have not been general enough to deal with what Tucker has called “interactions” among dimensions. This article presents a proof of unique axis orientation for a considerably more general parallel profiles model which incorporates interacting dimensions. The model, X_k=A^AD_k H^BD_k B', does not assume symmetry in the data or in the interactions among factors. A second proof is presented for the symmetrically weighted case (i.e., where^AD_k=^BD_k). The generality of these models allows one to impose successive restrictions to obtain several useful special cases, including PARAFAC2 and three-way DEDICOM. We want to express appreciation for the contributions of several colleagues: Jos M. F. ten Berge and Henk A. L. Kiers carefully went through more than one version of this article, found an important error, and contributed many improvements. J. Douglas Carroll and Shizuhiko Nishisato acted with unusual editorial preserverance and flexibility, thereby making possible the successful completion of a difficult assessment and revision process. Joseph B. Kruskal has long provided crucial mathematical insights and inspiration to those working in this area, but this is particularly true for us. His contributions to this specific article include early discussion of basic questions and careful examination of some earlier attempted proofs, finding them to be invalid. The anonymous reviewers also made useful suggestions. Some portions of this work were supported in part by a grant from the Natural Sciences and Engineering Research Council of Canada.     

A new procedure for detection of crossing DIF

The purpose of this paper is to present a hypothesis testing and estimation procedure, Crossing SIBTEST, for detecting crossing DIF. Crossing DIF exists when the difference in the probabilities of a correct answer for the two examinee groups changes signs as ability level is varied. In item response theory terms, crossing DIF is indicated by two crossing item characteristic curves. Our new procedure, denoted as Crossing SIBTEST, first estimates the matching subtest score at which crossing occurs using least squares regression analysis. A Crossing SIBTEST statistic then is used to test the hypothesis of crossing DIF. The performance of Crossing SIBTEST is evaluated in this study.This research was partially supported by a grant from the Law School Admission Council and by National Science Foundation Mathematics Grant NSF-DMS-94-04327. The research reported here is collaborative in every respect and the order of authorship is alphabetical. The authors thank Jeff Douglas and Louis Roussos for their useful comments and discussions.     

Improved bounds for optimal intervals in weakly constrained regression problems

The solution of weakly constrained regression problems typically requires the iterative search, in a given interval, of a point where a certain function has a zero derivative. This note deals with improved bounds for the interval to be searched.     

The stability and clinical significance of distress: A rejoinder to pepper and coyne

Past research has established that some individuals with high Beck Depression Inventory (BDI) scores at one time point have scores that are lower at a second time point. Recently, we provided evidence indicating that the temporal instability of certain BDI scores may be due partly to the regression to the mean phenomenon. Pepper and Coyne (1996) question this statistical interpretation; they argue that distress among students is unstable for substantive reasons. In the current paper, we reaffirm our view that statistical and measurement factors may account, in part, for changes in BDI scores over time. Given this possibility, inferences about distress or depression as a latent construct in student samples are not warranted if these inferences are based on the administration of a single instrument such as the BDI; any conclusions about distress as a psychological construct must be qualified by acknowledging the possible roles of error and method variance. Clearly, empirical research is needed in order to obtain a better understanding of the nature of distress as a latent variable, especially in light of evidence which indicates that subthreshold levels of depression have a high degree of clinical significance.     

Factors influencing responding under multiple schedules of conditioned and unconditioned reinforcement

Two experiments examined pigeons' responses under multiple schedules of conditioned and unconditioned reinforcement. In one component, responses produced food according to a fixed-interval schedule; in a second component, responses produced brief stimuli according to a fixed-ratio schedule. When brief-stimulus presentations were paired with food in the first component, rates in the second component were usually higher than 10 responses per minute. When pairing in the first component was eliminated, responding continued to be maintained in the second component. Elimination of food presentation from the first component substantially decreased responding in the second component, even though the brief stimulus had not been paired with food. Experiment II demonstrated that response rate was affected by the duration of both the second component and the brief stimulus. The results suggest that three conditions are important in maintaining responding with brief-stimulus presentations: (1) pairing the brief stimulus, at least initially, with food, (2) maintaining unconditioned reinforcement in one component, and (3) employing optimal brief-stimulus and component durations.     

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.     

Principal component analysis of three-mode data by means of alternating least squares algorithms

A new method to estimate the parameters of Tucker's three-mode principal component model is discussed, and the convergence properties of the alternating least squares algorithm to solve the estimation problem are considered. A special case of the general Tucker model, in which the principal component analysis is only performed over two of the three modes is briefly outlined as well. The Miller & Nicely data on the confusion of English consonants are used to illustrate the programs TUCKALS3 and TUCKALS2 which incorporate the algorithms for the two models described.     

Scale freeness in factor analysis

The notion of scale freeness does not seem to have been well understood in the factor analytic literature. It has been believed that if the loss function that is minimized to obtain estimates of the parameters in the factor model is scale invariant, then the estimates are scale free. It is shown that scale invariance of the loss function is neither a necessary nor a sufficient condition for scale freeness. A theorem that ensures scale freeness in the orthogonal factor model is given in this paper.The authors are grateful for the suggestions of the referees.