Three-way metric unfolding via alternating weighted least squares

Three-way unfolding was developed by DeSarbo (1978) and reported in DeSarbo and Carroll (1980, 1981) as a new model to accommodate the analysis of two-mode three-way data (e.g., nonsymmetric proximities for stimulus objects collected over time) and three-mode, three-way data (e.g., subjects rendering preference judgments for various stimuli in different usage occasions or situations). This paper presents a revised objective function and new algorithm which attempt to prevent the common type of degenerate solutions encountered in typical unfolding analysis. We begin with an introduction of the problem and a review of three-way unfolding. The three-way unfolding model, weighted objective function, and new algorithm are presented. Monte Carlo work via a fractional factorial experimental design is described investigating the effect of several data and model factors on overall algorithm performance. Finally, three applications of the methodology are reported illustrating the flexibility and robustness of the procedure.We wish to thank the editor and reviewers for their insightful comments.     

Iterative least squares estimates of communality: Initial estimate need not affect stabilized value

A common criticism of iterative least squares estimates of communality is that method of initial estimation may influence stabilized values. As little systematic research on this topic has been performed, the criticism appears to be based on cumulated experience with empirical data sets. In the present paper, two studies are reported in which four types of initial estimate (unities, squared multiple correlations, highestr, and zeroes) and four levels of convergence criterion were employed using four widely available computer packages (BMDP, SAS, SPSS, and SOUPAC). The results suggest that initial estimates have no effect on stabilized communality estimates when a stringent criterion for convergence is used, whereas initial estimates appear to affect stabilized values employing rather gross convergence criteria. There were no differences among the four computer packages for matrices without Heywood cases.     

Multifactor measurement of bodily feelings: Conceptual development,scale construction,and empirical validation

A series of studies is described demonstrating a coherent exploratory and confirmatory factor-analytic approach to the scaling of self-reported bodily feelings. This approach attempts to optimize the orthogonality, parsimony, and meaningfulness of a multifactor inventory. Psychometric properties of the resulting 35-item Bodily Feeling Scale (BFS) are presented and its comparability with other inventories is discussed. A validity study using item-content-based scales of the Minnesota Multiphasic Personality Inventory showed both concurrent and discriminative validity of the BFS. Implications for clinical and research utility are discussed.Portions of this research were conducted while the first author was supported by a University Graduate Fellowship awarded by the Graduate School of Arts and Sciences at Vanderbilt University.Professor Nunnally passed away in August 1982. His major contributions to the several stages of this research program are recognized through coauthorship.     

Millon Clinical Multiaxial Inventory (MCMI) computer-generated diagnoses: How do they compare to clinician judgment?

During the past several decades, computers have achieved increasing prominence in psychological assessment procedures. This is particularly true for computer-based test interpretation and diagnosis. This study reports on a study designed to compare the accuracy of computer-based diagnoses with clinician-generated diagnoses. The Millon Clinical Multiaxial Inventory (MCMI) was administered to 151 consecutively admitted inpatients at a large private psychiatric hospital. The computer-generated diagnoses were compared with those generated by admitting psychiatrists. The results indicated that the MCMI diagnostic impressions underestimated the severity of depressive disorders when compared with clinician diagnoses on Axis I. Specifically, clinicians diagnosed major depression much more frequently than did the MCMI. In addition, clinicians diagnosed anxiety disorders much less frequently than did the MCMI.     

A brief neuropsychological screening battery to detect brain damage in a psychiatric population

Seventy-five patients admitted to the psychiatric unit of a general hospital were administered a brief neuropsychological screening battery. Discharge diagnoses obtained from the medical records revealed that 20% had brainbased pathology. A discriminant function analysis resulted in a five-variable model (Symbol-Digit Modalities Test, educational level, Psychiatric-Organic subscale of the MMPI, and Shipley Vocabulary and Abstraction scores) which correctly classified 84% of the subjects, with 87% correct identification of the brain-damaged group. A jackknife cross-validation procedure resulted in comparable hit rates.     

Relative allocation on concurrent schedules can depend on schedule parameters when behavioral parameters are constant

We develop a simple model of switching between the initial links of a concurrent-chain procedure. Behavior is determined by four parameters μ₁, μ₂, q₁, and q₂. The first two are the basic rates of switching from Schedule 1 and Schedule 2, respectively. The second two are the probabilities of leaving Schedule 1 and Schedule 2 after the corresponding terminal link has been completed. We show that for fixed values of these four parameters, the relative allocation on the initial links may change as a result of changes in initial-link schedules. The effect can be quite large if the switching rates are low. An implication is that relative allocation is not necessarily a good measure of behavior.     

A nonparametric approach for assessing latent trait unidimensionality

Assuming a nonparametric family of item response theory models, a theory-based procedure for testing the hypothesis of unidimensionality of the latent space is proposed. The asymptotic distribution of the test statistic is derived assuming unidimensionality, thereby establishing an asymptotically valid statistical test of the unidimensionality of the latent trait. Based upon a new notion of dimensionality, the test is shown to have asymptotic power 1. A 6300 trial Monte Carlo study using published item parameter estimates of widely used standardized tests indicates conservative adherence to the nominal level of significance and statistical power averaging 81 out of 100 rejections for examinee sample sizes and psychological test lengths often incurred in practice.The referees' comments were remarkably detailed and greatly enhanced the writeup and sensitized the author to certain pertinent issues. Discussions with Fritz Drasgow, Lloyd Humphreys, Dennis Jennings, Brian Junker, Robert Linn, Ratna Nandakumar, and Robin Shealy were also very useful.This research was supported by the Office of Naval Research under grant N00014-84-K-0186; NR 150-533, and by the National Science Foundation under grant DMS 85-03321.     

On structural equation modeling with data that are not missing completely at random

A general latent variable model is given which includes the specification of a missing data mechanism. This framework allows for an elucidating discussion of existing general multivariate theory bearing on maximum likelihood estimation with missing data. Here, missing completely at random is not a prerequisite for unbiased estimation in large samples, as when using the traditional listwise or pairwise present data approaches. The theory is connected with old and new results in the area of selection and factorial invariance. It is pointed out that in many applications, maximum likelihood estimation with missing data may be carried out by existing structural equation modeling software, such as LISREL and LISCOMP. Several sets of artifical data are generated within the general model framework. The proposed estimator is compared to the two traditional ones and found superior.The research of the first author was supported by grant No. SES-8312583 from the National Science Foundation and by a Spencer Foundation grant. We wish to thank Chuen-Rong Chan for drawing the path diagram.     

The choice of constraints in correspondence analysis

A discussion of alternative constraint systems has been lacking in the literature on correspondence analysis and related techniques. This paper reiterates earlier results that an explicit choice of constraints has to be made which can have important effects on the resulting scores. The paper also presents new results on dealing with missing data and probabilistic category assignment.I am most grateful to the following for their helpful comments. Arto Demirjian, Michael Greenacre, Michael Healy, Shizuhiko Nishisato, Roderick Mcdonald, and several anonymous referees.     

TESTICULAR SELF-EXAMINATION: VALIDATION OF A TRAINING STRATEGY FOR EARLY CANCER DETECTION

Testicular self-examination (TSE) can lead to early diagnosis and treatment of testicular cancer, the third leading cause of death in young men. We evaluated the effectiveness of a brief and specific checklist for teaching TSE skills. Ten men were videotaped while performing testicular self-examinations before and after training. The TSE training resulted in large and significant increases in the number of TSE steps completed and duration of the TSE. Two urological validation measures supported the improvements observed in the mens' self-examinations. Subjects reported continued performance of TSE during a follow-up telephone interview. This pilot study indicates that a brief and specific checklist is an effective strategy for teaching early cancer detection skills.