Recovery of structure in incomplete data by alscal

A Monte Carlo study was carried out in order to investigate the ability of ALSCAL to recover true structure inherent in simulated proximity measures when portions of the data are missing. All sets of simulated proximity measures were based on 30 stimuli and three dimensions, and selection of missing elements was done randomly. Properties of the simulated data varied according to (a) the number of individuals, (b) the level of random error, (c) the proportion of missing data, and (d) whether the same entries or different entries were deleted for each individual. Results showed that very accurate recovery of true distances, stimulus coordinates, and weight vectors could be achieved with as much as 60% missing data as long as sample size was sufficiently large and the level of random error was low.     

Some results on proper eigenvalues and eigenvectors with applications to scaling

Conditions are given under which the stationary points and values of a ratio of quadratic forms in two singular matrices can be obtained by a series of simple matrix operations. It is shown that two classes of optimal weighting problems, based respectively on the grouping of variables and on the grouping of observations, satisfy these conditions. The classical treatment of optimal scaling of forced-choice multicategory data is extended for these cases. It is shown that previously suggested methods based on reparameterization will work only under very special conditions.     

Validation of the Preschool and Early Childhood Functional Assessment Scale (PECFAS)

Efforts to determine the prevalence of serious emotional disturbance in preschool-aged children have been hampered by the lack of a validated measure. The Preschool and Early Childhood Functional Assessment Scale (PECFAS) is a multi-dimensional measure that assesses the psychosocial functioning of children aged 3–7 years. The concurrent validity and reliability of the PECFAS were assessed in a sample of 30 preschool-aged children in a large Head Start program in Ventura, California. PECFAS ratings based on in-depth interviews were significantly related to parental ratings that the children had mental health problems, psychiatric diagnoses, teacher ratings of the child's need for mental health evaluations, teacher ratings of behavior problems on a standardized screening inventory (DIAL-R), and actual referrals for mental health evaluations. Interrater reliability for the total PECFAS score was high (r = .90) as was internal consistency of the five subscales (alpha = .86). Using the PECFAS scores as a standard, the weighted prevalence of serious emotional disturbance in this West Coast Head Start program was 17%, at the lower end of the current estimated rate of SED for older children in low income samples (18–26%).     

Loglinear multidimensional IRT models for polytomously scored items

A loglinear IRT model is proposed that relates polytomously scored item responses to a multidimensional latent space. The analyst may specify a response function for each response, indicating which latent abilities are necessary to arrive at that response. Each item may have a different number of response categories, so that free response items are more easily analyzed. Conditional maximum likelihood estimates are derived and the models may be tested generally or against alternative loglinear IRT models.Hank Kelderman is currently affiliated with Vrije Universiteit, Amsterdam.We thank Linda Vodegel-Matzen of the Division of Developmental Psychology of the University of Amsterdam for making available the data used in the example in this article.     

Scaling pigeons' choice of feeds: bigger is better.

Preferences of hungry pigeons among 10 grains and pellets were analyzed using a Thurstone scaling procedure. The recovered scales were positively correlated with size of the feed. The correlations improved when the Thurstonian assumption of equal-sized discriminal dispersions (Case V) was replaced with the assumption of proportional-sized dispersions (Case VI), as entailed by Weber's law. The correlations weakened when the experiments were conducted with the pigeons close to their free-feeding weights, where the probability of sampling alternative grains increased. In the final experiment, exposure to a large pellet shifted the preferences between two smaller pellets.     

Analysis of asymmetry by a slide-vector

The slide-vector scaling model attempts to account for the asymmetry of a proximity matrix by a uniform shift in a fixed direction imposed on a symmetric Euclidean representation of the scaled objects. Although no method for fitting the slide-vector model seems available in the literature, the model can be viewed as a constrained version of the unfolding model, which does suggest one possible algorithm. The slide-vector model is generalized to handle three-way data, and two examples from market structure analysis are presented.     

Points of view analysis revisited: Fitting multidimensional structures to optimal distance components with cluster restrictions on the variables

Points of view analysis (PVA), proposed by Tucker and Messick in 1963, was one of the first methods to deal explicitly with individual differences in multidimensional scaling, but at some point was apparently superceded by the weighted Euclidean model, well-known as the Carroll and Chang INDSCAL model. This paper argues that the idea behind points of view analysis deserves new attention, especially as a technique to analyze group differences. A procedure is proposed that can be viewed as a streamlined, integrated version of the Tucker and Messick Process, which consisted of a number of separate steps. At the same time, our procedure can be regarded as a particularly constrained weighted Euclidean model. While fitting the model, two types of nonlinear data transformations are feasible, either for given dissimilarities, or for variables from which the dissimilarities are derived. Various applications are discussed, where the two types of transformation can be mixed in the same analysis; a quadratic assignment framework is used to evaluate the results.The research of the first author was supported by the Royal Netherlands Academy of Arts and Sciences (KNAW); the research of the second author by the Netherlands Organization for Scientific Research (NWO Grant 560-267-029). An earlier version of this paper was presented at the European Meeting of the Psychometric Society, Leuven, 1989. We wish to thank Willem J. Heiser for his stimulating comments to earlier versions of this paper, and we are grateful to the Editor and anonymous referees for their helpful suggestions.     

The psychopathology of anorexia nervosa: A factor analytic investigation

To examine the psychopathology of anorexia nervosa, behavioral assessment measures sampling a wide range of relevant constructs were collected on 150 women diagnosed as having anorexia nervosa. The data were subjected to an exploratory factor analysis using maximum-likelihood estimation and oblique rotation. Five factors were extracted, which were titled Fasting and Restrictive Eating, Depression, Anxiety, and Negative Self-image, Bulimic Behaviors, Fear of Fatness/Body Image Disturbance, and Impulsive Behavior/Post-Traumatic Response. Discriminate function analysis suggested that, other than the bulimic behaviors factor, the Impulsive Behavior/Post-Traumatic Response factor best discriminated between bulimic and restrictor subtypes of anorexics. These data suggest that the underlying dimensions of anorexia nervosa are very similar to those of bulimia nervosa. The findings also have implications for the multidimensional assessment and treatment of anorexia nervosa as well as conceptual models of the disorder.     

How do applicants fake? A response process model of faking on multidimensional forced-choice personality assessments

Faking on personality assessments remains an unsolved issue, raising major concerns regarding their validity and fairness. Although there is a large body of quantitative research investigating the response process of faking on personality assessments, for both rating scales (RS) and multidimensional forced choice (MFC), only a few studies have yet qualitatively investigated the faking cognitions when responding to MFC in a high-stakes context (e.g., Sass et al., 2020). Yet, it could be argued that only when we have a process model that adequately describes the response decisions in high stakes, can we begin to extract valid and useful information from assessments. Thus, this qualitative study investigated the faking cognitions when responding to MFC personality assessment in a high-stakes context. Through cognitive interviews with N = 32 participants, we explored and identified factors influencing the test-takers' decisions regarding specific items and blocks, and factors influencing the willingness to engage in faking in general. Based on these findings, we propose a new response process model of faking forced-choice items, the Activate-Rank-Edit-Submit (A-R-E-S) model. We also make four recommendations for practice of high-stakes assessments using MFC.