Testing a unidimensional,qualitative unfolding model for attitudinal or developmental data

Assuming that subject responses rank order stimuli by preference, statistical methods are presented for testing the hypothesis that responses conform to a unidimensional, qualitative unfolding model and to an a priori stimulus ordering. The model postulates that persons and stimulus variables are ordered along a single continuum and that subjects most prefer stimuli nearest their own position. The underlying continuum need not form an interval scale of the stimulus attribute. The general assumptions of the test for the unfolding model make it suitable for the analysis of structure in attitude responses, preference data, and developmental stage data.This research was supported by a grant from the U.S. Public Health Service (Grant No. 1-R01-MH27861-01) to the University of Minnesota. I wish to thank Sanford Weisberg for his helpful suggestions. I also wish to thank Karen Kitchener and Patricia King for letting me use their data.     

Probabilistic multidimensional scaling: Complete and incomplete data

Simple procedures are described for obtaining maximum likelihood estimates of the location and uncertainty parameters of the Hefner model. This model is a probabilistic, multidimensional scaling model, which assigns a multivariate normal distribution to each stimulus point. It is shown that for such a model, standard nonmetric and metric algorithms are not appropriate. A procedure is also described for constructing incomplete data sets, by taking into consideration the degree of familiarity the subject has for each stimulus. Maximum likelihood estimates are developed both for complete and incomplete data sets. This research was supported by National Science Grant No. SOC76-20517. The first author would especially like to express his gratitude to the Netherlands Institute for Advanced Study for its very substantial help with this research.     

Direct fit of a theoretical model of phase transition in oscillatory finger motions

This paper presents a general method to fit the Schöner‐Haken‐Kelso (SHK) model of human movement phase transitions directly to time series data. A robust variant of the extended Kalman filter technique is applied to the data of a single subject. The options of covariance resetting and iteration within recursion were used to obtain time‐dependent estimates of both the α and β parameters in the SHK model. Comparison between transition onset time and the time at which |β(t|T)/α(t|T)| becomes critical indicates that the transitions are advanced by noise. The method can be extended to handle non‐normal data and generalization across subjects and/or experimental conditions.     

Estimating item and order information

In a common psychological procedure, the subject is presented a sequence of items and is asked to recall them in order. His response is scored for items reported correctly in their correct position (position score) and for items reported correctly independently of position (item score). Such data are analyzed in terms of a model which assumes that a particular stimulus item may be forgotten entirely (State 0), may be remembered but without any knowledge of its position in the sequence, or may be remembered together with knowledge of its position (State 2). State 2 is related to the position score, and we define a nonexclusive State 1 (which contains all items not in State 0) that is related to the item score. In Part 1, we use the observed item and position scores to derive estimates of the trial-to-trial distribution of the number of items in States 1 and 2. In Part 2 we consider separately each serial position of the stimulus, and derive estimates of the probability that each individual item is in State 1 and State 2. The model handles omissions, second guesses, and gives sensitive estimates of partial information. Fast Fortran computer programs are available for all computations. In general, whenever responses are scored for items and/or for position, and when no alternative model is being tested, it is recommended that the above model be used to correct for the effects of guessing.     

Probabilistic,multidimensional unfolding analysis

A probabilistic, multidimensional version of Coombs' unfolding model is obtained by assuming that the projections of each stimulus and each individual on each axis are normally distributed. Exact equations are developed for the single dimensional case and an approximate one for the multidimensional case. Both types of equations are expressed solely in terms of univariate normal distribution functions and are therefore easy to evaluate. A Monte Carlo experiment, involving 9 stimuli and 3 subjects in a 2 dimensional space, was run to determine the degree of accuracy of the multidimensional equation and the feasibility of using iterative methods to obtain maximum likelihood estimates of the stimulus and subject coordinates. The results reported here are gratifying in both respects.     

Constrained maximum likelihood estimation of two-level covariance structure model via EM type algorithms

In this paper, the constrained maximum likelihood estimation of a two-level covariance structure model with unbalanced designs is considered. The two-level model is reformulated as a single-level model by treating the group level latent random vectors as hypothetical missing-data. Then, the popular EM algorithm is extended to obtain the constrained maximum likelihood estimates. For general nonlinear constraints, the multiplier method is used at theM-step to find the constrained minimum of the conditional expectation. An accelerated EM gradient procedure is derived to handle linear constraints. The empirical performance of the proposed EM type algorithms is illustrated by some artifical and real examples.This research was supported by a Hong Kong UCG Earmarked Grant, CUHK 4026/97H. We are greatly indebted to D.E. Morisky and J.A. Stein for the use of their AIDS data in our example. We also thank the Editor, two anonymous reviewers, W.Y. Poon and H.T. Zhu for constructive suggestions and comments in improving the paper. The assistance of Michael K.H. Leung and Esther L.S. Tam is gratefully acknowledged.     

Cerebral lateralization in bilinguals: Methodological issues

The literature on lateralization for language in bilinguals manifests two apparent contradictions. Some papers demonstrate differences in lateralization between bilinguals and monolinguals; others demonstrate none. In studies with exclusively bilingual subjects, some papers demonstrate differences between the lateralization for the two languages, while others demonstrate none. This paper discusses the range of methodological parameters which must be borne in mind when conducting or evaluating studies of lateralization for language in bilinguals. These include issues of subject selection, language and stimulus selection, testing procedures, data analysis, and interpretation of results.     

Similarity between Fourier transforms of objects predicts their experimental confusions

Two sets of stimuli were presented tachistoscopically to 4 subjects. On each trial, a single stimulus was presented, and the subject was required to identify the stimulus by verbal response. An exposure duration was chosen such that the subject's identification performance fell within a range from faultless identification to chance guessing. The object-identification data of each subject obtained for all stimulus exposures were pooled to form an object confusion matrix. A model of visual processing based on two-dimensional spatial frequency content (Fourier transforms) was used to predict confusions among stimulus pairs. The model properties that appear to be the most essential are those that allow it (1) to account for the obvious dependence of the Fourier transform on the choice of an origin point; and (2) choose the point of origin for each object separately, irrespective of other objects of the set. The point of origin of the reference frame, in which Fourier transforms are performed, is chosen so as to minimize the low-frequency phase component for each object. A high correlation (up to .96) between confusion matrices and model interobject distances was attained. The results demonstrate that such a distance measure gives a good prediction of object confusability.     

A note on the analysis of designs in which subjects receive each stimulus only once

In social psychological experiments, the manipulations of interest are often presented to subjects along with, or as part of, some stimulus. An example would be a manipulation of the verbal label associated with a stimulus photograph, in a person perception study. Ordinarily it is not possible for stimuli to be completely crossed with treatments because subjects cannot be exposed to any stimulus more than once. In such designs it is wise to counterbalance the assignment of stimuli to treatment conditions, but this gives rise to difficulties in the analysis of the experimental data. Data from such designs have frequently been misanalyzed in the published literature. This paper presents a method of constructing a counter-balancing scheme to simplify the analysis, and appropriate methods of analysis for both the simplified and the general case. It is emphasized that stimuli are generally best treated as a random factor in such designs, permitting increased generalizability, but the case where the stimulus factor is fixed is also considered.     

Covariance structure analysis in several populations

This paper is concerned with the study of covariance structural models in several populations. Estimation theory of the parameters that are subject to general functional restraints is developed based on the generalized least squares approach. Asymptotic properties of the constrained estimator are studied; and asymptotic chi-square tests are presented to evaluate appropriate model comparisons. The method of multipliers and the standard reparametrization technique are discussed in obtaining the estimates. The methodology is demonstrated by a set of real data.Computer facilities were provided by the Computer Services Center, The Chinese University of Hong Kong. The authors are indebted to several anonymous reviewers for suggestions for improvement of this paper.     

The influence of state and prandial condition upon the reactivity of the newborn to auditory stimulation

Two experiments were conducted to examine the effects of the successive state epochs following feeding on the motor and cardiac reactivity of 3-day-old human newborns. In the first experiment 19 subjects were examined using a 75 dB auditory stimulus. In the second experiment 16 subjects were used with an 85 dB stimulus. It was found that the reactivity of the newborn was dependent on the state of the subject and upon prandial condition, stimulus intensity, and the response parameter measured. All four factors have, therefore, to be taken into account before any general statement concerning neonatal reactivity can be made.     

A marginalization model for the multidimensional unfolding analysis of ranking data

A marginalization model for the multidimensional unfolding analysis of ranking data is presented. A subject samples one of a number of random points that are multivariate normally distributed. The subject perceives the distances from the point to all the stimulus points fixed in the same multidimensional space. The distances are error perturbed in this perception process. He/she produces a ranking dependent on these error-perturbed distances. The marginal probability of a ranking is obtained according to this ranking model and by integrating out the subject (ideal point) parameters, assuming the above distribution. One advantage of the model is that the individual differences are captured using the posterior probabilities of subject points. Three sets of ranking data are analyzed by the model.     

State-Space Analysis of Working Memory in Schizophrenia: An FBIRN Study

The neural correlates of working memory (WM) in schizophrenia (SZ) have been extensively studied using the multisite fMRI data acquired by the Functional Biomedical Informatics Research Network (fBIRN) consortium. Although univariate and multivariate analysis methods have been variously employed to localize brain responses under differing task conditions, important hypotheses regarding the representation of mental processes in the spatio-temporal patterns of neural recruitment and the differential organization of these mental processes in patients versus controls have not been addressed in this context. This paper uses a multivariate state-space model (SSM) to analyze the differential representation and organization of mental processes of controls and patients performing the Sternberg Item Recognition Paradigm (SIRP) WM task. The SSM is able to not only predict the mental state of the subject from the data, but also yield estimates of the spatial distribution and temporal ordering of neural activity, along with estimates of the hemodynamic response. The dynamical Bayesian modeling approach used in this study was able to find significant differences between the predictability and organization of the working memory processes of SZ patients versus healthy subjects. Prediction of some stimulus types from imaging data in the SZ group was significantly lower than controls, reflecting a greater level of disorganization/heterogeneity of their mental processes. Moreover, the changes in accuracy of predicting the mental state of the subject with respect to parametric modulations, such as memory load and task duration, may have important implications on the neurocognitive models for WM processes in both SZ and healthy adults. Additionally, the SSM was used to compare the spatio-temporal patterns of mental activity across subjects, in a holistic fashion and to derive a low-dimensional representation space for the SIRP task, in which subjects were found to cluster according to their diagnosis.     

ON THE DANGERS OF AVERAGING ACROSS SUBJECTS WHEN USING MULTIDIMENSIONAL SCALING OR THE SIMILARITY-CHOICE MODEL

Abstract— When ratings of judged similarity or frequencies of stimulus identification are averaged across subjects, the psychological structure of the data is fundamentally changed. Regardless of the structure of the individual-subject data, the averaged similarity data will likely be well fit by a standard multidimensional scaling model, and the averaged identification data will likely be well fit by the similarity-choice model. In fact, both models often provide excellent fits to averaged data, even if they fail to fit the data of each individual subject. Thus, a good fit of either model to averaged data cannot be taken as evidence that the model describes the psychological structure that characterizes individual subjects. We hypothesize that these effects are due to the increased symmetry that is a mathematical consequence of the averaging operation.     

Psychological analyses of haptic and haptic-visual judgements of extent

Magnitude estimates of haptic extent resulted in positively accelerated psychophysical power function with an exponent of 1.18. However, in two further experiments right-handed male subjects made rating-scale judgements of the combined width of two stimulus blocks. Six widths were used and five replications of the 36 factorial combinations were presented to each subject. In Experiment II both stimuli were out of view and one was held between the thumb and index finger of each hand. In Experiment III one stimulus was held out of view between thumb and finger of the right hand and the second was shown to the subject. Mean ratings in both experiments were fit by a model which assumes that responses are a weighted average of the scale values of the two stimuli (Anderson, 1974a).     

Weak stimulus generalization using sinusoidal gratings: A cautionary note in animal psychophysics

Psychophysical techniques involving operant and classical conditioning are used commonly to determine the visual thresholds of nonverbal subjects. Typically, subjects are conditioned to respond to a particular stimulus, and once trained sufficiently, the subject’s sensitivity to this and similar stimuli can be determined by decreasing the stimulus intensity until the animal no longer responds. However, this assumes that the animal’s tendency to respond correlates with its sensory abilities. Stimulus generalization to sinusoidal gratings of different spatial frequencies was examined in goldfish. Subjects were classically conditioned to suppress respiration upon presentation of a sinusoidal grating. Animals’ learning curves to each spatial frequency grating were compared in order to determine whether the animals generalized across stimuli. Results indicate that fish show weak stimulus generalization across spatial frequencies. Also, the shape of the contrast sensitivity function, a common measure of the animal’s visual capabilities, is distorted by insufficient training. We conclude that when the goal is to obtain accurate data on visual capabilities, either subjects should be trained to each stimulus to be tested or their generalization gradients should be measured.     

Surviving a failure: Efficacy and a laboratory based test of the hopelessness model of depression

Abramson, Metalsky and Alloy's (1989) revision of the reformulated model of helplessness and depression to hopelessness theory introduced the possibility of additional diatheses for depression. The present paper describes a laboratory-based test of the hopelessness model which provides an opportunity to explore the role of efficacy in relation to the new model and to extend its application to anxiety. Undergraduate students were asked to complete a general ability test and received false feedback which led them to believe that they had performed less well than they had anticipated. Attributional style was found to be predictive of increase in anxiety following failure feedback. The interaction between attributional style and eficacy was found to predict depression. Among subjects who were low in efficacy attributional style was significantly related to depression. While the study provided partial support for hopelessness theory it indicates a role for the assessment of efficacy as a moderator variable within the model.     

A latent class unfolding model for analyzing single stimulus preference ratings

A multidimensional unfolding model is developed that assumes that the subjects can be clustered into a small number of homogeneous groups or classes. The subjects that belong to the same group are represented by a single ideal point. Since it is not known in advance to which group of class a subject belongs, a mixture distribution model is formulated that can be considered as a latent class model for continuous single stimulus preference ratings. A GEM algorithm is described for estimating the parameters in the model. The M-step of the algorithm is based on a majorization procedure for updating the estimates of the spatial model parameters. A strategy for selecting the appropriate number of classes and the appropriate number of dimensions is proposed and fully illustrated on some artificial data. The latent class unfolding model is applied to political science data concerning party preferences from members of the Dutch Parliament. Finally, some possible extensions of the model are discussed.The first author is supported as Bevoegdverklaard Navorser of the Belgian Nationaal Fonds voor Wetenschappelijk Onderzoek. Part of this paper was presented at the Distancia meeting held in Rennes, France, June 1992.