A phonological interpretation of two acoustic confusion matrices

Multidimensional scaling and principal component analysis methods are used to examine two acoustic confusion matrices. It is suggested that three of the dimensions isolated by means of these techniques can be identified with phonological phenomena which could have contributed to the confusions.

     

Feature lists and confusion matrices

This report compares three feature list sets for capital letters, previously proposed by different investigators, on the ability of each to predict empirical confusion matrices. Toward this end, several variants of assumed information processes in recognition were also compared. The best model incorporated: (1) variable feature retrieval probabilities, (2) a goodness-of-match lower threshold below which guessing determines response, and (3) response bias on guessing trials. This model, when combined with one particular proposed feature list set, produced stress values of less than 9% in comparisons to empirical matrices for each of three different Ss. The feature retrieval probability vectors associated with these minimum-stress predictions were highly correlated ( \(\bar r = .83\) ), suggesting considerable generality of process and feature sets between Ss.     

Analysis of tactile and visual confusion matrices

Confusion matrices were compiled for uppercase letters and for braille characters presented to observers in two ways: as raised touch stimuli and as visual stimuli that had been optically filtered of their higher spatial frequencies. These and other existing matrices were subjected to a number of analyses, including the choice model and hierarchical clustering. The strong similarity of the visual and tactile matrices from this study lends additional support to the claim that visual recognition of low-pass filtered characters, to a first approximation, can be taken as a model of tactile recognition of small two-dimensional raised patterns. Besides this, the analysis questions the widely held assumption that response bias contributes significantly to the stimulus-response contingencies in a character-recognition task.     

On the prediction of confusion matrices from similarity judgments

Three observers viewed visual representations of eight complex sounds in both a pairwise similarity-judgment task and an identification task. A multidimensional scaling procedure applied to the similarity judgments yielded a three-dimensional perceptual space and the relative positions of the stimuli in that space. A probabilistic decision model based on weighted interstimulus distances served to predict well the confusion matrices of the identification task. Three conditions of the identification task, calling for identification of different subsets of the eight stimuli, led the observers to vary the weights they placed on the dimensions; they apparently adjusted the weights to maximize the percent correct identification. An additional group of 14 subjects, participating only in the similarity-judgment task, manifested the same three dimensions as the observers (corresponding to the locus of low-frequency energy, the locus of midfrequency energy, and visual contrast), and also a fourth dimension (corresponding to the periodicity, or waxing and waning, of the sound). Although not evident in the scaling analysis for the three observers, our utilization of the additional dimension increased significantly the variance accounted for in their identification responses. The overall accuracy of the predictions from a perceptual space to identification responses supplies a substantial validation of the use of multidimensional scaling procedures to reveal perceptual structure in demonstrating the ability of that structure to account for behavior in an independent task. The empirical success of this approach, furthermore, suggests a relatively simple and practical means of predicting, and possibly enhancing, identification performance for a given set of visual or auditory stimuli.     

Compact integer-programming models for extracting subsets of stimuli from confusion matrices

This paper presents an integer linear programming formulation for the problem of extracting a subset of stimuli from a confusion matrix. The objective is to select stimuli such that total confusion among the stimuli is minimized for a particular subset size. This formulation provides a drastic reduction in the number of variables and constraints relative to a previously proposed formulation for the same problem. An extension of the formulation is provided for a biobjective problem that considers both confusion and recognition in the objective function. Demonstrations using an empirical interletter confusion matrix from the psychological literature revealed that a commercial branch-and-bound integer programming code was always able to identify optimal solutions for both the single-objective and biobjective formulations within a matter of seconds. A further extension and demonstration of the model is provided for the extraction of multiple subsets of stimuli, wherein the objectives are to maximize similarity within subsets and minimize similarity between subsets.     

Graph coloring, minimum-diameter partitioning, and the analysis of confusion matrices

It is well known that minimum-diameter partitioning of symmetric dissimilarity matrices can be framed within the context of coloring the vertices of a graph. Although confusion data are typically represented in the form of asymmetric similarity matrices, they are also amenable to a graph-coloring perspective. In this paper, we propose the integration of the minimum-diameter partitioning method with a neighborhood-based coloring approach for analyzing digraphs corresponding to confusion data. This procedure is capable of producing minimum-diameter partitions with the added desirable property that vertices with the same color have similar in-neighborhoods (i.e., directed edges entering the vertex) and out-neighborhoods (i.e., directed edges exiting the vertex) for the digraph corresponding to the minimum partition diameter.     

Constrained multidimensional unfolding of confusion matrices: Goal point and slide vector models

Two constrained multidimensional unfolding models, the goal point and slide vector models, are proposed for analyzing confusion matrices. In both models, the row and column stimuli are expressed as two sets of points in a low-dimensional space, where the difference vector connecting a column point to the corresponding row point indicates the change in the stimulus representation through a cognitive process. The difference vector is constrained by the hypothesis that the trend in the representational change is invariant across stimuli: the goal point model constrains all difference vectors to point toward a single point, and the slide vector model constrains all difference vectors to be parallel to each other. In both models the coordinates of points are estimated by the maximum-likelihood method. Examples illustrate that the two models allow us to examine hypotheses about invariant trends in representational changes and to grasp such trends from the resulting configurations.     

On the concordance among empirical confusion matrices for visual and tactual letter recognition

In this article, we examine the concordance among 19 empirical confusion matrices for visual and tactual recognition of capital letters of the alphabet. As a measure of concordance, we employed an index based on within-stimulus triads of letters. Unlike correlation measures of agreement that are based on a one-to-one matching of matrix elements, the selected index directly captures the internal structures of the confusion matrices prior to the comparison. Permutation tests revealed statistically significant concordance among 166 of 171 pairs of matrices in the study. Concordance of confusion structure among tactual matrices tended to be somewhat stronger than concordance among the visual matrices.     

The multidimensional analysis of asymmetries in alphabetic confusion matrices: Evidence for global-to-local and local-to-global processing

This study examined the ability of an asymmetric multidimensional scaling program (DEDICOM) to reveal information about letter-perception processes. To demonstrate its potential, we applied it to the controversy concerning local-to-global versus global-to-local letter perception. These two theories lead to different predictions about stimulus confusion asymmetries. Since DEDICOM is capable of recovering the structure of asymmetric or directional patterns, it should reveal whether a stimulus-response confusion matrix contains patterns of asymmetry more consistent with one or the other perceptual theory. This was tested using two data sets. The first (from Lupker, 1979) revealed an additive hierarchy of asymmetry strongly consistent with global-tolocal processing, although unexpected additional structure and reliable anomalies indicated the need for a more refined theoretical account. The second (a full alphabetic confusion matrix combining data from Gilmore et al., 1979; Loomis, 1982; and Towasend, 1971) revealed five distinct patterns, each consisting of transformations attributable to the failure to detect specific local letter features. This solution strengthened support for local-to-global processing, in sharp contrast to the first analysis. Possible reasons for this divergence are discussed, including differences in the stimuli, exposure durations, and a hypothetical two-stage process of perception. Despite their differences, both solutions demonstrated how asymmetric scaling can reveal structure in asymmetries, which is relevant to perceptual theory and which would have been difficult to recover by other means.     

Confirmatory factor analyses of DSM-IV Cluster C personality disorder criteria

Notwithstanding its research and clinical relevance, the dimensionality and validity of the DSM-IV avoidant, dependent, and obsessive-compulsive personality disorders (PDs) criteria is still a largely unexplored topic. The aim of this study was to test the factor structure for DSM-IV Cluster C PD criteria in a sample of 641 consecutively admitted outpatients. Factor analysis results suggested that avoidant, dependent, and obsessive-compulsive PDs share a common latent dimension, and supported the three-factor structure of both observer and self-report ratings of DSM-IV Cluster C PD criteria. The pattern of factor loadings, however, was different from the one expected according to the DSM-IV classification.     

Orthogonal procrustes rotation for two or more matrices

Necessary and sufficient conditions for rotating matrices to maximal agreement in the least-squares sense are discussed. A theorem by Fischer and Roppert, which solves the case of two matrices, is given a more straightforward proof. A sufficient condition for a best least-squares fit for more than two matrices is formulated and shown to be not necessary. In addition, necessary conditions suggested by Kristof and Wingersky are shown to be not sufficient. A rotation procedure that is an alternative to the one by Kristof and Wingersky is presented. Upper bounds are derived for determining the extent to which the procedure falls short of attaining the best least-squares fit. The problem of scaling matrices to maximal agreement is discussed. Modifications of Gower's method of generalized Procrustes analysis are suggested.     

Perceptual equivalence of two acoustic cues for stop-consonant manner

The first experiment examined the effects of orthogonal variation in two acoustic cues that are both produced by the articulation of a stop consonant. One component of the articulation produces a temporal cue, the other a spectral cue. In a phonetic identification task, these quite different cues were found to engage in a trading relation: One cue could, within limits, substitute for the other. In a second experiment, the perceptual equivalence implied by that trading relation was put to a stricter test. If the cues are truly equivalent in perception, then they should have their effects on the same perceptual dimension. That being so, it should be possible to combine them in such a way that, working at cross purposes in the perceptual domain, they effectively cancel each other. Pairs of patterns so produced should, then, be harder to discriminate than pairs produced by either cue alone, and still harder than those produced when the (same) two cues are combined in the opposite way and so cooperate. That expectation was confirmed. We suggest that the equivalence thus demonstrated comes about because the two cues are processed by a system specialized to take account of their common origin in speech production. So interpreted, the equivalence may be viewed as an instance of distinctively phonetic perception.     

A synthesis of two factor analyses of intermediate algebra

A battery of 18 tests of intermediate algebra and 20 reference tests was administered to two successive second-year algebra classes. Each battery was separately factor analyzed by Thurstone methods, and the two analyses were synthesized by the Tucker method. The five congruent factors obtained were identified as: Verbal Comprehension, Deductive Reasoning, Algebraic Manipulative Skill, Number Ability, and Adaptability to a New Task.This paper is a condensation of a thesis. The work was begun while the author was a Psychometrics Fellow of the Educational Testing Service. The work was further supported by Contract N6onr-270-20 of the Office of Naval Research and by Grant NSF G-642 of the National Science Foundation. The writer is indebted to Professors Harold Gulliksen and Ledyard R Tucker for their guidance throughout this study.