Discriminal Processes Research Articles

Perception as Interacting Psychophysical Functions. Could the Configuring of Features Replace a Specialised Receptor?

This paper illustrates how perception is achieved through interactions among the psychophysical functions of judged features of an object. The theory is that the perceiver places processed features in a multidimensional space of discriminal processes. Each dimension is scaled in units of discrimination performance. The zero coordinate of each feature is its level in an internal standard (norm) established by previous experience of that category of object in context. Experiments are reported which show that one, two, or three concurrent single-featured objects matched the multiple features of another object in two ways. Either stimulation from the two objects had discrimination distances from norm that added, or the stimulation by one object was processed through a concept describing stimulation by the other object. It follows that, in this case, perception via a receptor for the multi-featured object can be replaced by a point of balance among receptors for each single feature. The object with its own receptor is the gustatory stimulant L-glutamic acid as its monosodium salt. The features that stimulate diverse gustatory receptors of their own are sodium chloride, citric acid, sucrose, and caffeine. A more complex approach to dimensional coding was developed earlier for photoreceptors in colour judgments. The present approach is modality independent, mathematically simple, and economical in experimental data.

Effects of typicality and interstimulus interval on the discrimination of speech stimuli

To investigate the effects of processing time and retention interval on the perceptual judgment for speech sounds, Japanese listeners were tested with the AX discrimination task in various interstimulus intervals. Speech stimuli were synthesized to comprise both typical and stypical stimulus sets. In the typical set, the standard stimulus had characteristics of the typical Japanese /aba/ sound. In the atypical set, the standard was not a good exemplar of the Japanese /aba/ sound although it was usually recognized as /aba/. The performance of the subjects was analyzed in terms of both the center and width of discriminal processes. At relatively short intervals, there was a slight tendency for the typical standard to have a smaller width score than the atypical standard. At long intervals, there was no effect of the standard stimulus. Although the center shifted to the direction of more plosive counterparts at longer intervals, there was no effect of the standard on the center of discriminal process. The re...

A Probabilistic IRT Model for Unfolding Preference Data

A probabilistic model is developed for the pair- comparison design in which the unfolding principle that governs the choice process uses a discriminal pro cess analogous to Thurstone's Law of Comparative Judgment. However, this process is governed by the square of the distance between the location of the per son and the stimulus, rather than controlled by the lo cation of the stimulus as in Thurstone's formulation. A simulation study demonstrates the feasibility of esti mation, and two examples use real data to show the implications of the unfolding models for psychological research. Index terms: choice data, item response theory, pair comparisons, preference data, unfolding.

A geometrization of the discriminal process model on the sensory system with several inputs and a single output

AbstractThis paper presents a geometrical version of Thurstone's discriminal process model for the multiinput single‐output sensory system. As the first step, the probability density function for the discriminant process is defined. The parameters of the probability density function is the mean and the variance of n stochastic variables. It is assumed that each of the variances is given as a linear function of the mean values. The space spanned by the parameters (n means) is defined and called the discriminal space. The fundamental metric is introduced into the discriminal space using Fisher's information matrix, and the resulting space is regarded as an n‐dimensional Riemannian space. The geometrical structure of the discriminal space is examined, and clear descriptions are made for the essential meaning of the response function, the relation between the discriminal process model and the psychophysical function, and a pertinent analogy between the concept of difference thresholds and the discriminal process model.

The Application of an Unfolding Model of the PIRT Type to the Measurement of Attitude

Unfolding data for unidimensional variables con structed from direct responses (e.g., agreement or dis agreement) are characterized by single peaked func tions involving the locations of each person and each stimulus. A continuous discrirninal process, of the form postulated by Thurstone when he proposed his Law of Comparative Judgment, is suggested. This process is transformed to a qualitative dichotomous re sponse in which the probability of endorsement is governed by the square of the distance between the lo cations of the person and the stimulus. Maximum like lihood estimates of the parameters are derived, and it is shown that the information associated with any re sponse is a bimodal function of the difference between the person and stimulus locations. The feasibility of parameter estimation is demonstrated with a limited simulation study. The model is applied to a set of statements designed to measure attitudes toward capi tal punishment and scaled by the methods of Thur stone. The responses conformed to the unfolding mechanism, and the scale values of the statements are statistically equivalent to those obtained by Thur stone's methods. Index terms: Attitude measure ment, Developmental data, Discriminal process, Item response theory, Person response theory, Thurstone scaling, Unfolding data, Unidimensional scaling.

The geometrization of the discriminal process model and the psychophysical functions

AbstractThurstone's discriminal process model is geometrized and discussed from the information‐system theoretical point of view. That is, a probability density function (p.d.f.) based on the discriminal processes is defined in the state space (this is the concept of grasping simultaneously the physical stimulus and its response. A parameter space spanned by parameters of the p.d.f. is defined, and fundamental metrics are introduced into the space based on Fisher's information; thus, the space is considered to be a Riemannian space. In the space, the psychophysical functions are derived as certain geometrical invariants. As the results, when the “discriminal dispersion,” i.e., the distribution of the response (the response function) to the input stimulus is to be Gaussian, the power law and the logarithmic law are obtained as psychophysical laws with respect to the mean values of the distributions. From this, relations between difference thresholds, the discriminal process and the psychophysical function are clarified. At the same time, the formalization of the problems and conclusions in [2] are justified from the information‐system theoretical point of view. Further the functional forms of the response functions are also investigated, and it is shown that almost the same conclusions can be obtained even if the Gaussian assumption is repalced by the exponential, the two‐sided exponential, or the logarithmic Gaussian distributions.

Extremism, Intensity, and Perception in Congressional Voting

Social psychology, since the days of Thurstone, has emphasized the study of attitude distributions on quantitative dimensions. The discipline has, moreover, emphasized the study of individual differences. In particular, social psychologists – and sociologists and political scientists as well – have emphasized that the behavior of extremists differs sharply from that of moderates. Economists, in contrast, have been concerned with the development of mathematical models of choice along a dimension based on the concept, in one dimension, of a single-peaked indirect utility function. At the same time, empirical work by economists has neglected individual differences at the psychological level. In economic models, individuals typically differ only in their ideal points (which may differ because of budget constraints or socioeconomic characteristics) but not in the form of the utility function. In this paper, we use the findings on extremism developed in social psychology to inform a choice model commonly used in econometrices. This is the logit or double exponential model. In fact, as shown by Yellott (1977), the double exponential distribution is the only distribution that satisfies Thurstone case V discriminal processes, equivalent to Luce's choice axiom, for all possible choice experiments. Consequently, the research reported here accomplishes a form of Thurstone scaling that allows for the behavior of extremists to differ from that of moderates.

Thurstone's discriminal processes fifty years later

Four issues are discussed concerning Thurstone's discriminal processes: the distributions governing the representation, the nature of the response decision rules, the relation of the mean representation to physical characteristics of the stimulus, and factors affecting the variance of the representation. A neural schema underlying the representation is proposed which involves samples in time of pulse trains on individual neural fibers, estimators of parameters of the several pulse trains, samples of neural fibers, and an aggregation of the estimates over the sample. The resulting aggregated estimate is the Thurstonian representation. Two estimators of pulse rate, which is monotonic with signal intensity, are timing and counting ratios and two methods of aggregation are averaging and maximizing. These lead to very different predictions in a speed-accuracy experiment; data indicate that both estimators are available and the aggregation is by averaging. Magnitude estimation data are then used both to illustrate an unusual response rule and to study the psychophysical law. In addition, the pattern of variability and correlation of magnitude estimates on successive trials is interpreted in terms of the sample size over which the aggregation takes place. Neural sample size is equated with selective attention, and is an important factor affecting the variability of the representation. It accounts for the magical number seven phenomenon in absolute identification and predicts the impact of nonuniform distributions of intensities on the absolute identification of two frequencies.

The relationship between Luce's Choice Axiom, Thurstone's Theory of Comparative Judgment, and the double exponential distribution

Holman and Marley have shown that Thurstone's Case V model becomes equivalent to the Choice Axiom if its discriminal processes are assumed to be independent double exponential random variables instead of normal ones. It is shown here that for pair comparisons, this representation is not unique; other discriminal process distributions (specifiable only in terms of their characteristic functions) also yield a model equivalent to the Choice Axiom. However, none of these models is equivalent to the Choice Axiom for triple comparisons: There the double exponential representation is unique. It is also shown that within the framework of Thurstone's theory, the double exponential distribution, and hence the Choice Axiom, is implied by a weaker assumption, called “invariance under uniform expansions of the choice set.”

Simple reaction time with markovian evolution of gaussian discriminal processes

Simple reaction time with markovian evolution of gaussian discriminal processes

Simple reaction time with markovian evolution of gaussian discriminal processes

If the discriminal distributions of signal-detectability theory evolve in time according to a normal Markov process, they can be characterized by Brownian motion generalized with a constant bias determined by signal strength. If the process is stopped at the first occurrence of a preset criterion displacement, the resulting latency distribution provides a model for the central component of simple reaction time. Discussed are properties of the distribution which should be useful in obtaining experimental predictions from neural-counting assumptions, and in relating reaction times to basic variables of the theory of signal-detectability.

THE MULTIDIMENSIONAL ANALYSIS OF ‘ELASTIC’ DISTANCES

A new orientation to the problem of multidimensional scaling is presented using the notion of ‘elastic’ distances. Making use of a rational theory of judgement variability (in line with Thurstone's remarks about discriminal processes); a monotonic distance function (in line with Shepard's suggestions); an algorithm for determining the monotonic transformations at each iteration (as provided by Kruskal); and a criterion which yields information about the tolerance for variability of judgement that any solution demands, a hybrid analytical approach is proposed as a practical multidimensional scaling procedure. The approach is illustrated using experimental data.

Signal detection theory and Crozier's law: Derivation of a new sensory scaling procedure

The relation between sensory thresholds and the “sensory scale” is examined in the light of the threshold model given by signal detection theory. The problem is seen as that of determining the function relating E, the central effect of a stimulus serving as the decision axis when threshold judgments are made, and I, the physical intensity of the stimulus. Consideration of the model shows that when deviations from Weber's law occur they may be accompanied by departures from Crozier's law and that the occurrence and extent of the latter depend on the relation between E and I and can be used to define it. The argument is applied to some of the data on visual brightness discrimination in the literature. The results suggest that E may be related to I by a power function with an exponent of the order of 1.0. The disparity between this function and the psychophysical laws given by classical scaling procedures is discussed, and it is suggested that it may prove useful to hypothecate a distinction between central discriminal and metric processes.

THE LAW OF COMPARATIVE JUDGEMENT IN THE SUCCESSIVE INTERVALS AND GRAPHIC RATING SCALE METHODS

ABSTRACTIn the present study the use of the law of comparative judgement is generalized to the successive intervals and graphic rating scale methods. A procedure for calculating the modal discriminal process and discriminal dispersion of the stimuli, as well as the values of any selected point on the continuum, is given.From the estimated values it is possible to determine the theoretical proportions and to compare them with the actual experimental proportions. The agreement between these values is an indication of the adequacy of the assumptions made in the development of the procedures described.The experimental results indicate that the procedure followed in this paper gives an accurate reproduction of the actual values.

A law of comparative judgment.

This chapter describes a new psychophysical law which may be called the law of comparative judgment and to show some of its special applications in the measurement of psychological values. The law of comparative judgment is applicable not only to the comparison of physical stimulus intensities but also to qualitative comparative judgments such as those of excellence of specimens in an educational scale. The scale difference between the discriminal processes of two specimens which are involved in the same judgment will be called the discriminal difference on that occasion. The law of comparative judgment is basic for all experimental work on Weber's law, Fechner's law, and for all educational and psychological scales in which comparative judgments are involved. The formulation of the law of comparative judgment involves the use of a new psychophysical concept, namely, the discriminal dispersion.