Extensions of Narens' theory of ratio magnitude estimation

Stevens postulated that the responses of a participant in a ratio scaling experiment can be used directly to construct a psychophysical function. Today, it is generally accepted that the axioms of commutativity and multiplicativity are crucial for the interpretation of the subjects' ratio scaling behaviour. Empirical findings provide evidence that commutativity holds, whereas multiplicativity fails to hold across different sensory modalities. This shows that, in principle, Stevens' direct scaling methods yield measurements on a ratio scale level, but that the numerals occurring in a ratio scaling experiment cannot be taken at face value. Thus, Narens and others introduced a transformation function f, which converts the numerals used in an experiment into the latent mathematical numbers. The aim of the present paper is to specify the (unknown) shape of the transformation function f, by analysing different extensions of the multiplicative property. The results provide evidence that f is either a power function or a logarithmic function.     

Performances on ratio and interval schedules of reinforcement: Data and theory

Two differences between ratio and interval performance are well known: (a) Higher rates occur on ratio schedules, and (b) ratio schedules are unable to maintain responding at low rates of reinforcement (ratio “strain”). A third phenomenon, a downturn in response rate at the highest rates of reinforcement, is well documented for ratio schedules and is predicted for interval schedules. Pigeons were exposed to multiple variable-ratio variable-interval schedules in which the intervals generated in the variable-ratio component were programmed in the variable-interval component, thereby “yoking” or approximately matching reinforcement in the two components. The full range of ratio performances was studied, from strained to continuous reinforcement. In addition to the expected phenomena, a new phenomenon was observed: an upturn in variable-interval response rate in the midrange of rates of reinforcement that brought response rates on the two schedules to equality before the downturn at the highest rates of reinforcement. When the average response rate was corrected by eliminating pausing after reinforcement, the downturn in response rate vanished, leaving a strictly monotonic performance curve. This apparent functional independence of the postreinforcement pause and the qualitative shift in response implied by the upturn in variable-interval response rate suggest that theoretical accounts will require thinking of behavior as partitioned among at least three categories, and probably four: postreinforcement activity, other unprogrammed activity, ratio-typical operant behavior, and interval-typical operant behavior.     

Intentionality: A Fundamental Idea of Husserl's Phenomenology

Simone de Beauvoir has written of the sense of excitement that marked Jean-Paul Sartre's first encounter with the thought of Husserl and Heidegger. Perhaps no work of Sartre's communicates this excitement, and the reason for it, quite so transparently as his brief 1939 essay on Husserl's notion of intentionality. Husserl here appears as a revolutionary, almost as a saviour, who has provided the necessary key for putting philosophy back in touch with the ordinary experience which both French realism and French idealism had vainly sought to characterize. Realism and idealism alike had been guilty in effect of a reduplication of things in consciousness, dependence on an often unexpressed correspondence theory which made mental surrogates for the real the only reality available to man. But if the present essay testifies to Sartre's attempt to return French thought to immediate contact with things, it enters into a fascinating dialectical tension with another of Sartre's chief motives—to purify immediate experience of its deceptions through a highly reflective, analytic mediation. The essay first appeared in Nouvelle Revue Francaise, LII, January 1939. (Tr.)     

Two-group classification in latent trait theory: Scores with monotone likelihood ratio

This paper deals with two-group classification when a unidimensional latent trait,, is appropriate for explaining the data,X. It is shown that ifX has monotone likelihood ratio then optimal allocation rules can be based on its magnitude when allocation must be made to one of two groups related to. These groups may relate to probabilistically via a non-decreasing functionp(), or may be defined by all subjects above or below a selected value on.In the case where the data arise from dichotomous items, then only the assumption that the items have nondecreasing item characteristic functions is enough to ensure that the unweighted sum of responses (the number-right score or raw score) possesses this fundamental monotone likelihood ratio property.     

Human visual motion sensitivity: Evidence against a ratio theory of sensory coding

Luminance thresholds for downward moving contours were measured under several conditions of adaptation. Included was one condition which desensitized visual mechanisms responsive to downward motion. Another condition exerted equal effects on both up- and down-sensitive mechanisms. Thresholds for moving contours were unaffected by exposure to contours which moved in the opposite direction. This indicates that the perception of motion does not depend upon the relative activity in oppositely tuned, directionally selective visual mechanisms.     

A recruitment theory of force-time relations in the production of brief force pulses: the parallel force unit model

A theory, the parallel force unit model, is advanced in which the buildup and decline of force in rapid responses of short duration are assumed to reflect variability in timing of several parallel force units. Response force is conceived of as being a summation of a large number of force units, each acting independently of one another. Force is controlled by either the number of recruited force units or the duration each unit contributes its force. Several predictions are derived on the basis of this theory and are shown to be in qualitative agreement with empirical findings about both the mean and variability of brief force impulses. The model also has consequences for the temporal properties of a response. For example, under certain circumstances, it predicts a reciprocal relation between reaction time and response force. Although the theory is proposed as a psychological account, relations between the assumptions and basic principles in neurophysiology are considered. Possible future applications and generalizations of the theory are discussed.     

Auditory threshold,signal-to-noise ratio and signal detection theory

The use of Signal Detection Theory has demonstrated that there is not an auditory threshold at the level supposed by classical psychophysics, but has not disproved the existence of an auditory threshold at a lower level. Following the recommended signal detection theory procedure fairly closely, an experiment obtained evidence either of the existence of a signal-to-noise ratio audi tory threshold, or a nonlinear relationship between stimulus and response which could not be statistically distiguished from such a threshold , Using the same apparatus and subjects, audi tory thresholds were also obtained using the classical method of limits. The acoustic pressure for the classical thresholds was about five times as great as for the signal detection theory method.     

Decompositional Equivalence: A Fundamental Symmetry Underlying Quantum Theory

Decompositional equivalence is the principle that there is no preferred decomposition of the universe into subsystems. It is shown here, by using a simple thought experiment, that quantum theory follows from decompositional equivalence together with Landauer’s principle. This demonstration raises within physics a question previously left to psychology: how do human—or any—observers identify or agree about what constitutes a “system of interest”?     

A note on monotone likelihood ratio of the total score variable in unidimensional item response theory

This note provides a direct, elementary proof of the fundamental result on monotone likelihood ratio of the total score variable in unidimensional item response theory (IRT). This result is very important for practical measurement in IRT, because it justifies the use of the total score variable to order participants on the latent trait. The proof relies on a basic inequality for elementary symmetric functions which is proved by means of few purely algebraic, straightforward transformations. In particular, flaws in a proof of this result by Huynh [(1994) . A new proof for monotone likelihood ratio for the sum of independent Bernoulli random variables. Psychometrika, 59, 77–79] are pointed out and corrected, and a natural generalization of the fundamental result to non‐linear (quasi‐ordered) latent trait spaces is presented. This may be useful for multidimensional IRT or knowledge space theory, in which the latent ‘ability’ spaces are partially ordered with respect to, for instance, coordinate‐wise vector‐ordering or set‐inclusion, respectively.     

K-Lines: A theory of memory

Most theories of memory suggest that when we learn or memorize something, some drepresentation of that something is constructed, stored and later retrieved. This raises questions like: How is information represented? How is it stored? How is it retrieved? Then, how is it used? This paper tries to deal with all these at once. When you get an idea and want to “remember” it, you create a “K-line” for it. When later activated, the K-line induces a partial mental state resembling the one that created it. A “partial mental state” is a subset of those mental agencies operating at one moment. This view leads to many ideas about the development, structure and physiology of memory, and about how to implement framelike representations in a distributed processor.     

A derivation of a measure of relative balance for social structures and a characterization of extensive ratio systems

As an extension of the Heider and Cartwright-Harary theory of balance in social structures (signed digraphs), a measure of relative balance which is derived from some plausible axioms is needed. Such a measure should reflect the balance ordering, i.e., the relation ‘one social structure is more balanced than another’.     

The Sign Redeemed: A Study in Christian Fundamental Semiotics

A Christian engagement with the question of the nature of the sign has to begin in a theology of the creation. Signs exhibit features of both reference and address. The meaning of the incarnation is that in a world of God's making the referring signs which constitute the world also implicitly function as divine address. The words of institution of the Lord's Supper, taken as an integral part of the Passion narrative, are the fulfilment of this addressive function of the world and thus also mark the point at which the Church is constituted as the human community who are called to receive the divine address.     

Color measurement and color theory: I. Representation theorem for Grassmann structures

For trichromatic color measurement, the empirically based structure consists of the set of colored lights, with its operations of additive mixture and scalar multiplication, and the binary relation of metameric matching. The representing numerical structure is a vector space. The important axioms are Grassmann's laws. The vector representation is constructed in a canonical or coordinate-free manner, mainly using Grassmann's additivity law. Trichromacy is used only to fix the dimensionality.Color theories attempt to get a more unique homomorphism by enriching the basic empirical structure with new empirical relations, subject to new axioms. Examples of such enriching relations include: discriminability or dissimilarity ordering of color pairs; dichromatic matching relations; and unidimensional matching relations, or codes. Representation theorems for the latter two examples are based on Grassmann-type laws also. The relationship between a Grassmann structure and its unidimensional Grassmann codes is modeled by the relationship between a vector space and its dual space of linear functionals. Dual spaces are used to clarify theorems relating to the three-pigment hypothesis and to reduction dichromacy.     

Repair theory: A generative theory of bugs in procedural skills

This paper describes a generative theory of bugs. It claims that all bugs of a procedural skill can be derived by a highly constrained form of problem solving acting on incomplete procedures. These procedures are characterized by formal deletion operations that model incomplete learning and forgetting. The problem solver and the deletion operator have been constrained to make it impossible to derive “star-bugs”—algorithms that are so absurd that expert diagnosticians agree that the alogorithm will never be observed as a bug. Hence, the theory not only generates the observed bugs, it fails to generate star-bugs. The theory has been tested on an extensive data base of bugs for multidigit subtraction that was collected with the aid of the diagnostic systems buggy and debuggy. In addition to predicting bug occurrence, by adoption of additional hypotheses, the theory also makes predictions about the frequency and stability of bugs, as well as the occurrence of certain latencies in processing time during testing. Arguments are given that the theory can be applied to domains other than subtraction and that it can be extended to provide a theory of procedural learning that accounts for bug acquisition. Lastly, particular care has been taken to make the theory principled so that it can not be tailored to fit any possible data.     

A theory of criterion setting: an alternative to the attention band and response ratio hypotheses in magnitude estimation and cross-modality matching

The attention band and response ratio hypotheses of Green and Luce (1974) and Luce and Green (1974) are discussed and some difficulties are noted. An alternative hypothesis is put forward. This is based on a Thurstonian model for magnitude estimation in which the presented stimulus intensities are subjected to a logarithmic transformation. Response criteria are then applied to the resulting quantities to select corresponding responses. The setting and maintenance of these response criteria are accounted for by a theory of criterion setting previously developed by the senior author (Treisman & Williams, 1984). A similar model is developed for cross-modality matching, and it is shown that these models can predict the V pattern for the coefficient of variation of response ratios, can predict the inverted V pattern for correlations between successive responses, and can account for some of the difficulties found in the literature.