Algebraic models for integration of painful and nonpainful electric shocks

Subjects rated the average intensity of two sequentially presented electric shocks, which were either painful (intensity range from 1 to 4 mA, Experiment 1) or nonpainful (intensity range from .6 to .9 mA). In both experiments, stimuli were presented in a 4 by 4 factorial design to allow tests of algebraic models of the integration process under analysis of variance (Anderson, 1970, 1974). Both sets of data were fit by the equation R_{i j}=w₁s₁+w₂+s₂, (w₁+w₂=1), where R_{i j}is the rating scale response, s₁ and s₂ the scale values for the first and second stimuli, respectively, and w₁ and w₂ associated weights. When stimuli were painful, w₁=w₂, and when stimuli were nonpainful, w₁< w₂. Subjective scale values as a function of stimulus intensity appear to increase nonlinearly for painful stimuli and linearly for nonpainful stimuli. Some implications of the results for pain research are discussed.     

Reliability for the law of comparative judgment

A variance-components analysis is presented for paired comparisons in terms of three components:s, the scale value of the stimuli;d, a deviation from the linear model specified by the law of comparative judgment; andb, a binomial error component. Estimates are given for each of the three variances, _s ² , _d ² , and _b ² . Several coefficients, analogous to reliability coefficients, based on these three variances are indicated. The techniques are illustrated in a replicated comparison of handwriting specimens.This research was jointly supported in part by Princeton University, the Office of Naval Research under contract Nonr-1858(15), and the National Science Foundation under grant NSF G-642, and in part by Educational Testing Service. Reproduction in whole or in part is permitted for any purpose of the United States Government.Thanks are due to Ledyard Tucker and Frederic Lord for valuable suggestions on the development presented here.     

Utility of extension of functional equations—when possible

Jean-Claude Falmagne observed in 1981 [On a recurrent misuse of classical functional equation result. Journal of Mathematical Psychology, 23, 190-193] that, even under regularity assumptions, not all solutions of the functional equation k(s+t)=k(s)+k(t), important in many fields, also in the theory of choice, are of the form k(s)=Cs. This is certainly so when the domain of the equation (the set of (s,t) for which the equation is satisfied) is finite. We mention an example showing that this can happen even on some infinite, open, connected sets (open regions). The more general equations k(s+t)=?(s)+n(t) and k(s+t)=m(s)n(t), called Pexider equations, have been completely solved on R². In case they are assumed valid only on an open region, they have been extended to R² and solved that way (the latter if k is not constant). In this paper their common generalization

k(s+t)=?(s)+m(s)n(t)     

Does test-enhanced learning transfer for triple associates?

Test-enhanced learning and transfer for triple-associate word stimuli was assessed in three experiments. In each experiment, training and final-test trials involved the presentation of two words per triple associate (triplet), with the third word having to be retrieved. In agreement with the prior literature on different stimuli, training through testing with feedback yielded markedly better final-test performance than did restudy. However, in contrast to the positive transfer reported for paired associate stimuli, minimal or no positive transfer was observed, relative to a restudy control, from a trained cue combination (e.g., A, B, ?) to other cue combinations from the same triplet that required a different response (e.g., B, C, ?). That result also held when two unique cue combinations per triplet were tested during training, and for triplets with low and high average associative strengths. Supplementary analyses provided insight into the overall transfer effect: An incorrect response during training appears to yield positive transfer relative to restudy, whereas a correct response appears to yield no, or even negative, transfer. Cross-experiment analyses indicated that test-enhanced learning is not diminished when two or three cue combinations are presented during training. Thus, even though learning through testing is highly specific, testing on all possible stimulus–response combinations remains the most efficient strategy for the learning of triple associates.     

An analysis of the solution of PAN ambiguous-cue problems by rhesus monkeys

Twenty-four monkeys were given 2-choice discrimination problems composed of three planometric plaque stimuli: P, the rewarded stimulus; N, the nonrewarded stimulus; and A, the ambiguous stimulus which was negative when paired with P, but positive when paired with N. When both pair of stimuli, PA and NA, were presented within a given session S was forced either to approach or to avoid the A plaque depending upon the stimulus with which it was paired. The results corroborated previous reports for plaque stimuli by showing PA performance to be superior to NA. The data also revealed that when plaque stimuli with distinctive cues were employed, NA performance exceeded PA as previously reported for stereometric object stimuli. Pretraining Ss with plaque stimuli possessing distinctive cues, then switching to plaques with less distinctive cues, also resulted in superior NA performance. These findings are discussed in the context of an interference-cue theory.     

A covariance analysis of multiple paired comparisons

In the method of multiple paired comparisons the dominance of objectj over objectk is observed uponp attributes. The present paper develops a covariance analysis for these paired comparisons in terms of a linear model which includes scale, bias, and interaction effects, along withs covariants upon which the comparisons are presumably dependent. The covariance model gives rise to adjusted parameter estimates and hypothesis tests for the residual pairwise layout from which the effects of thes covariants have been removed. These estimation and testing procedures are illustrated with an analysis of political judgment data, and their relevance to the general problem of residual scaling is discussed.This research was supported by National Institute of Mental Health grants MH 12972 and MH 15506. The author would like to express his appreciation to Jerry Solomon and Wei-Ching Chang of the Oregon Research Institute for the data analysis reported at the end of the paper. Computing assistance was obtained from the Health Sciences Computing Facility, UCLA, sponsored by N.I.H. Grant FR-3.     

Pavlovian processes do mediate control of the “advance” response strategy

Two parallel experiments used pigeons in a transfer of control design to determine the basis of the transfer of the use of the “advance strategy” across successive discriminations (W. K. Honig & H. Lindsay, Learning and Motivation, 1975, 6, 157–178). Pigeons were first trained under instrumental contingencies to use an “advance” response to maximize their exposure to S^D and minimize their exposure to S^Δ. Then orthogonal stimuli (key lights in Experiment 1 and diffuse illuminations in Experiment 2) were independently established through separate discriminative Pavlovian procedures as CS+ and CS? or as CS^o's. Later in special tests, it was demonstrated that the associative values of the Pavlovian CS's were a major factor governing the use of the advance strategy: only pigeons exposed to $\text{CS+}\text{CS?}$ used the advance response to regulate their exposure to either CS. Although these experiments showed that the necessary and sufficient conditions for utilization of the advance strategy are the Pavlovian associative values of the discriminative stimuli, opportunity for differential “operant” responding during the discriminative stimuli seems to be a contributor to the optimal use of the advance response across successive discriminations.     

Low-Level Phenomenal Vision Despite Unilateral Destruction of Primary Visual Cortex

GY, an extensively studied human hemianope, is aware of salient visual events in his cortically blind field but does not call this “vision.” To learn whether he has low-level conscious visual sensations or whether instead he has gained conscious knowledge about, or access to, visual information that does not produce a conscious phenomenal sensation, we attempted to image process a stimulus s presented to the impaired field so that when the transformed stimulus T(s) was presented to the normal hemifield it would cause a sensation similar to that caused by s in the impaired field. While degradation of contrast, spatio-temporal filtering, contrast reversal, and addition of smear and random blobs all failed to match the response to a flashed bar s_f, moving textures of low contrast were accepted to match the response to a moving contrast-defined bar, s_m. Orientation and motion direction discrimination of the perceptually matched stimuli [s_m and T(s_m)] was closely similar. We suggest that the existence of a satisfactory match indicates that GY has phenomenal vision.     

An efficient adaptive procedure for psychophysical discrimination experiments

We present an adaptive procedure to conduct psychophysical discrimination experiments. In a discrimination experiment, an observer senses (sees, hears, feels, etc.) two stimuli (separated in space or time) and is asked to order these stimuli with respect to a particular parameter (say,s). Under the usual assumption of a locally linear internal representation ofs, perturbed by additive Gaussian noise, the probabilityP(s ₂)—of judging test stimuluss ₂ “larger” than a reference stimuluss ₁—is an error function (a cumulative normal distribution). Such an error function,Erf [(s ₂μ)/σ], is parametrized by two parameters: μand σ. The parameter μ is the value for whichP(s ₂) = 50% and is related to possible bias effects in the internal representation of the observer. The parameter σ is √2 times the standard deviation of the noise distribution and is generally called thediscrimination threshold. In this paper, we present (1) an algorithm to estimate μ and σ given the data generated by such an observer, (2) an analysis of the efficiency of a stimulus presentation with respect to the estimation of μ and σ , and (3) a method that controls the specific choice of stimulus values during an experiment so that an optimal estimation of μ and σ is obtained.     

Classification of concatenation measurement structures according to scale type

A relational structure is said to be of scale type (M,N) iff M is the largest degree of homogeneity and N the least degree of uniqueness (Narens, 1981a, Narens, 1981b) of its automorphism group.Roberts (in Proceedings of the first Hoboken Symposium on graph theory, New York: Wiley, 1984; in Proceedings of the fifth international conference on graph theory and its applications, New York: Wiley, 1984) has shown that such a structure on the reals is either ordinal or M is less than the order of at least one defining relation (Theorem 1.2). A scheme for characterizing N is outlined in Theorem 1.3. The remainder of the paper studies the scale type of concatenation structures 〈X, ?, ° 〉, where ? is a total ordering and ° is a monotonic operation. Section 2 establishes that for concatenation structures with M>0 and N<∞ the only scale types are (1,1), (1,2), and (2,2), and the structures for the last two are always idempotent. Section 3 is concerned with such structures on the real numbers (i.e., candidates for representations), and it uses general results of Narens for real relational structures of scale type (M, M) (Theorem 3.1) and of Alper (Journal of Mathematical Psychology, 1985, 29, 73–81) for scale type (1, 2) (Theorem 3.2). For M>0, concatenation structures are all isomorphic to numerical ones for which the operation can be written $\text{x°y = yf(}\text{x}\text{y}\text{)}$, where f is strictly increasing and $\text{f(x)}\text{x}$ is strictly decreasing (unit structures). The equation f(x^?)=f(x)^? is satisfied for all x as follows: for and only for ? = 1 in the (1,1) case; for and only for ?=kⁿ, k > 0 fixed, and n ranging over the integers, in the (1, 2) case; and for all ?>0 in the (2, 2) case (Theorems 3.9, 3.12, and 3.13). Section 4 examines relations between concatenation catenation and conjoint structures, including the operation induced on one component by the ordering of a conjoint structure and the concept of an operation on one component being distributive in a conjoint structure. The results, which are mainly of interest in proving other results, are mostly formulated in terms of the set of right translations of the induced operation. In Section 5 we consider the existence of representations of concatenation structures. The case of positive ones was dealt with earlier (Narens & Luce (Journal of Pure & Applied Algebra27, 1983, 197–233). For idempotent ones, closure, density, solvability, and Archimedean are shown to be sufficient (Theorem 5.1). The rest of the section is concerned with incomplete results having to do with the representation of cases with M>0. A variety of special conditions, many suggested by the conjoint equivalent of a concatenation structure, are studied in Section 6. The major result (Theorem 6.4) is that most of these concepts are equivalent to bisymmetry for idempotent structures that are closed, dense, solvable, and Dedekind complete. This result is important in Section 7, which is devoted to a general theory of scale type (2, 2) for the utility of gambles. The representation is a generalization of the usual SEU model which embodies a distinctly bounded form of rationality; by the results of Section 6 it reduces to the fully rational SEU model when rationality is extended beyond the simplest equivalences. Theorem 7.3 establishes that under plausible smoothness conditions, the ratio scale case does not introduce anything different from the (2, 2) case. It is shown that this theory is closely related to, but somewhat more general, than Kahneman and Tversky's (Econometrica47, 1979, 263–291) prospect theory.     

Maximum likelihood estimation for Luce's choice model

A terminology for general choice models based on the choice axiom is given. It applies to all kinds of choice experiments, such as confusion choice experiments, paired comparisons, triadic comparisons, directional rankings, scores on binary test items, and others. Maximum likelihood estimation for such general choice models is considered. Conditions for the uniqueness of maximum likelihood estimates are given, and it is shown that the estimates can be derived by iterative proportional fitting. This offers the opportunity of a general test of the choice axiom for all kinds of choice experiments using the likelihood ratio. The estimation and testing procedure is applied to data from a form recognition experiment, reported by W. A. Wagenaar (Nederlands Tijdschrift voor de Psychologie, 1968, 23, 96–108).     

Simultaneous classical conditioning of two effector systems

The experiment reported here was an attempt to develop an experimental procedure for independent classical conditioning of two different response systems, the skin conductance response (SCR) and the eyelid response. In a differential conditioning design with human subjects (N=50) two different unconditioned stimuli were used, a white noise (US₁) and an airpuff (US₂). Two conditioned stimuli (CS₁₁ and CS₁₂) were paired with US₁, and two other CSs (CS₂₁ and CS₂₂) were paired with US₂. A special trial architecture was used to accomplish measurement of both anticipatory SCR and eyelid responses during each trial. Significant eyelid differentiation as well as significant SCR (especially second interval responses) differentiation developed.     

Testing for selectivity in the dependence of random variables on external factors

Random variables A and B, whose joint distribution depends on factors (x,y), are selectively influenced by x and y, respectively, if A and B can be represented as functions of, respectively, (x,S_A,C) and (y,S_B,C), where S_A,S_B,C are stochastically independent and do not depend on (x,y). Selective influence implies selective dependence of marginal distributions on the respective factors: thus no parameter of A may depend on y. But parameters characterizing stochastic interdependence of A and B, such as their mixed moments, are generally functions of both x and y. We derive two simple necessary conditions for selective dependence of (A,B) on (x,y), which can be used to conduct a potential infinity of selectiveness tests. One condition is that, for any factor values x,x^′ and y,y^′,

s_xy≤s_xy^′+s_x^′y^′+s_x^′y,     

Ambiguous-cue learning in preschool children: A test of the dimensional characteristics of task stimuli

Sixteen preschool children were administered a two-choice discrimination problem consisting of three stimulus compounds: the consistently rewarded stimulus, the consistently nonrewarded stimulus, and the ambiguous stimulus which was nonrewarded when paired with the positive, but rewarded when paired with the negative. When both pair of stimuli, positive-ambiguous and negative-ambiguous, were presented together the subject was required either to choose or to avoid the ambiguous stimulus depending upon the stimulus with which it was paired. In Experiment 1, when each of three stimuli (positive, negative, ambiguous) varied along one nonspatial cue dimension (color), performance was better on negative-ambiguous trials than positive-ambiguous trials. In Experiment 2, when the positive and negative stimuli varied along three nonspatial cue dimensions (colors and form) and the ambiguous stimulus varied along one of these dimensions (color), superior positive-ambiguous over negative-ambiguous performance was obtained. These findings complement those reported for other subjects and confirm Berch's (D. B. Berch, Learning and Motivation, 1974, 5, 135–148) predictions regarding use of differential numbers of cue dimensions.     

Further evaluation of the use of preference categories to identify novel reinforcers: A systematic replication

Preference assessments are frequently used to identify reinforcers for individuals with autism spectrum disorder and intellectual and developmental disabilities. Although well‐established procedures have been shown to identify preferred stimuli for individual items that can be used in skill acquisition and behavior reduction programs, little research has been conducted on identifying categories of preferred items. In this study, paired‐stimulus preference assessments were conducted with 4 individuals with autism spectrum disorder. Researchers classified the edible stimuli as belonging to 1 of 4 categories: chocolate (e.g., chocolate chips and M&M's^®), salty/crunchy (e.g., chips and crackers), gummy (e.g., Swedish Fish^® and Starburst^®), or fruit/vegetable (e.g., grape and apple). Preference hierarchies were identified for individual stimuli and for categories of stimuli. For all participants, at least 3 of the 4 most preferred items came from the same category. Novel items (i.e., items not included in the preference assessments) identified by the researchers as belonging to the high‐preference category functioned as effective reinforcers during subsequent reinforcer assessments for all participants. This finding suggests that clinicians could identify likely effective edible reinforcers based on an individual's categorical preference without explicit testing.     

On a functional equation related to Thurstone models

If f and g are nonvanishing characteristic functions the functional equation g(s)g(t)g(?s ? t) = f(as)f(at)f(?as ? at) implies g(s) = e^ibsf(as), i.e., f and g corresponding to probability distributions of the same type. It is shown here that when f and g are allowed to vanish this equation also has solutions in which f and g correspond to distributions of different types. The practical implication is that there are nonequivalent. Thurstone models which cannot be discriminated by any choice experiment with three objects.     

Complex Visual Learning by Rats

Rats’ learning about visual patterns was studied in a computerized Y-maze where wide-angle stimuli were viewed from a distance. Many patterns were available; some were spatially complex and others were more homogeneous figures. Experiment 1 used a discrimination paradigm in which a single S⁺could be paired with any one of 15 different S⁻s. Hooded rats learned successively six such discrimination problems. Their learning rate improved across the series, and comparison with controls suggested that the learning-set did not merely reflect simple habituation. Experiments 2 and 3 employed Dark Agouti rats, again learning many discrimination problems. Each problem comprised a constant stimulus which was paired with stimuli which varied in trial-unique fashion. The version in which the constant stimulus was nonrewarded (S⁻) and the varying stimuli rewarded was performed better than the converse, constant S⁺and varying nonrewarded, reflecting rats’ preference for relatively unfamiliar stimuli. In the constant S⁻task, rats showed substantial within-problem learning when three novel problems were given per day for 20 trials each. Rats are capable of rapid learning about complex visual displays if we engage their natural dispositions to use vision for distal stimuli and to approach relatively unfamiliar cues.     

Pavlovian conditioning with proximal stimuli

This experiment was conducted with the objective of demonstrating that the effective stimuli in Pavlovian Conditioning are not environmental stimuli but internal physiological processes elicited by environmental input (proximal stimuli). In order to achieve the objective, afterimages in color vision were used: looking at a diffuse lightened circle after seeing a red circle yields an image of a green circle. A differential conditioning paradigm with two sequential compounds was run. In one group (G⁺B^?: n₁=10), a red circle followed by a green circle was paired with shock, whereas a red circle followed by a blue circle remained unpaired. A second group (G^?B⁺: n₂=10) received red-blue paired trials and unpaired red-green trials. Immediately after that training, subjects were tested with a new, never trained sequential compound: a red circle followed by a diffuse lightened circle. Furthermore, they were tested with the already trained compounds. Taking the environmental point of view, the never trained stimulus should elicit an orienting response lying inbetween the excitatory reaction to the paired stimulus and the inhibitory reaction to the unpaired stimulus. From the proximal point of view, the diffuse light should elicit an excitatory reaction in group G⁺B^? and an inhibitory reaction in group G^?B⁺. Electrodermal conditioned anticipatory and omission responses were measured. The results supported the proximal hypothesis. Hence, defining input in environmental terms may be the wrong way. Instead, in conceptualizing the stimulus in conditioning, the following should be considered: the processing organism itself is creating the effective stimuli.     

The magical number seven and some other features of category scaling: Properties of a model for absolute judgment

A model for absolute judgment is presented. This is derived from a theory of the processes which set and maintain response criteria (M. Treisman & T. C. Williams, 1984, Psychological Review, 91, 68–111) which has been applied to a number of problems in psychophysics. A Thurstonian model is assumed as a basis for absolute judgment, and criterion-setting theory is applied to the criteria in this model. The question is then considered, to what extent can such a model account for the main findings that have been obtained in category scaling? The range of explanations that the model can provide is investigated by means of computer simulation. It appears that features such as the upper limit on information transmission as the number of stimuli increases, the effect of stimulus range on information transmission, the accuracy edge effect, the resolution edge effect, the central tendency of judgment, stimulus and response dependencies, and related phenomena can be reproduced by simulations of the model.