Electrocutaneous psychophysical input-output functions and temporal integration

Electrocutaneous magnitude estimation functions were generated by stimuli ranging from 1.0 to 5.0 mA and from 100 to 6,400 msec in duration. The results indicate that when these functions are fitted by a two-parameter power function (ME = aI^b), the values of the constant, a, and the exponent, b, are altered by increases in stimulus duration, with a increasing and b decreasing. The exponent decreases from around 1.4 to 0.93 as duration increases from 100 to 6,400 sec. Equal magnitude estimation contours drawn for estimates ranging from “2“ to “50“ can be fitted by an equation representing partial integration, I × t^a = K. The exponent a decreases as a function of the level of the magnitude estimation, indicating less partial integration at higher than at lower levels of estimated magnitude. The electrocutaneous data are compared to data in other sensory modalities.     

The perceptual properties of electrocutaneous stimulation: Sensory quality,subjective intensity,and intensity-duration relation

A preliminary and two main experiments designed to examine the perceptual properties of electrocutaneous stimulation are reported. The stimuli used were single short pulses varying in intensity and duration. In Experiment 1, the exponents of power functions fitted to electrocutaneous magnitude estimation data were determined together with the sensory qualities induced by electrical stimulation. The results showed that there was no correlation between the exponent values and the sensory qualities. The mean exponent was 1.2. In Experiment 2, an intensity-duration trading function was constructed from the data obtained from identifying the induced sensory qualities. The results showed that the critical duration increases from 30 to 300 msec with increasing sensation level. These findings are compared with the properties of other sense modalities.     

Magnitude estimates for electrical pulses: evidence for two neural mechanisms

The hypothesis that there are two neural mechanisms for electrocutaneous stimulation--one that is sensitive to low current and is adaptive to repeated stimulation and another that is responsive to high current and is less adaptive--was tested in a control and four main experiments. In the main experiments, magnitude estimates obtained for single electrical pulses (of 2-msec duration) were described by a simple power function for each combination of high- and low-current levels and 10 trial blocks. The results were: (1) The slope of the power function for low current was steeper than was that for high current; (2) for low current, the intercept of the power function decreased with increasing block, whereas for high current, it remained constant over blocks; (3) this decrease of the intercept for low current disappeared when judgmental blocks were separated by a rest period of 8 min; (4) the modulus did not affect the slope; (5) for a large modulus combined with low current, the intercept decreased rapidly over trial blocks, whereas for a small modulus combined with high current, the intercept increased over trial blocks. The first four findings support the two-mechanism hypothesis, but the last one may also be interpretable in terms of the regression to absolute scale values.     

Latent growth curve analysis with dichotomous items: Comparing four approaches

A Monte Carlo study was used to compare four approaches to growth curve analysis of subjects assessed repeatedly with the same set of dichotomous items: A two‐step procedure first estimating latent trait measures using MULTILOG and then using a hierarchical linear model to examine the changing trajectories with the estimated abilities as the outcome variable; a structural equation model using modified weighted least squares (WLSMV) estimation; and two approaches in the framework of multilevel item response models, including a hierarchical generalized linear model using Laplace estimation, and Bayesian analysis using Markov chain Monte Carlo (MCMC). These four methods have similar power in detecting the average linear slope across time. MCMC and Laplace estimates perform relatively better on the bias of the average linear slope and corresponding standard error, as well as the item location parameters. For the variance of the random intercept, and the covariance between the random intercept and slope, all estimates are biased in most conditions. For the random slope variance, only Laplace estimates are unbiased when there are eight time points.     

Pain combines additively across different sensory systems: a further support for the functional theory of pain

Subjects made magnitude estimations of noxious stimuli produced by a 6 X 6 factorial design of electric shocks (pulse trains) and loud tones. Group data and all individual results conformed to a linear additive model of pain. The estimates of pain approximated the linear sum of the pain estimates of the individual electrocutaneous and auditory components. Pain related differently to the two inducing stimuli. It grew as a mildly expansive power function of current intensity (with an exponent of about 1.2) but as a mildly compressive power function of sound-pressure level (with an exponent of about 0.8). These results replicate recent findings by the same authors in 1986 using a more aversive type of electric stimulation. They are interpreted as supportive of a new functional approach to understand pain and pain-related phenomena.     

Stimulus range,number of categories,and the “virtual” exponent

Three different stimulus modalities (line length, number, and sound pressure) were judged by magnitude scaling techniques and by 7-, 15-, 31-, and 75-point category scales. All of the 40 subjects were given the same number stimuli, but two different sound-pressure ranges were presented (each to 20 subjects) and four different line-length ranges were presented (each to 10 subjects). Analyses of lack of fit for various simple functions were performed to determine bestfitting functions. The simple power function was often found to be an adequate fit to the data for all the response modalities used, although all of the response modalities were sensitive to changes in stimulus range. For simple power functions, the category-scale exponent was a function of both the range of stimuli and the number of categories provided. Category scales did not always produce exponents smaller than those obtained with magnitude estimation, which calls into question the concept of a virtual exponent for category scales.     

On the “absoluteness” of category and magnitude scales of pain

The concept of “absolute scaling” (Zwislocki & Goodman, 1980) implies that direct judgments of sensory magnitude not only reflect the relative positions of the stimuli being judged, but also permit us to assess level differences in sensation. In order to explore this notion for different scaling methods, in the present investigation we compared magnitude estimation with category partitioning, a verbally anchored categorization procedure, in scaling painful pressure stimuli covering different intensity ranges. The results indicate that when the same stimulus range was presented after 1 week, both methods appeared to be highly reliable, with category partitioning faring somewhat better than magnitude estimation. When the stimulus range was unobtrusively changed between sessions, both methods reflected the within-subjects shift in absolute level. When two different sets of subjects judged the slightly different stimulus ranges, both methods resulted in scale values consistent with absolute scaling, though only category partitioning was sensitive enough to differentiate the two stimulus ranges. The results are discussed in the context of different possibilities of anchoring direct scaling methods in order to obtain “absolute” level information.     

On the "absoluteness" of category and magnitude scales of pain

The concept of "absolute scaling" (Zwislocki & Goodman, 1980) implies that direct judgments of sensory magnitude not only reflect the relative positions of the stimuli being judged, but also permit us to assess level differences in sensation. In order to explore this notion for different scaling methods, in the present investigation we compared magnitude estimation with category partitioning, a verbally anchored categorization procedure, in scaling painful pressure stimuli covering different intensity ranges. The results indicate that when the same stimulus range was presented after 1 week, both methods appeared to be highly reliable, with category partitioning faring somewhat better than magnitude estimation. When the stimulus range was unobtrusively changed between sessions, both methods reflected the within-subjects shift in absolute level. When two different sets of subjects judged the slightly different stimulus ranges, both methods resulted in scale values consistent with absolute scaling, though only category partitioning was sensitive enough to differentiate the two stimulus ranges. The results are discussed in the context of different possibilities of anchoring direct scaling methods in order to obtain "absolute" level information.     

Contextual effects in difference judgments

Manipulating stimulus spacing, stimulus frequency, or stimulus range usually affects intensity judgments. In six experiments, I investigated the locus of analogues of these contextual effects in a “difference” estimation task. When all stimuli elicited the same taste quality, stimulus distribution affected the scale values only when water was included in the stimulus set (Experiments 1–3). When the subjective ranges of two taste qualities were manipulated, different scale values were obtained for the separate qualities in the two conditions (Experiment 4). Manipulation of the expected response distribution did not affect the scale values or the responses (Experiments 5–6). It is concluded that shifts in stimulus distributions or stimulus ranges result in shifts in subjective scale values. The contextual effects can be interpreted as relative shifts of a number of gustatory continua, with water lying on a separate continuum. Proposed is a model for context-dependent judgments, consisting of four stages: stimulus classification, stimulus placement, continuum placement, and continuum projection.     

The range effect as a function of stimulus set,presence of a standard,and modulus

The intramodal range effect (an inverse relationship between stimulus range and exponent in Stevens’s power law) has been well documented, but its conditions have not been tested. Both the estimates of stimulus magnitudes and their exponents are affected by context, stimulus location, and different standards and moduli, but how these variables might interact with the variable of stimulus range has not been studied. In the present research, exponents were derived from magnitude estimates of line length for each of three different stimulus: ranges at two different locations on the scale of length, with or without a modulus. Moduli of 50 and 500 permitted an analysis of the effect of response magnitude on the range effect. Because different ranges had stimulus values in common, the effect of range and location on exponents from those common values could be determined. Exponents decreased as stimulus range increased, but only in the free-modulus condition. For that condition, exponents derived from magnitude estimates of only the common stimuli also showed the range effect and response magnitude did not influence the range effect. Exponents were higher for stimulus ranges at the lower location, but location does not appear to contribute to the range effect. Although the range effect is not explained, the conditions under which it holds and some factors that may influence it are considered.     

Unmasking the magnitude estimation response

The fuzzy judgement model of Ward (1979) predicts an inverse relation between the amount of stimulus information available to subjects and the magnitude of sequential dependencies on previous stimuli and responses in psychophysical scaling tasks. Ward confirmed this prediction for magnitude estimations of interdot distance for previous responses but not for previous stimuli, although the inverse relation has been repeatedly reported for both the previous stimuli and responses in absolute identification (e.g., Mori, 1989). This paper further explores this seemingly puzzling contradiction. A magnitude estimation of loudness experiment was conducted in which the amount of stimulus information available to subjects was manipulated by a modified version of informational masking (Watson, 1987). An absolute-identification-with-feedback experiment was also conducted to check the effectiveness of the informational masking in reducing the amount of stimulus information. The results of the magnitude estimation experiment show a striking similarity with those of Ward and generalize the failure of sequential dependencies on previous stimuli to vary inversely with stimulus information. An additional assumption that judgement strategies are altered under low-information conditions is necessary to explain this result.     

SCALES OF UNPLEASANTNESS OF ELECTRICAL STIMULATION

The subjective unpleasantness elicited by an A.C. current of 50 c/sec. applied to two fingers was scaled by 14 subjects using the methods of magnitude and of category estimation. Nine current intensities, ranging between 2 and 10 times the individual sensation thresholds, were used as stimuli. A power function yielded a good fit to the magnitude-estimation data; the exponent was 1.81. The difference between this value and a considerably higher exponent reported by previous investigators was interpreted in terms of the wider stimulus range used in the present study. The relation between the category scale and the magnitude scale had the same general form as that found in several previous investigations.     

Apparent haptic movement

When Os were presented with ISO-Hz vibrotactile bursts at two loci on the skin of the thigh and permitted to adjust the time between burst onsets, they reported good apparent movement between the loci. The time between stimulus onsets for optimal movement was found to vary directly with the duration of the stimulus. Replication of the experiment with electrocutaneous stimuli at 1 KHz yielded similar results. Comparison of the data with results from a study of visual apparent movement revealed no difference between the two modalities for the relationship between stimulus onset intervals and stimulus duration. The significance of the results for hypotheses about the processes underlying perception of apparent movement is discussed.     

Response probability and response latency to threshold electrocutaneous stimuli

A comparison was made between two measures of somatosensory sensitivity, response probability, and reaction time to electrocutaneous constant current pulses of 350-microsec duration. The psychometric functions are steeper than those obtained for other sensory modalities. Similarly, the reaction-time/intensity functions are also steeper than those obtained in other modalities, i.e., larger decreases in reaction time as a function of small increases in stimulus intensity. Ss exposed to a broad stimulus range, including high intensities, yield psychometric and reaction time functions displaced into a higher intensity region than when they are exposed to a narrow low-intensity range of stimuli. The data are discussed in terms of a decision-theory model of reaction time.     

Integration of noxious stimulation across separate somatosensory communications systems: a functional theory of pain

Functional measurement analyses and psychophysical techniques were used to assess how separate, cross-modal, aversive events are integrated in judgements of pain. Subjects made magnitude estimations of noxious stimuli produced by a 6 X 6 factorial design of electric shocks and loud tones. Group data and most of the individual results were consistent with a model of linear pain summation: The estimates of pain approximated the linear sum of the pain estimates of the individual electrocutaneous and auditory components. The relation between painful sensation and current intensity could be described by a mildly expansive power function with an exponent of about 1.1. Auditorily produced painful sensation related to sound pressure level by a mildly compressive power function with an exponent of about 0.90 as a representative figure. Results are interpreted in terms of a functional theory of pain. Noxious events are first transformed to psychological scale values via stimulus-specific psychophysical transfer functions. The outputs of these functions are then combined with other pain-related internal representations of either sensory or cognitive origin, according to simple algebraic models.     

Pervasiveness and magnitude of context effects: evidence for the relativity of absolute magnitude estimation

To test the assertion that absolute magnitude estimation serves to minimize context effects, two experiments were conducted in which area stimuli were judged under differing conditions. In Experiment 1, four groups of subjects made magnitude estimations of triangles ranging in area from 1.5 to 3,072 cm2. No standard or modulus was used, and instructions were similar to those used in absolute magnitude estimation experiments. Each group first judged a different subrange of the stimuli (1.5-24; 48-768; 6-96; or 192-3,072 cm2) before making judgments of the remaining stimuli. In Experiment 2, two groups of subjects made magnitude estimations of triangles ranging in area from 1.5 to 12,288 cm2, with each group first judging a different subrange of stimuli (1.5-24 cm2 or 768-12,288 cm2). The design and instructions were virtually identical to those used in absolute magnitude estimation experiments. Our results indicate that the wording of the instructions is not crucial and that judgments are influenced in two ways that are not predicted by proponents of absolute magnitude estimation. First, the power functions fit to the initially presented subranges (e.g., 1.5-24 cm2), which were judged without contextual effects produced by previously presented stimuli, were inconsistent with one another. Second, judgments of the remaining stimuli were influenced by the subrange of stimuli judged initially. The prevalence of context effects in both experiments, in spite of instructional differences, suggests that although one should avoid using a standard and modulus, there is little else to be gained by adopting the absolute magnitude estimation procedure.     

Intensity resolution and subjective magnitude in psychophysical scaling

Several successful theories of psychophysical judgment imply that exponents of power functions in scaling tasks should covary with measures of intensity resolution such asd’ in the same tasks, whereas the prevailing metatheory of ideal psychophysical scaling asserts the independence of the two. In a direct test of this relationship, three prominent psychophysical scaling paradigms were studied: category judgment without an identification function, absolute magnitude estimation, and cross-modality matching with light intensity as the response continuum. Separate groups of subjects for each scaling paradigm made repeated judgments of the loudnesses of the pure tones that constituted each of two stimulus ensembles. The narrow- and wide-range ensembles shared six identical stimulus intensities in the middle of each set. Intensity resolution, as measured byd’-like distances, of these physically identical stimuli was significantly worse for the wide-range set for all three methods. Exponents of power functions fitted to geometric mean responses, and in magnitude estimation and cross-modality matching the geometric mean responses themselves, were also significantly smaller in the wide-range condition. The variation of power function exponents, and of psychophysical scale values, for stimulus intensities that were identical in the two stimulus sets with the intensities of other members of the ensembles is inconsistent with the metatheory on which modern psychophysical scaling practice is based, although it is consistent with other useful approaches to measurement of psychological magnitudes.     

Apparent haptic movement

When as were presented with 150-Hz vibrotactile bursts at two loci on the skin of the thigh and permitted to adjust the time between burst onsets, they reported good apparent movement between the loci. The time between stimulus onsets for optimal movement was found to vary directly with the duration of the stimulus. Replication of the experiment with electrocutaneous stimuli at 1 KHz yielded similar results. Comparison of the data with results from a study of visual apparent movement revealed no difference between the two modalities for the relationship between stimulus onset intervals and stimulus duration. The significance of the results for hypotheses about the processes underlying perception of apparent movement is discussed.     

Individual pitch functions and pitch-duration cross-dimensional matching

Eight young adult subjects scaled the auditory dimensions of duration and pitch using a modified method of numerical magnitude balance and adjustment of the stimuli for individual equal-loudness differences. Individual duration and pitch functions for magnitude estimation and for magnitude production fit the power law well. When compared with the revised reel scale and the pitch function obtained by S. S. Stevens and Galanter (Journal of Experimental psychology, 1957,54, 377–411), the group magnitude estimation and magnitude production pitch functions plotted in log-log coordinates showed high degrees of linearity. This was due mostly to the absence of a rollover in the high-frequency range of the continuum. It was hypothesized that pitch may be viewed as a linear function. This hypothesis was further supported when the exponents of the pitch and duration functions were used to predict closely the group exponent of cross-dimension matches.