Two- versus three-alternative concurrent-chain schedules: a test of three models

Two experiments with pigeons used concurrent-chain procedures with variable-interval schedules as initial links and different delays to food as terminal links. Two schedules were present in all sessions, but a 3rd schedule was alternately present and absent in successive sessions. When the 3rd schedule delivered food with no terminal-link delay, the presence of this schedule led to an increase in preference for the schedule with the shorter terminal link of the 2 unchanged schedules. When the terminal-link delay for the 3rd schedule was 30 s, the presence of this schedule led to a decrease in preference for the schedule with the shorter terminal link of the 2 unchanged schedules. These results are inconsistent with the predictions of R. Grace's (1994) contextual-choice model, but they are consistent with 2 other mathematical models--delay-reduction theory and the hyperbolic value-added model.     

Two-alternative learning situations with partial reinforcement

The comparative effects of reward and nonreward on learning are considered in connection with a two-alternative learning situation. Conditions are more general in nature than those discussed in an earlier article. In the statistical model proposed, the question of whether reward and nonreward are equivalent in their effects on learning reduces to testing a composite hypothesis on a multivariate probability distribution. An asymptotic test of this hypothesis is described, and its use is illustrated with data from psychological experiments.This paper was prepared with the partial support of the Office of Naval Research, and may be reproduced in whole or in part for any purpose of the United States government.I wish to express my gratitude to Professors J. Neyman and E. L. Scott of the University of California, Department of Statistics, for their constant assistance and encouragement throughout the research that led to this paper and during its preparation, and to Professor F. W. Irwin of the University of Pennsylvania Department of Psychology for his many helpful suggestions and comments.     

Information matrix estimation procedures for cognitive diagnostic models

Two new methods to estimate the asymptotic covariance matrix for marginal maximum likelihood estimation of cognitive diagnosis models (CDMs), the inverse of the observed information matrix and the sandwich-type estimator, are introduced. Unlike several previous covariance matrix estimators, the new methods take into account both the item and structural parameters. The relationships between the observed information matrix, the empirical cross-product information matrix, the sandwich-type covariance matrix and the two approaches proposed by de la Torre (2009, J. Educ. Behav. Stat., 34, 115) are discussed. Simulation results show that, for a correctly specified CDM and Q-matrix or with a slightly misspecified probability model, the observed information matrix and the sandwich-type covariance matrix exhibit good performance with respect to providing consistent standard errors of item parameter estimates. However, with substantial model misspecification only the sandwich-type covariance matrix exhibits robust performance.     

Adaptive threshold estimation with unforced-choice tasks

This paper evaluates an adaptive staircase procedure for threshold estimation that is suitable for unforced-choice tasks—ones with the additional response alternativedon’t know. Within the framework of a theory of indecision, evidence is developed that fluctuations of the response criterion are much less detrimental to unforced-choice tasks than to yes/no tasks. An adaptive staircase procedure for unforced-choice tasks is presented. Computer simulations show a slight gain in efficiency ifdon’t know responses are allowed, even if response criteria vary. A behavioral comparison with forcedchoice and yes/no procedures shows that the new procedure outdoes the other two with respect to reliability. This is especially true for naive participants. For well-trained participants it is also slightly more efficient than the forced-choice procedure, and it produces a smaller systematic error than the yes/no procedure. Moreover, informal observations suggest that participants are more comfortable with unforced tasks than with forced ones.     

Three-stimulus procedures in olfactory psychophysics: An experimental comparison of Thurstone-Ura and three-alternative forced-choice models of signal detection theory

The experimental differences between the triangular method and three-alternative forcedchoice (3-AFC) signal detection theory procedure are briefly reviewed, and the conditions to be met for a valid application of the respective procedures under the Thurstone-Ura and 3-AFC models are described. The assumptions of both of these unidimensional probabilistic models are given, and the functions relating the probability of a correct response to d, a parameter of sensory stimulus distance, are specified. Since the two models both contain d, the hypothesis of invariability of this parameter with the triangular method and the 3-AFC procedure was tested using olfactory stimuli. This hypothesis was strongly confirmed, since the functions relating d to the logarithm of the ratio of the physical stimulus values were virtually identical for the two methods and their concomitant models. The results are important not only for the field of olfactory psychophysics; they also have wider methodological and psychophysical interest. The bias against the middle stimulus of a triangle in the triangular method observed when olfactory stimuli are used can be explained as the resultant of sensory adaptation. Finally, some practical implications of the present results for application of the triangular method are discussed.     

Adaptive threshold estimation with unforced-choice tasks.

This paper evaluates an adaptive staircase procedure for threshold estimation that is suitable for unforced-choice tasks-ones with the additional response alternative don't know. Within the framework of a theory of indecision, evidence is developed that fluctuations of the response criterion are much less detrimental to unforced-choice tasks than to yes/no tasks. An adaptive staircase procedure for unforced-choice tasks is presented. Computer simulations show a slight gain in efficiency if don't know responses are allowed, even if response criteria vary. A behavioral comparison with forced-choice and yes/no procedures shows that the new procedure outdoes the other two with respect to reliability. This is especially true for naive participants. For well-trained participants it is also slightly more efficient than the forced-choice procedure, and it produces a smaller systematic error than the yes/no procedure. Moreover, informal observations suggest that participants are more comfortable with unforced tasks than with forced ones.     

Effects of the discriminability of alternatives in three-alternative concurrent-schedule performance

Six pigeons were trained on two- and three-alternative concurrent schedules in which the alternatives were signaled by different wavelengths of light on the main pecking key. The schedules were arranged according to a switching-key procedure in which pecks on a white side key produced a 3-s blackout and, intermittently, a change in the variable-interval schedule of food programmed on the main (center) key after the blackout. In Part 1, a two-alternative concurrent variable-interval schedule was arranged in which the alternatives were signaled by 560 nm and 630 nm. Parts 2 and 3 arranged three-alternative concurrent variable-interval schedules with the alternatives signaled by 560 nm, 600 nm, and 630 nm (Part 2) and 560 nm, 623 nm, and 630 nm (Part 3). Within each part, the relative rate of food reinforcers available on the alternatives was varied across a wide range. In all parts of the experiment, the ratios of responses emitted between pairs of alternatives were more extreme than the ratios of reinforcers obtained on the pairs of alternatives, a result termed overmatching. In Parts 2 and 3, generalized matching sensitivities between pairs of alternatives were found to be higher when the reinforcer rate on the third alternative was low than when it was high—an apparent failure of the constant-ratio rule. The data were well described by an extension of the Davison and Jenkins (1985) model, which assumes differing discriminabilities between concurrent-schedule alternatives in combination with a punishing effect of blackout following changeovers.     

An empirical comparison of several interval estimation procedures for coefficient alpha

Following a general introduction to Tukey's Jackknife technique and the construction of approximate confidence intervals, ten variants of the procedure are defined for giving interval estimates for coefficient alpha. A data base of known population characteristics was generated and used to compare the robustness of the ten Jackknife alternatives with Feldt's well-known sampling theory based upon the assumptions of normality. The empirical results indicate that out of the ten variants, defined by five transformations and two methods of data subdivision, only two are justifiable competitors to Feldt's approach.     

Hearing threshold shift during auditory magnitude estimation.

The purpose of the present experiment was to determine the extent of hearing threshold shift that may occur during an auditory magnitude-estimation task involving stimulus intensities as great as 80 dB sensation level. Also, possible influences of hearing threshold shift on numerical magnitude-estimation responses and magnitude-function slopes were investigated. Results indicated that hearing threshold shift was insignificant (1-2 dB). Consistent small increases in numerical magnitude responses were observed on a magnitude-estimation task where hearing thresholds were retested between stimulus presentations versus a magnitude-estimation task where hearing thresholds were not retested. The stability of auditory magnitude functions across different conditions in the current investigation was in agreement with vibrotactile magnitude-scaling behavior observed by Fucci, et al. in 1989 and 1991. The over-all results supported the concept of an absolute, internal sensory-scaling mechanism being operable during magnitude estimation of auditory stimuli as discussed by Zwislocki and Goodman in 1980.     

A review on equivalence-based procedures to teach food-portion estimation skills

This review involved a systematic analysis of equivalence-based instruction (EBI) that aimed to improve food-size interventions in diverse populations. Systematic searches identified seven studies published since 2010 that met inclusion criteria. These studies were analyzed according to their participants, design, setting, content taught, training structures, training protocol, testing format, treatment integrity, and outcomes. Results showed EBI procedures for teaching food estimation skills have been mostly implemented with adults. The type of content taught in the identified studies included carbohydrate ranges, portion size with food and non-food items, measuring cups and nutritional content of calories. Majority of included studies used one-to-many training structure and simultaneous protocols for teaching stimulus relations. Five studies completed a generalization probe and three studies reported treatment integrity data. Overall, all participants demonstrated skill acquisition of novel relations between food and portion measurement aides. Recommendations for future research and clinical applications of EBI in teaching food portion estimation are presented.     

On the psychophysical law and estimation procedures in psychophysical scaling

A general formulation of the power law is presented which has two special features: (1) negative exponents are admissible; and (2) the log law is a special limiting case. Estimation procedures, which provide joint estimates of the exponent and the absolute threshold, are derived for the direct ratio scaling methods. A solution is provided for theaveraging problem for ratio production and bisection scaling, two methods generating observations on the physical scale, and Monte Carlo methods are used to evaluate the resulting estimators.     

Discrete threshold versus continuous strength models of perceptual recognition.

Two experiments were designed to test discrete-threshold models of letter and word recognition against models that assume that decision criteria are applied to measures of continuous strength. Although our goal is to adjudicate this matter with respect to broad classes of models, some of the specific predictions for discrete-threshold are generated from Grainger and Jacobs' (1994) Dual-Readout Model (DROM) and some of the predictions for continuous strength are generated from a revised version of the Activation-Verification Model (Paap, Newsome, McDonald, & Schvaneveldt, 1982). Experiment 1 uses a two-alternative forced-choice task that is followed by an assessment of confidence and then a whole report if a word is recognized. Factors are manipulated to assess the presence or magnitude of a neighbourhood-frequency effect, a lexical-bias effect, a word-superiority effect, and a pseudoword advantage. Several discrepancies between DROM's predictions and the obtained data are noted. Both types of models were also used to predict the distribution of responses across the levels of confidence for each individual participant. The predictions based on continuous strength were superior. Experiment 2 used a same-different task and confidence ratings to enable the generation of receiver operating characteristics (ROCs). The shapes of the ROCs are more consistent with the continuous strength assumption than with a discrete threshold.     

Small-sample characterization of stochastic approximation staircases in forced-choice adaptive threshold estimation

Despite the widespread use of up-down staircases in adaptive threshold estimation, their efficiency and usability in forced-choice experiments has been recently debated. In this study, simulation techniques were used to determine the small-sample convergence properties of stochastic approximation (SA) staircases as a function of several experimental parameters. We found that satisfying some general requirements (use of the accelerated SA algorithm, clear suprathreshold initial stimulus intensity, large initial step size) the convergence was accurate independently of the spread of the underlying psychometric function. SA staircases were also reliable for targeting percent-correct levels far from the midpoint of the psychometric function and performed better than classical up-down staircases with fixed step size. These results prompt the utilization of SA staircases in practical forced-choice estimation of sensory thresholds.     

Constrained versus unconstrained estimation in structural equation modeling

Recently, R. D. Stoel, F. G. Garre, C. Dolan, and G. van den Wittenboer (2006) reviewed approaches for obtaining reference mixture distributions for difference tests when a parameter is on the boundary. The authors of the present study argue that this methodology is incomplete without a discussion of when the mixtures are needed and show that they only become relevant when constrained difference tests are conducted. Because constrained difference tests can hide important model misspecification, a reliable way to assess global model fit under constrained estimation would be needed. Examination of the options for assessing model fit under constrained estimation reveals that no perfect solutions exist, although the conditional approach of releasing a degree of freedom for each active constraint appears to be the most methodologically sound one. The authors discuss pros and cons of constrained and unconstrained estimation and their implementation in 5 popular structural equation modeling packages and argue that unconstrained estimation is a simpler method that is also more informative about sources of misfit. In practice, researchers will have trouble conducting constrained difference tests appropriately, as this requires a commitment to ignore Heywood cases. Consequently, mixture distributions for difference tests are rarely appropriate.