Joint consistency of nonparametric item characteristic curve and ability estimation

The simultaneous and nonparametric estimation of latent abilities and item characteristic curves is considered. The asymptotic properties of ordinal ability estimation and kernel smoothed nonparametric item characteristic curve estimation are investigated under very general assumptions on the underlying item response theory model as both the test length and the sample size increase. A large deviation probability inequality is stated for ordinal ability estimation. The mean squared error of kernel smoothed item characteristic curve estimates is studied and a strong consistency result is obtained showing that the worst case error in the item characteristic curve estimates over all items and ability levels converges to zero with probability equal to one.     

Best linear prediction of composite universe scores

The problem of predicting universe scores for samples of examinees based on their responses to samples of items is treated. A general measurement procedure is described in which multiple test forms are developed from a table of specifications and each form is administered to a different sample of examinees. The measurement model categorizes items according to the cells of such a table, and the linear function derived for minimizing error variance in prediction uses responses to these categories. In addition, some distinctions are drawn between aspects of the approach taken here and the familiar regressed score estimates.The author thanks Robert L. Brennan, Michael J. Kolen, and Richard Sawyer for helpful comments and corrections, and anonymous reviewers for suggested improvements.     

Fast acquisition of cooperation and trust: A two-stage view of trusting behavior

Trustful behavior was defined in terms of the consecutive numbers of matching-to-sample problems worth money that each subject worked during sessions that ended in an equitable distribution. Two stages of acquisition are inherent in this definition; the first stage requires acquisition of an equitable method of distributing reinforcers (cooperation) to show that the within-session deviations (trust) from equity that develop during the second stage are temporary and are not part of an inequitable method of distributing reinforcers. Previous research has indicated that a contingency to trust is necessary to override the aversiveness of the inequity inherent in trusting and to produce consistent and maximal trust (half of the problems worked consecutively by each subject). The present experiment examined such a contingency. The trust contingency was an increased requirement for changing the direction of problem allocation. Only the subject who had been allocated a problem could change that allocation, by pulling a lever 45 or more times. On the other hand, no separate responses were required to allow the person who worked the last problem to also work the next one (passive trust). Hence, giving a problem was the only way to increase the distribution of problems to the other person and hence prevent oneself from receiving all of the reinforcers. All eight pairs of subjects cooperated from the outset. Trusting behavior developed for all four pairs exposed to the contingency to trust and expanded to maximal levels by the second session for three of the four pairs.     

Sample-specific ratio effects in matching to sample

In a symbolic matching-to-sample task, pigeons were trained using sample-specific, fixed-ratio “observing responses.” Subsequently, in a mixed condition, each sample was presented equally often with each ratio requirement, i.e., the ratios were no longer correlated with the samples. In a second experiment, pigeons were trained initially in the mixed condition and subsequently shifted to the sample-specific condition in which the required ratios were correlated with the samples. Results of both experiments suggested joint control of choices by ratio value and by the exteroceptive stimuli. The discriminative properties of the ratios appeared to outweigh absolute ratio-size effects.     

A COMPARISON OF INDIRECT MEASURES FOR LONG-DURATION BEHAVIORS1

A computer program was developed to simulate long-duration behavior. The program generated data by using two time-series models linked together by a covariance parameter. By varying the parameters of the program, the characteristics of the simulated behavior were altered, including the mean and variance of the durations of behavior, the mean and variance of the interresponse time, and the degree of relationship within and between durations of behavior and interresponse times. Four data-collection methods were applied to the simulated data: whole interval, partial interval, momentary time-sampling, and continuous measures. The accuracies of the first three recording measures were judged by comparing them to the continuous measure. The results indicated that only the momentary time-sampling approach yielded unbiased results. The degree of bias for the whole and partial interval measures was a function of the ratio of the interval recording length to the sum of the mean duration of behavior and the mean interresponse time. Unfortunately, it was concluded that researchers cannot estimate the magnitudes of these latter two parameters for most behaviors of interest and, consequently, are unable to choose an appropriate interval length. Therefore, it was recommended that the use of interval recording approaches be greatly restricted and that momentary time-sampling be substituted where possible.     

Same/different concept learning in the pigeon: the effect of negative instances and prior adaptation to transfer stimuli

Pigeons were trained on a matching-to-sample or oddity-from-sample task with shapes (circle and plus). Half of each group was exposed to “negative instance” trials i.e., for matching birds, neither comparison key matched the sample, and for oddity birds both comparison keys matched the sample. When all birds were transferred to a new task involving colors (red and green), nonshifted birds (transferred from matching to matching, or oddity to oddity) performed significantly better than shifted birds (transferred from matching to oddity, or oddity to matching), but only if they had experienced negative instances of the training concept. When all birds were exposed to negative instances of the transfer task and then transferred to a new color task (yellow and blue), dramatic transfer effects were observed. The effect of pre-exposure to the yellow and blue colors, in order to reduce transfer-stimulus novelty, had a minor effect on transfer.     

Scale freeness in factor analysis

The notion of scale freeness does not seem to have been well understood in the factor analytic literature. It has been believed that if the loss function that is minimized to obtain estimates of the parameters in the factor model is scale invariant, then the estimates are scale free. It is shown that scale invariance of the loss function is neither a necessary nor a sufficient condition for scale freeness. A theorem that ensures scale freeness in the orthogonal factor model is given in this paper.The authors are grateful for the suggestions of the referees.     

Pigeons' spatial memory: factors affecting delayed matching of key location.

The delayed-matching-to-sample procedure was modified to study pigeons' spatial memory. Nine pecking keys, arranged as a three-by-three matrix, served as the spatial cues. Trials began with a brief "ready" stimulus (dimming of the houselight). Then a randomly chosen key was lit briefly as a sample. After a short delay the sample key was lit again along with one of the other eight keys. A peck at the key that had served as the sample produced grain reinforcement, where as a peck to the other key produced only the intertrial interval. After delayed matching of key location was learned, the effects of sample and delay duration, number of keys illuminated as sample and comparisons, and organization of three-key samples were studied. Matching accuracy decreased as sample duration decreased, delay increased, the number of locations serving as samples increased, the number and proximity of comparisons increased, and when the three-key samples were "discontinuous" rather than "lines".     

A search for symmetry in the conditional discriminations of rhesus monkeys, baboons, and children.

Procedures for generating arbitrary matching-to-sample performances may generate only conditional discriminations. Rational grounds for this distinction are proposed, based on the properties that any equivalence relation must possess. Empirical tests are described for determining whether subjects trained on conditional discriminations are also engaged in true matching to sample. A series of studies than leads to the conclusion that proof of true matching to sample by monkeys, pigeons, or baboons is yet to be provided. Whether the absence of such proof reflects experiential factors or species-defined limitations is not presently clear.     

Psychophysics of remembering

We present a new model of remembering in the context of conditional discrimination. For procedures such as delayed matching to sample, the effect of the sample stimuli at the time of remembering is represented by a pair of Thurstonian (normal) distributions of effective stimulus values. The critical assumption of the model is that, based on prior experience, each effective stimulus value is associated with a ratio of reinforcers obtained for previous correct choices of the comparison stimuli. That ratio determines the choice that is made on the basis of the matching law. The standard deviations of the distributions are assumed to increase with increasing retention-interval duration, and the distance between their means is assumed to be a function of other factors that influence overall difficulty of the discrimination. It is a behavioral model in that choice is determined by its reinforcement history. The model predicts that the biasing effects of the reinforcer differential increase with decreasing discriminability and with increasing retention-interval duration. Data from several conditions using a delayed matching-to-sample procedure with pigeons support the predictions.