Elimination of reinforced behavior: intermittent schedules of not-responding

Pigeons' key pecking resulted in food according to either a variable-ratio or a variable-interval schedule. At the same time, food was available for not pecking for a specified time. The required time of not-pecking was segmented into not-responding units, and these units were followed by food according to a fixed-ratio schedule. Both unit duration and the number required were varied. In general, the shorter the time unit or the smaller the ratio, the lower was response rate. When total required not-responding time was constant, but changes in unit duration and the number required altered how the total was achieved, shorter units produced lower rates. Other conditions involved substitution of food delivered independent of responding for the not-responding schedule. With low and moderate total times to food presentation, the not-responding schedule produced lower rates; with the longest times, the response-independent schedule generated less responding. When considered in terms of relative frequency of food presentation available from a source other than pecking, the not-responding schedule reduced rate more effectively than did the response-independent schedule. Comparisons with other research suggested that food presented dependent on not responding compared favorably with punishment as a procedure for reducing response rate. Transient effects differed. Although punishment temporarily depresses rate when first imposed and temporarily enhances it when first removed, food given for not responding quickly generated steady-state rates.     

Optimal test length for maximum battery validity

Having given a fixed amount of total testing time it is important to know how long each test in the battery should be so that the correlation of the battery with the criterion will be a maximum. The precise solution for the test lengths will depend on a particular set of conditions which may be specified. The writer has previously presented solutions for two sets of conditions. This article presents the solution for a third set of conditions. These are: (1) The total number of items or testing time is fixed. (2) The score is the total number of items correctly answered. (3) The test lengths are determined in such a way that the correlation of total score with the criterion is a maximum. The solutions for the two previous sets of conditions, together with the current set, are summarized. A set of experimental data is submitted to each solution and the three sets of results are compared.     

On the oblique rotation of a factor matrix to a specified pattern

This paper presents a procedure for rotating an arbitrary factor matrix to maximum similarity with a specified factor pattern. The sum of squared distances between specified vectors and rotated vectors in oblique Euclidian space is minimized. An example of the application of the procedure is given.This research was supported in part by the National Institute of Child Health and Human Development, Research Grant 1 PO1 HDO1762.The names of the authors are given in alphabetical order. Their contributions to the paper are equal.     

Conversion of a printing calculator to an inexpensive printing counter

A procedure is described for simple conversion of a printing calculator to an inexpensive printing counter. The unit is particularly useful for unattended data collection. A timing circuit controls printout of accumulated data at specified time intervals.     

Utilizing response times in cognitive diagnostic computerized adaptive testing under the higher-order deterministic input,noisy ‘and’ gate model

Methods of cognitive diagnostic computerized adaptive testing (CD-CAT) under higher-order cognitive diagnosis models have been developed to simultaneously provide estimates of the attribute mastery statuses of examinees for formative assessment and estimates of a latent continuous trait for overall summative evaluation. In a typical CD-CAT environment, examinees are often subject to a time limit, and the examinees’ response times (RTs) for specific test items can be routinely recorded by custom-made programs. Because examinees are individually administered tailored sets of test items from the item pool, they may experience different levels of speededness during testing and different levels of risk of running out of time. In this study, RTs were considered during the item-selection procedure to control the test speededness and the RTs were treated as useful information for improving latent trait estimation in CD-CAT under the higher-order deterministic input, noisy ‘and’ gate (DINA) model. A modified posterior-weighted Kullback–Leibler (PWKL) method that maximizes the item information per time unit and a shadow-test method that assembles a provisional test subject to a specified time constraint were developed. Two simulation studies were conducted to assess the effects of the proposed methods on the quality of CD-CAT for fixed- and variable-length exams. The results show that, compared with the traditional PWKL method, the proposed methods preserve a lower risk of running out of time while ensuring satisfactory attribute estimation and providing more accurate estimates of the latent trait and speed parameters. Finally, several suggestions for future research are proposed.     

Integration of motion parallax with binocular disparity specifying different surface shapes

We investigated the interaction between motion parallax and binocular disparity cues in the perception of surface shape and depth magnitude by the use of the random dot stimuli in which these cues specified sinusoidal depth surfaces undulating with different spatial frequencies. When ambiguous motion parallax is inconsistent with unambiguous disparity cue, the reasonable solution for the visual system is to convert the motion signal to the flow on the surface specified by disparity. Two experiments, however, found that the visual system did not always use this reasonable solution; observers often perceived the surface specified by a composite of the two cues, or the surface specified by parallax alone. In the perception of this composite of the two cues, the apparent depth magnitude increased with the increase of the depth magnitude specified by both cues. This indicates that the visual system can combine the depth magnitude information from parallax and disparity in an additive fashion. The interference with parallax by disparity implies that the parallax processing is not independent of the disparity processing.     

The classification of individuals into two criterion groups on the basis of a discontinuous payoff function

An analytic method is presented for optimally classifying individuals into two subgroups on the basis of a cutting score on a test or test composite. The development assumes the test and criterion scores to be normally distributed, and the correlation surface to be bivariate normal. It is further assumed that individuals belong to the first or second sub-group depending on whether their criterion score is above or below a specified value. The predictor cutting score is determined so as to maximize the expected value of the decision procedure, taking gains and losses associated with correct and incorrect assignments into account.The opinions expressed are those of the authors and do not necessarily reflect those of the Navy Department. This research was supported in part by a grant from the National Institute of Mental Health, MH 10449-01.     

Regression weights as a function of test length

A battery of pencil-and-paper tests is commonly used for predicting a single criterion. If the score on each test is the number of correct answers, the composite battery score would normally be the sum of the weighted test scores, where the weights are the raw score regression weights. Knowing the reliability of each test, it is possible to alter the lengths of the tests in a manner such that the weights will all be equal. The composite battery score would then simply be the total number of items answered correctly and scoring would be greatly simplified. Such simplification is particularly desirable where the volume of testing is large. Section I of the article outlines the procedure for altering the lengths of the tests, and Section II gives a proof of the method.     

Maximizing predictive efficiency for a fixed total testing time

For any fixed total time of testing it is possible, through proper item-and-time allotment, to combine tests into a battery so that the multiple correlation with a pre-assigned criterion will be maximized. By holding constant the ratio of the length in number of items to the time length for each test, a set of general equations has been derived which will yield this maximum value of the multipleR and will enable one to determine, in any given case, the optimal fraction of total testing time that should be devoted to each type of test under consideration. The set of general equations is applied to a two-test-battery problem to obtain the optimal length of each type of test for one hour total testing time. If two other tests had been selected for the two-test sample problem, different subdivisions of the total time would generally occur. The manner in which the results would change when using other tests with different initial reliability, validity, and intercorrelation values is briefly presented. Some general implications of this method of battery development are also discussed.The writer is indebted to Max Woodbury for his assistance and especially to Dr. N. J. F. Van Steenberg and Dr. Anna S. Henriques, who provided valuable guidance and aid in the development of the solution to this problem. This paper is a revision of a thesis submitted in 1939 at the University of Utah in partial fulfillment of the requirements for the master's degree.     

A feasible method for standard errors of estimate in maximum likelihood factor analysis

A jackknife-like procedure is developed for producing standard errors of estimate in maximum likelihood factor analysis. Unlike earlier methods based on information theory, the procedure developed is computationally feasible on larger problems. Unlike earlier methods based on the jackknife, the present procedure is not plagued by the factor alignment problem, the Heywood case problem, or the necessity to jackknife by groups. Standard errors may be produced for rotated and unrotated loading estimates using either orthogonal or oblique rotation as well as for estimates of unique factor variances and common factor correlations. The total cost for larger problems is a small multiple of the square of the number of variables times the number of observations used in the analysis. Examples are given to demonstrate the feasibility of the method.The research done by R. I. Jennrich was supported in part by NSF Grant MCS 77-02121. The research done by D. B. Clarkson was supported in part by NSERC Grant A3109.     

An IBM method for computing intraserial correlations

A method for computing intraserial correlations using a 602-A Calculating Punch, an 077 Collator, a 513 Gang Punch, and a 403 Tabulator is described. An example of the use of the procedure and an estimate of the time needed with each machine are given. This procedure is compared with another method, which makes use of a more powerful IBM machine.This research was supported in part by the United States Air Force under Contract No. AF 33(038)-25726, monitored by the Air Force Personnel and Training Research Center. Permission is granted for reproduction, translation, publication, use and disposal in whole and in part by or for the United States Government.     

The KIM-1 microcomputer as an eight-channel data logger

A machine language program and interface hardware to operate the KIM-1 microcomputer as an eight-channel data logger are described. All channels can operate simultaneously, and the data are stored in a specified area of memory. Double precision is used, enabling numbers greater than 255 to be recorded. Data can be collected over sampling intervals of 1 to 255 times 5 sec or 1 to 255 times 10 min. The time base is derived from 50- or 60-Hz mains ac. A method of transferring the data to a PET microcomputer and storing it on eight separate tape or disk files is also given.     

Proportion of general factor variance in a hierarchical multiple‐component measuring instrument: A note on a confidence interval estimation procedure

A confidence interval construction procedure for the proportion of explained variance by a hierarchical, general factor in a multi‐component measuring instrument is outlined. The method provides point and interval estimates for the proportion of total scale score variance that is accounted for by the general factor, which could be viewed as common to all components. The approach may also be used for testing composite (one‐tailed) or simple hypotheses about this proportion, and is illustrated with a pair of examples.     

The order-restricted association model: Two estimation algorithms and issues in testing

This paper presents a row-column (RC) association model in which the estimated row and column scores are forced to be in agreement with an a priori specified ordering. Two efficient algorithms for finding the order-restricted maximum likelihood (ML) estimates are proposed and their reliability under different degrees of association is investigated by a simulation study. We propose testing order-restricted RC models using a parametric bootstrap procedure, which turns out to yield reliablep values, except for situations in which the association between the two variables is very weak. The use of order-restricted RC models is illustrated by means of an empirical example. Francisca Galindo performed this research as a part of her PhD. dissertation project at Tilburg University.     

Human movement initiation: specification of arm, direction, and extent

This article presents a method for discovering how the defining values of forthcoming body movements are specified. In experiments using this movement precuing technique, information is given about some, none, or all of the defining values of a movement that will be required when a reaction signal is presented. It is assumed that the reaction time (RT) reflects the time to specify those values that were not precued. With RTs for the same movements in different precue conditions, it is possible to make detailed inferences about the value specification process for each of the movements under study. The present experiments were concerned with the specification of the arm, direction, and extent (or distance) of aimed hand movements. In Experiment 1 it appeared that (a) specification times during RTs were longest for arm, shorter for direction, and shortest for extent, and (b) these values were specified serially but not in an invariant order. Experiment 2 suggested that the precuing effects obtained in Experiment 1 were not attributable to stimulus identification. Experiment 3 suggested that subjects in Experiment 1 did not use precues to prepare sets of possible movements from which the required movement was later selected. The model of value specification supported by the data is consistant with a distinctive-feature view, rather than a hierarchical view, of motor programming.     

Examining change in maximal reliability for multiple‐component measuring instruments

A method for examining change in maximal reliability for pre‐specified sets of congeneric measures when developing a multi‐component instrument is outlined. The approach is applicable for purposes of estimation and testing of gain or loss in the maximal reliability coefficient as a consequence of adding or dropping one or more measures from a homogeneous composite with uncorrelated errors, as well as when one is concerned with optimal component choice for highest increase or correspondingly smallest drop in maximal reliability. The method is compared with a procedure for ascertaining change in unweighted sum score reliability, and implications for instrument construction and revision are discussed. The approach is illustrated with a numerical example.     

Convergence properties of an iterative procedure of ipsatizing and standardizing a data matrix,with applications to parafac/candecomp preprocessing

Centering a matrix row-wise and rescaling it column-wise to a unit sum of squares requires an iterative procedure. It is shown that this procedure converges to a stable solution. This solution need not be centered row-wise if the limiting point of the interations is a matrix of rank one. The results of the present paper bear directly on several types of preprocessing methods in Parafac/Candecomp.     

A specific calculating ability

We report two experiments that investigate the calculating strategy used by a low IQ savant to identify prime numbers. Hermelin and O'Connor (1990) had suggested previously that this subject may use a procedure first described by Eratosthenes to detect a prime number, namely, dividing a target number by all primes up to the square root of the target number and testing for a remainder. In the first experiment, we compare the reaction times of the savant to decide whether a number is prime with those of a control subject proficient in mathematical calculation. In addition, we measured the savant's speed of information processing using an inspection time task. We found that the reaction times of the savant, although generally faster, followed the same pattern of the control subject who reported using the Eratosthenes procedure. The savant's inspection time indicated that his speed of processing was far superior to that expected from someone of his IQ. In the second experiment, we measured the time it takes mathematics students to divide by different prime numbers and we also tested them on the prime identification task. We used their division times to simulate their performance on the prime number identification task under the assumption that they used the Eratosthenes procedure. We also simulated the reaction times that would result from a simple memory-based procedure for identifying primes. We found that the Eratosthenes simulation, in contrast to the memory simulation, provided a good fit to both the students' and the savant's reaction times. We conclude that the savant is using a complex computational algorithm to identify primes and suggest two explanations of how the apparent contradiction between his low general intelligence and his superior numerical ability might be resolved.     

Implementation of experimental procedures in the PACER system of on-line control

PACER comprises an Executive and associated routines that together provide the run-time facilities commonly needed by experiment control programs. Although the implementation is specific to a particular PDP-11 installation, the nature of the support provided is of more general interest. Simple experimental procedures are straightforwardly handled by direct program control of timing and of external apparatus, and by direct inspection of the states of input lines connected to such apparatus. For more complicated situations, where events may not occur in a strict sequence, it becomes more convenient to make use of priority interrupts to inititiate response to events. Tasks to be performed under interrupt control are coded by the user as special subroutines known as “Actions.” It is a feature of PACER that the user can arrange for the Executive to run Actions automatically at specified times. The main program is then able to carry out processing that it would not be able to undertake if it had to make repeated checks on the time.     

An efficient procedure for selecting equal probability samples

FORTRAN code that implements an algorithm for selecting equal probability samples is given. The procedure is brief and decides to include or not include a record as it is called. Consequently, storage requirements are minimal. The procedure gives the exact number of values specified, with each record in the population having an equal probability for inclusion in the sample, including the last.