Reliability of multiple classifications

Cohen's kappa index is reformulated for multiple classifications based on exchangeable random variables. It is found that kappa is between 0 and 1 inclusive. Two characterizations for kappa are stated in terms of the relationship between such random variables. Within the normal test score model, kappa increases with test reliability and test length. Furthermore, when based on binary classifications, kappa is an inverse U-shaped function of the cutoff score. These trends also hold for the beta-binomial test score model.Paper read at the Spring meeting of the Psychometric Society, Bell Laboratories (Murray Hill, New Jersey), March 1976.The editorial assistance and helpful comments of Leonard S. Feldt, Sarah P. Seaman-Huynh, and the three referees are gratefully acknowledged.     

On the discriminability of stimulus duration.

The performance of pigeons trained to detect differences in the duration of stimuli was analysed using a matching model of signal detection. Two white stimuli, S1 and S2, differing in duration, were arranged with equal probability on the center key of a three-key chamber. S1 was systematically varied from 5 seconds to 25 seconds while S2 remained constant at 30 seconds. On completion of the center-key stimulus, a peck on the center key turned on the two red side keys. A left-key response was "correct" when S1 had been in effect on the center key and a right-key response was "correct" on S2 trials. A correct response produced a 3-second magazine light accompanied intermittently by food. Incorrect responses produced 3-second blackouts. Detection performance was measured under two procedures. In the first, the obtained reinforcement ratio was uncontrolled by allowing the number of food reinforcements obtained for correct left- and right-key responses to vary as the stimuli were changed. In the second procedure, the presentation of food reinforcement was controlled by holding the obtained reinforcement ratio constant. Discriminability changed as a function of stimulus differences under both procedures. No such trend was found in response bias.     

Effect of delay-interval stimuli on delayed symbolic matching to sample in the pigeon

In Experiment 1, food-deprived pigeons received delayed symbolic matching to sample training in a darkened Skinner box. Trials began with the illumination of the grain feeder lamp (no food sample), or illumination of this lamp, accompanied by the raising of the feeder tray (food sample). After a delay of a few seconds, the two side response keys were illuminated, one with red and one with green light, with positions counterbalanced over trials. Pecking the red (green) comparison produced grain reinforcement if the trial had started with food (no food); pecking red after a no-food sample or green after a food sample was not reinforced. Once matching performance was stable, four stimuli were presented during the delay interval, and their effects on matching accuracy were evaluated. Both illumination of the houselight and the center key with white geometric forms decreased matching accuracy, whereas presentation of a tone and vibration of the test chamber did not. In Experiment 2, pecking the red center key was reinforced with food according to a variable interval schedule. The effects of occasional brief presentations of the four stimuli used in the first experiment on ongoing pecking were assessed. The houselight and form disturbed key pecking, but the tone and vibration did not. Thus, stimuli that interfered with delayed matching also interfered with simple operant behavior. Implications of these results for theories of remembering are discussed.     

Stimulus control of respondent and operant key pecking: A single key procedure

Pigeons' responses to a uniformly illuminated response key were either reinforced on a variable-interval one-minute schedule of reinforcement or extinguished for one-minute periods. When 1.5 second signals were presented at the beginning of each component, so as to differentially predict reinforcement, the pigeons pecked at the signals, at rates higher than rates during the remainder of the component. When the brief signals were not differentially predictive of reinforcement, pecking in their presence decreased to near zero levels. Similar results were obtained with signals based upon colors and upon line orientations. Changes in rates of (unreinforced) pecking occurred during the signal whether pigeons responded differentially during the remainder of the component or not. Experiment II demonstrated that the presence of the signal correlated with extinction was not necessary for pecking to develop at the signal which preceded the component in which responding was intermittently reinforced. The experiments demonstrated a clear dissociation of respondent control from operant control of a response. In addition, operant behavior was shown to be relatively insensitive to differing rates of reinforcement, as compared to the sensitivity of respondent behavior to differing rates of reinforcement produced by the very same operant behavior.     

The effects of modifying consummatory behavior on the topography of the autoshaped pecking response in pigeons

The autoshaped responses of two debeaked pigeons that had developed modified eating behavior were compared to the autoshaped responses of three control subjects that ate grain normally. The control subjects exhibited keylight responding that was judged normal by two independent raters. The debeaked subjects pecked the key and ate grain with both normal and modified responses. The results of this study demostrate that an autoshaping procedure using grain as an appetitive stimulus may be used to establish a response that is not biologically preorganized.     

DINING OUT WITH CHILDREN: EFFECTIVENESS OF A PARENT ADVICE PACKAGE ON PRE-MEAL INAPPROPRIATE BEHAVIOR

The effectiveness of an advice package designed to restructure the restaurant environment and encourage parent praise was examined. Experiment 1 assessed the usefulness of the package when used with experimenter assistance. Videotapes were used to record the target child's behavior. Pre-meal inappropriate behavior decreased an average of 51% across target children. Mealtime inappropriate behavior and parent praise and disapproval were also measured. Experiment 2 was designed to determine whether families could implement the package without experimenter assistance and whether effects obtained would generalize to a different restaurant. Data were taken in vivo. Nine families were randomly assigned to one of three groups. Group assignment determined the order in which families went to two restaurants, the number of dinners each family participated in, and the point at which parents received the advice package. The order in which the families went to the two restaurants as well as the number of baseline meals was counterbalanced. Results of Experiment 2 showed that, when using the advice package, parents in all sequences were able to decrease pre-meal inappropriate behavior of their children, and that these effects generalized to a second restaurant.     

The development of derived stimulus relations through training in arbitrary-matching sequences

Five-year-old children were taught three-stage sequences of arbitrary matching: A-C, B-C, A-D; A-C, B-D, B-C; or A-C, A-D, B-C. Each stage refers to a sample-comparison relation between stimuli. Unreinforced test probes revealed untrained arbitrary matches (B-D, A-D, and B-D, respectively), derivable by substitution of stimuli with a common sample or comparison function. Additional probes revealed further untrained sample-comparison relations derivable by substitution and identity, including the commuted relations D-B, D-A, and D-B, respectively. These processes may have relevance to conceptual and verbal behavior.     

The interaction between stimulus and reinforcer control on remembering.

In a symbolic matching-to-sample task, 6 pigeons obtained food by pecking a red side key when the brighter of two white lights had been presented on the center key and by pecking a green side key when the dimmer of two white lights had been presented on the center key. Across Part 1 and Parts 6 to 10, the delay between sample-stimulus presentation and the availability of the choice keys was varied between 0 s and 25 s. Across Parts 1 to 5, the delay between the emission of a correct choice and the delivery of a reinforcer was varied between 0 s and 30 s. Although increasing both types of delay decreased stimulus discriminability, lengthening the stimulus-choice delay produced a greater decrement in choice accuracy than did lengthening the choice-reinforcer delay. Additionally, the relative reinforcer rate for correct choice was varied across both types of delay. The sensitivity of behavior to the distribution of reinforcers decreased as discriminability decreased under both procedures. These data are consistent with the view, based on the generalized matching law, that sample stimuli and reinforcers interact in their control over remembering.     

Essential independence and likelihood-based ability estimation for polytomous items

A definition ofessential independence is proposed for sequences of polytomous items. For items satisfying the reasonable assumption that the expected amount of credit awarded increases with examinee ability, we develop a theory ofessential unidimensionality which closely parallels that of Stout. Essentially unidimensional item sequences can be shown to have a unique (up to change-of-scale) dominant underlying trait, which can be consistently estimated by a monotone transformation of the sum of the item scores. In more general polytomous-response latent trait models (with or without ordered responses), anM-estimator based upon maximum likelihood may be shown to be consistent for under essentially unidimensional violations of local independence and a variety of monotonicity/identifiability conditions. A rigorous proof of this fact is given, and the standard error of the estimator is explored. These results suggest that ability estimation methods that rely on the summation form of the log likelihood under local independence should generally be robust under essential independence, but standard errors may vary greatly from what is usually expected, depending on the degree of departure from local independence. An index of departure from local independence is also proposed.This work was supported in part by Office of Naval Research Grant N00014-87-K-0277 and National Science Foundation Grant NSF-DMS-88-02556. The author is grateful to William F. Stout for many helpful comments, and to an anonymous reviewer for raising the questions addressed in section 2. A preliminary version of section 6 appeared in the author's Ph.D. thesis.