Separating the effects of salience and disparity on the rate of observing

Pigeons producing deliveries of grain on a mixed variable-interval, extinction schedule by pecking a center key could also produce discriminative stimuli on concurrent variable-interval schedules by pecking the left or right observing key. The stimuli produced by each observing key were varied independently. In the first experiment, the negative discriminative stimulus was at the far end of the spectrum from the key illumination accompanying the mixed schedule and from the positive discriminative stimulus. When the magnitude of the difference between the latter two stimuli (salience) was varied, more pecks occurred on the observing key producing the larger of the two differences than on the key producing the smaller difference. In the second experiment, the stimulus accompanying the mixed schedule was at the far end of the spectrum, and the magnitude of the difference between the two discriminative stimuli (disparity) was varied. The proportion of pecks occurring on each observing key shifted systematically in the direction of the key producing the larger difference. The salience of the discriminative stimuli and their disparity each has an independent influence on the frequency of observing when the other is controlled, but the effect of the salience appears to be the more substantial.     

Undermatching on concurrent variable-interval schedules and the power law.

The phenomenon of undermatching on concurrent variable-interval schedules is shown to be derivable by transforming the individual interreinforcement intervals of each variable-interval schedule and averaging the transformed values to produce an "estimate" of the rate of reinforcement the schedules deliver. If the transformation is based on a power function with a fractional exponent, such as is found in many studies of temporal control in animals, matching response rations to the ratios of these estimated rates of reinforcement yields undermatching. If the concurrent variable-interval schedules are arranged such that the individual intervals in each schedule have a constant proportionality (a procedure found in many commonly used variable-interval schedules) the slope of the line relating logarithms of response ratios and of programmed reinforcement ratios is identical to the exponent of the power transformation applied to the individual time intervals in the variable-interval schedules. In other cases this simple relation does not hold but the degree of undermatching is greater the lower the value of the exponent of the power function. This account of undermatching predicts values similar to those typically observed.     

Constrained multidimensional scaling inN spaces

A gradient method is used to obtain least squares estimates of parameters of them-dimensional euclidean model simultaneously inN spaces, given the observation of all pairwise distances ofn stimuli for each space. The procedure can estimate an additive constant as well as stimulus projections and the metric of the reference axes of the configuration in each space. Each parameter in the model can be fixed to equal some a priori value, constrained to be equal to any other parameter, or free to take on any value in the parameter space. Two applications of the procedure are described.     

Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm

Maximum likelihood estimation of item parameters in the marginal distribution, integrating over the distribution of ability, becomes practical when computing procedures based on an EM algorithm are used. By characterizing the ability distribution empirically, arbitrary assumptions about its form are avoided. The Em procedure is shown to apply to general item-response models lacking simple sufficient statistics for ability. This includes models with more than one latent dimension.Supported in part by NSF grant BNS 7912417 to the University of Chicago and by SSRC (UK) grant HR6132 to the University of Lancaster.We are indebted to Mark Reiser and Robert Gibbons for computer programming. David Thissen clarified a number of points in an earlier draft.     

On the existence and uniqueness of maximum-likelihood estimates in the Rasch model

Necessary and sufficient conditions for the existence and uniqueness of a solution of the so-called unconditional (UML) and the conditional (CML) maximum-likelihood estimation equations in the dichotomous Rasch model are given. The basic critical condition is essentially the same for UML and CML estimation. For complete data matricesA, it is formulated both as a structural property ofA and in terms of the sufficient marginal sums. In case of incomplete data, the condition is equivalent to complete connectedness of a certain directed graph. It is shown how to apply the results in practical uses of the Rasch model.Paper read at the European Meeting of the Psychometric Society, Groningen, June 19–21, 1980.Part of the research reported herein was done while the author was staying at the Pulmologisches Zentrum der Stadt Wien; he is indebted to Professor Dr. F. Muhar and Dr. R. Mutschlechner for providing excellent working conditions.     

Antecedents to Fechner's law: the astronomers J. Herschel, W. R. Dawes, and N. R. Pogson

The history of the stellar magnitude scale is briefly traced from the second century b.c. until the middle of the nineteenth century. It becomes clear that astronomers formulated "Fechner's Law" by about 1850. While Fechner is credited with the grander view of things, the contention is made that the astronomers John Herschel, W. R. Dawes, and N. R. Pogson have not been given their due by historians of psychology.     

SCHEDULE-INDUCED DRINKING: ELICITATION,ANTICIPATION, OR BEHAVIORAL INTERACTION?

We carried out five experiments with rats on fixed-time schedules in order to define the relation between drinking and individual food-pellet presentations. In Experiment 1, unsignaled extra food occurred at the end of occasional fixed intervals, and we compared subsequent drinking patterns with drinking before the extra food presentation. In Experiment 2 we presented signaled and unsignaled extra food and measured elicited and anticipatory drinking patterns. In Experiment 3, we observed the persistence of modified drinking patterns when several consecutive intervals ended with extra pellets. In Experiments 4 and 5, we varied the magnitude of food delivery across (rather than within) sessions to replicate published findings. Results show that schedule-induced drinking is neither elicited by food presentations nor induced by stimuli associated with a high food rate. All subjects seemed to follow a simple rule: during any stimulus signaling an increase in the local probability of food delivery within a session, engage in food-related behavior to the exclusion of drinking. Schedule-induced drinking appears to be the result of dynamic interactions among food-related behavior, drinking, and other motivated behavior, rather than a direct effect of the contingencies of food reinforcement.     

A bayesian alternative to least squares and equal weighting coefficients in regression

This paper details a Bayesian alternative to the use of least squares and equal weighting coefficients in regression. An equal weight prior distribution for the linear regression parameters is described with regard to the conditional normal regression model, and resulting posterior distributions for these parameters are detailed. Some interesting connections between this Bayesian procedure and several other methods for estimating optimal weighting coefficients are discussed. In addition, results are presented of a Monte Carlo investigation which compared the effectiveness of the Bayesian procedure relative to least squares, equal weight, ridge, and Bayesian exchangeability estimations.     

Further evaluation of reinforcer magnitude effects in noncontingent schedules

We closely replicated the procedures of a previous study that showed a positive relationship between reinforcer magnitude and the response-rate-reducing effects of noncontingent schedules (NCS). NCS reduced response rates, as expected, but the NCS-magnitude effect was not reproduced, illuminating possible weaknesses of current arbitrary-response procedures and suggesting avenues for future research.     

Logit models and logistic regressions for social networks: III. Valued relations

This paper generalizes thep* model for dichotomous social network data (Wasserman & Pattison, 1996) to the polytomous case. The generalization is achieved by transforming valued social networks into three-way binary arrays. This data transformation requires a modification of the Hammersley-Clifford theorem that underpins thep* class of models. We demonstrate that, provided that certain (non-observed) data patterns are excluded from consideration, a suitable version of the theorem can be developed. We also show that the approach amounts to a model for multiple logits derived from a pseudo-likelihood function. Estimation within this model is analogous to the separate fitting of multinomial baseline logits, except that the Hammersley-Clifford theorem requires the equating of certain parameters across logits. The paper describes how to convert a valued network into a data array suitable for fitting the model and provides some illustrative empirical examples.This research was supported by grants from the Australian Research Council, the National Science Foundation (#SBR96-30754), and the National Institute of Health (#PHS-1RO1-39829-01).