Oral drug self-administration in rhesus monkeys: interactions between drug amount and fixed-ratio size.

During daily 3-hr sessions, 5 rhesus monkeys drank drug solutions and water that were concurrently available. The drug solutions were: 1 milligram per milliliter (mg/mL) pentobarbital (2 monkeys), 1 mg/mL pentobarbital plus 0.5% ethanol (1 monkey), 1 mg/mL pentobarbital plus 1% ethanol (1 monkey), and 8% ethanol (1 monkey). The drug solution and water were available under identical two-component tandem fixed-ratio continuous-reinforcement N schedules. Two variables were manipulated: the size of the fixed-ratio component and the number of liquid deliveries (N) in the second component. Deliveries of the drug solution maintained higher rates of responding than did deliveries of the drug vehicle, water. The number of drug deliveries per session increased with increases in the number of deliveries per fixed ratio and decreased with increases in fixed-ratio size. Analysis of the results in terms of the proportion of deliveries to responses showed that the number of drug deliveries per session was directly related to the size of this quotient. Finally, when fixed-ratio size was repeatedly doubled, the following orderly relationship emerged: The greater the number of available drug deliveries per fixed ratio, the less was the percent decrease in the number of fixed ratios completed per session. It was concluded that increases in the number of liquid deliveries per fixed ratio resulted in increases in reinforcing efficacy.     

Bayesian estimation in the three-parameter logistic model

A joint Bayesian estimation procedure for the estimation of parameters in the three-parameter logistic model is developed in this paper. Procedures for specifying prior beliefs for the parameters are given. It is shown through simulation studies that the Bayesian procedure (i) ensures that the estimates stay in the parameter space, and (ii) produces better estimates than the joint maximum likelihood procedure as judged by such criteria as mean squared differences between estimates and true values. The research reported here was performed pursuant to Grant No. N0014-79-C-0039 with the Office of Naval Research. A related article by Robert J. Mislevy (1986) appeared when the present paper was in the printing stage.     

Sizing Things Up: Colloquial Reflection as Practical Wisdom

This essay reintroduces Rhetoric as the principle art for giving emphasis and importance to contested matters; in other words, for making things matter. In a speculative reading of the Aristotelian rhetorical tradition, Aristotle's interpretations of magnitude, contengency and practical wisdom are critically examined from both an aesthetic and an ethical-political point of view. The concluding discussion attempts to apply these same concepts to a growing dilemma in the present age. The dilemma is that monumental changes in scale have all but eroded the prospects for engaged encounters with contemporary contingency. It remains the challenge of rhetorical practice to reframe actions and events so that they and we may hold some hope for an engaged civic life.     

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.     

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).     

Scaling pigeons' choice of feeds: bigger is better.

Preferences of hungry pigeons among 10 grains and pellets were analyzed using a Thurstone scaling procedure. The recovered scales were positively correlated with size of the feed. The correlations improved when the Thurstonian assumption of equal-sized discriminal dispersions (Case V) was replaced with the assumption of proportional-sized dispersions (Case VI), as entailed by Weber's law. The correlations weakened when the experiments were conducted with the pigeons close to their free-feeding weights, where the probability of sampling alternative grains increased. In the final experiment, exposure to a large pellet shifted the preferences between two smaller pellets.     

The effect of uncertainty of item parameter estimation on ability estimates

The conventional method of measuring ability, which is based on items with assumed true parameter values obtained from a pretest, is compared to a Bayesian method that deals with the uncertainties of such items. Computational expressions are presented for approximating the posterior mean and variance of ability under the three-parameter logistic (3PL) model. A 1987 American College Testing Program (ACT) math test is used to demonstrate that the standard practice of using maximum likelihood or empirical Bayes techniques may seriously underestimate the uncertainty in estimated ability when the pretest sample is only moderately large.This work was partially supported under contract No. N00014-85-K-0113, NR150-535, from the Cognitive Science Program, Office of Naval Research. The authors wish to thank Mark D. Reckase for providing the ACT data used in the illustration and two referees, Asociate Editor and Editor for helpful suggestions.