Subjective probability and delay.

Human subjects indicated their preference between a hypothetical $1,000 reward available with various probabilities or delays and a certain reward of variable amount available immediately. The function relating the amount of the certain-immediate reward subjectively equivalent to the delayed $1,000 reward had the same general shape (hyperbolic) as the function found by Mazur (1987) to describe pigeons' delay discounting. The function relating the certain-immediate amount of money subjectively equivalent to the probabilistic $1,000 reward was also hyperbolic, provided that the stated probability was transformed to odds against winning. In a second experiment, when human subjects chose between a delayed $1,000 reward and a probabilistic $1,000 reward, delay was proportional to the same odds-against transformation of the probability to which it was subjectively equivalent.     

A stochastic multidimensional scaling procedure for the empirical determination of convex indifference curves for preference/choice analysis

The vast majority of existing multidimensional scaling (MDS) procedures devised for the analysis of paired comparison preference/choice judgments are typically based on either scalar product (i.e., vector) or unfolding (i.e., ideal-point) models. Such methods tend to ignore many of the essential components of microeconomic theory including convex indifference curves, constrained utility maximization, demand functions, et cetera. This paper presents a new stochastic MDS procedure called MICROSCALE that attempts to operationalize many of these traditional microeconomic concepts. First, we briefly review several existing MDS models that operate on paired comparisons data, noting the particular nature of the utility functions implied by each class of models. These utility assumptions are then directly contrasted to those of microeconomic theory. The new maximum likelihood based procedure, MICROSCALE, is presented, as well as the technical details of the estimation procedure. The results of a Monte Carlo analysis investigating the performance of the algorithm as a number of model, data, and error factors are experimentally manipulated are provided. Finally, an illustration in consumer psychology concerning a convenience sample of thirty consumers providing paired comparisons judgments for some fourteen brands of over-the-counter analgesics is discussed.     

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.     

Pierre de La Ramée et le déclin de la rhétorique

This article provides a basic general introduction to Ramus, and evaluates his role in the history of logic and rhetoric, especially with relation to the study of argumentation. The author agrees with Ong and other historians of logic that Ramus is not to be taken seriously as a logician, and that his undoubted importance in the history of ideas is to be found elsewhere.Ramus advocates a belief in nature, experience and reason, and rejects the reliance on the authority of ancient philosophers, above all Aristotle, though experience does not mean scientific experiment and, paradoxically, includes the example of great philosophers and writers. In the end Ramus is seen as responsible for substituting for ancient classical rhetoric an entirely ornamental rhetoric of figures which was to take over education (with the exception of the Jesuit schools) almost until our own day. This curtailing and diminishing of rhetoric is seen as a degeneration. Ancient five-part rhetoric had been concerned with convincing and persuading: Aristotle distinguished the analytic, scientific reasoning of logic, from dialectic which was based on opinion and probability and had close links with rhetoric; by the time of Cicero and Quintilian, who addressed themselves to jurists and politicians, logic has given way to dialectic. In the Middle Ages and the Renaissance the two become assimilated; the evolution of this is traced here through the thirteenth-century Summulae logicales of Peter of Spain to the fifteenth-century German humanist logician Rudolph Agricola, who influenced Ramus partly through the intermediary of Johann Sturm. Ramus took over their topical theories but restricted them to logic/dialectic, and left rhetoric with little more than tropes and figures. He believed that there was only one method for teaching all the arts, and one dialectic common to them all. The distinction between analytical and dialectical has disappeared, with far-reaching consequences for the study of argumentation. Over the centuries logic has lost its connection with controversy and persuasion. With the development of the post-Cartesian, post-Baconian emphasis on the clarity of scientific discourse, and the mid-nineteenth-century interest in mathematical and formal logic, the process was complete. Argumentation, or the new rhetoric, aims to fill the gap thus created.

     

Confidence depends on level of aggregation

The credible intervals that people set around their point estimates are typically too narrow (cf. Lichtenstein, Fischhoff, & Phillips, 1982). That is, a set of many such intervals does not contain the actual values of the criterion variables as often as it should given the probability assigned to this event for each estimate. The typical interpretation of such data is that people are overconfident about the accuracy of their judgments. This paper presents data from two studies showing the typical levels of overconfidence for individual estimates of unknown quantities. However, data from the same subjects on a different measure of confidence for the same items, their own global assessment for the set of multiple estimates as a whole, showed significantly lower levels of confidence and overconfidence than their average individual assessment for items in the set. It is argued that the event and global assessments of judgment quality are fundamentally different and are affected by unique psychological processes. Finally, we discuss the implications of a difference between confidence in single and multiple estimates for confidence research and theory.     

Changes in a multiple-response repertoire during response-contingent punishment and response restriction: Sequential relationships

A multiple-response baseline of four activities was established using gerbils as subjects. When one of the baseline responses was punished (Experiment 1) or restricted (Experiments 2 and 3), only the most probable of the alternative baseline responses increased. The response most likely to follow the punished or restricted responses during baseline sessions was also suppressed during subsequent punishment or response-restriction treatment.     

Correlation and prediction in ordinal test theory

Based on the test theory model for ordinal measurements proposed by Schulman and Haden, the present paper considers correlations between tests, attenuation, regressions involving true and observed scores, and prediction of test reliability.The population correlation between tests is shown to be related to the expected sample correlation for samples of sizen ₁ andn ₂. Errors of estimation, measurement and prediction are found to be similar to their counterparts in interval test theory, while attenuation is identical to its counterpart. The bias in estimating population reliability from sample data is compared for Kendall's tau and Spearman's rho.The author wishes to thank the referees for their helpful comments on an earlier draft of this paper, and in particular, for the suggested alternative methods of establishing some of the presented results.     

The impacts of ignoring individual mobility across clusters in estimating a piecewise growth model

A three-level piecewise growth model (3L-PGM) can be used to break up nonlinear growth into multiple components, providing the opportunity to examine potential sources of variation in individual and contextual growth within different segments of the model. The conventional 3L-PGM assumes that the data are strictly hierarchical in nature, where measurement occasions (level 1) are nested within individuals (level 2) who are members of a single cluster (level 3). However, in longitudinal research, it is sometimes difficult for data structures to remain purely clustered during a study, such as when some students change classrooms or schools over time. One resulting data structure in this situation is known as a multiple membership structure, where some lower-level units are members of more than one higher-level unit. The new multiple membership PGM (MM-PGM) extends the 3L-PGM to handle multiple membership data structures frequently found in the social sciences. This study sought to examine the consequences of ignoring individual mobility across clusters when estimating a 3L-PGM in comparison to estimating a MM-PGM. MM-PGM estimates were less biased (especially in the cluster-level coefficient estimates), although we found substantial bias in cluster-level variance components across some conditions for both models.     

Stopping rules for multi-category computerized classification testing

Computerized classification testing (CCT) aims to classify persons into one of two or more possible categories to make decisions such as mastery/non-mastery or meet most/meet all/exceed. A defining feature of CCT is its stopping criterion: the test terminates when there is enough confidence to make a decision. There is abundant research on CCT with a single cut-off, and two common stopping criteria are the sequential probability ratio test (SPRT) statistic and the generalized likelihood ratio statistic (GLR). However, there is a relative scarcity of research extending the SPRT to the multi-hypothesis case for when there is more than one cut-off. In this paper, we propose a new multi-category GLR (mGLR) statistic as well as a stochastically curtailed version of the CCT with three or more categories. A simulation study was conducted to show that the mGLR statistic outperformed the existing stopping rules by generating shorter average test length without sacrificing classification accuracy. Results also revealed that the stochastically curtailed mGLR successfully increased test efficiency in certain testing conditions.     

Cognitive control models of multiple access IoT networks using LoRa technology

In this paper,we propose a random-access model for describing several wireless communication technologies. These networks have found application in the construction of wireless sensor networks, and the proposed model can be used for flows with different properties, considering the corresponding distribution functions. The model considers the technical features of the LoRa technology and subscriber traffic. We also address the management of random multiple wireless access in a Software-Defined Networking (SDN) like control architectures, and proposing a model for flows with different properties, considering the corresponding distribution functions. We develop a method for optimizing the parameters of an access network by the probability of data delivery. Then we describe the probability of bit error, frame loss, collision, and the choice of network parameters considering the heterogeneity of conditions for different users. Numerical results show the efficiency of our proposed scheme by maintaining the required network parameters in case of its function conditions changing.