An essay on inequalities and order-restricted inference

This essay was prompted by a concern on the part of many senior members of the Society for Mathematical Psychology that the training of contemporary cognitive scientists exhibits a trend away from quantitative sophistication. Such a trend, if it goes unchallenged, can only serve to further marginalize mathematical psychology. There are several ways to combat this disturbing situation. Members of the Society might involve themselves more vigorously with scientific problems that are widely viewed as substantively or methodologically important, problems that require technical skill for their resolution; one example, discussed here, concerns order-restricted inference. We can also do more to encourage graduate students to develop and explore sophisticated theoretical models by giving them the tools to do so; that last battle must take place in the classroom.     

Bayesian Estimation of Circumplex Models Subject to Prior Theory Constraints and Scale-Usage Bias

This paper presents a hierarchical Bayes circumplex model for ordinal ratings data. The circumplex model was proposed to represent the circular ordering of items in psychological testing by imposing inequalities on the correlations of the items. We provide a specification of the circumplex, propose identifying constraints and conjugate priors for the angular parameters, and accommodate theory-driven constraints in the form of inequalities. We investigate the performance of the proposed MCMC algorithm and apply the model to the analysis of value priorities data obtained from a representative sample of Dutch citizens. We wish to thank Michael Browne and two anonymous reviewers for their comments. The data for this study were collected as part of the project AIR2-CT94-1066, sponsored by the European Commission.     

Bounds on variances of estimators for multinomial processing tree models

When there are order constraints among the parameters of a binary, multinomial processing tree (MPT) model, methods have been developed for reparameterizing the constrained MPT into an equivalent unconstrained MPT. This note provides a theorem that is useful in computing bounds on the estimator variances for the parameters of the constrained model in terms of estimator variances of the parameters of the unconstrained model. In particular, we show that if X and Y are random variables taking values in [0,1], then Var[XY]?2(Var[X]+Var[Y]).     

When is search for meaning in life beneficial for well-being? A cross-national study

Previous research has found cross-national variations in the association between search for meaning in life (SMIL) and well-being (i.e. SMIL–WB link). This study extended and tested a “self-improvement hypothesis” that accounts for such cross-national variations based on an international database—the sixth wave of World Values Survey. SMIL represents a self-improvement effort which is more demanded in contexts with stronger external constraints. Thus, we expected a stronger positive SMIL–WB link in such contexts. A series of multilevel analyses was used to verify this hypothesis. The results showed that the SMIL–WB link varied across different societies, with well-being indexed by happiness, life satisfaction and subjective health. Moreover, external constraints from cultural, social-institutional, economic and ecological contexts (collectivism, peace threats, economic scarcity and environmental threats) moderated the SMIL–WB links. We thus call for advancing SMIL theory by considering person–context interaction.     

A non-linear utility theory with multiple objectives

The aim of this paper is to make optimum several objectives at the same time which would enable a measurement of utility for several possible alternatives. The problem is solved if a strong or weak dominance exists between the alternatives, otherwise a set of incomparable alternatives would be present. Therefore, indifference curve analysis offers the outcome but as these indifference loci are difficult to determine only the characteristics of this analysis are maintained viz. decreasing marginal utility, non-linearity and even non-convexity. Indifference and reference point theory with the Minkowski min–max-metric only respond to these characteristics. Also the problem of generating alternatives during the process is taken into consideration. © 1998 John Wiley & Sons, Ltd.     

Constraints for Input/Output Logics

In a previous paper we developed a general theory of input/output logics. These are operations resembling inference, but where inputs need not be included among outputs, and outputs need not be reusable as inputs. In the present paper we study what happens when they are constrained to render output consistent with input. This is of interest for deontic logic, where it provides a manner of handling contrary-to-duty obligations. Our procedure is to constrain the set of generators of the input/output system, considering only the maximal subsets that do not yield output conflicting with a given input. When inputs are authorised to reappear as outputs, both maxichoice revision in the sense of Alchourrón/Makinson and the default logic of Poole emerge as special cases, and there is a close relation with Reiter default logic. However, our focus is on the general case where inputs need not be outputs. We show in what contexts the consistency of input with output may be reduced to its consistency with a truth-functional combination of components of generators, and under what conditions constrained output may be obtained by a derivation that is constrained at every step.     

Erroneous choice and foregone gains in hoarding gray jays (Perisoreus canadensis)

Under the conventional assumption that natural selection favors choice behavior that maximizes some fitness-related currency, a forager making repeated binary choices should consistently choose the more valuable option. Under the alternative assumption that natural selection favors choice behavior that minimizes costly errors, erroneous choice is not only expected but is expected to be common when the cost of errors is low. This cost depends on the potential rate of return: the higher this rate, the smaller the cost of choosing the less valuable option. When this rate is very high, a forager may err frequently and yet forego no appreciable fitness gain. Errors should thus be more common when interruptions to foraging are shorter. Our experimental results supported this prediction: gray jays chose the less valuable option more frequently when subjected to shorter interruptions (experimentally imposed delays to access to food rewards). This tendency is consistent with the idea that an adaptive decision-making process may routinely produce errors, not because errors are in some way adaptive but because their fitness cost is minimal, particularly when delays are short. From a proximate perspective, this tendency to commit errors more frequently following shorter delays may be due to constraints on the jays’ information-processing capacity. In general, choice behavior should be viewed as the joint byproduct of adaptive decision making and cognitive constraints. Received: 8 June 2000 / Accepted after revision: 21 October 2000