Testing a stochastic foraging model in an operant simulation: Agreement with qualitative but not quantitative predictions

An operant simulation of foraging through baited and empty patches was studied with 4 pigeons. On a three-key panel, side keys were designated as patches, and successive opportunities to complete 16 fixed-ratio 10 schedules on side keys were defined as encounters with feeders. In a random half of the patches in any session, some of the fixed-ratio 10 schedules yielded reinforcement (baited feeders) and the other schedules yielded nonreinforcement (empty feeders). In the other half of the patches, all feeders were empty. Pigeons could travel between patches at any time by completing a fixed-ratio schedule on the center key. An optimal foraging model was tested in Experiments 1 and 2 by varying center-key travel time and number of baited feeders in baited patches. The ordinal predictions that number of feeders visited in empty patches would increase with travel time and decrease as number of baited feeders increased were supported, but pigeons visited far more feeders in empty patches than the optimal number predicted by the model to maximize energy/time. In Experiment 3, evidence was found to suggest that the number of empty feeders encountered before the first baited feeder in baited patches is an important factor controlling leaving empty patches.     

On the sampling theory roundations of item response theory models

Item response theory (IT) models are now in common use for the analysis of dichotomous item responses. This paper examines the sampling theory foundations for statistical inference in these models. The discussion includes: some history on the stochastic subject versus the random sampling interpretations of the probability in IRT models; the relationship between three versions of maximum likelihood estimation for IRT models; estimating versus estimating -predictors; IRT models and loglinear models; the identifiability of IRT models; and the role of robustness and Bayesian statistics from the sampling theory perspective.A presidential address can serve many different functions. This one is a report of investigations I started at least ten years ago to understand what IRT was all about. It is a decidedly one-sided view, but I hope it stimulates controversy and further research. I have profited from discussions of this material with many people including: Brian Junker, Charles Lewis, Nicholas Longford, Robert Mislevy, Ivo Molenaar, Donald Rock, Donald Rubin, Lynne Steinberg, Martha Stocking, William Stout, Dorothy Thayer, David Thissen, Wim van der Linden, Howard Wainer, and Marilyn Wingersky. Of course, none of them is responsible for any errors or misstatements in this paper. The research was supported in part by the Cognitive Science Program, Office of Naval Research under Contract No. Nooo14-87-K-0730 and by the Program Statistics Research Project of Educational Testing Service.     

Stochastic ordering using the latent trait and the sum score in polytomous IRT models

In a restricted class of item response theory (IRT) models for polytomous items the unweighted total score has monotone likelihood ratio (MLR) in the latent trait. MLR implies two stochastic ordering (SO) properties, denoted SOM and SOL, which are both weaker than MLR, but very useful for measurement with IRT models. Therefore, these SO properties are investigated for a broader class of IRT models for which the MLR property does not hold.In this study, first a taxonomy is given for nonparametric and parametric models for polytomous items based on the hierarchical relationship between the models. Next, it is investigated which models have the MLR property and which have the SO properties. It is shown that all models in the taxonomy possess the SOM property. However, counterexamples illustrate that many models do not, in general, possess the even more useful SOL property.Hemker's research was supported by the Netherlands Research Council, Grant 575-67-034. Junker's research was supported in part by the National Institutes of Health, Grant CA54852, and by the National Science Foundation, Grant DMS-94.04438.     

Multivariate stochastic processes compatible with “aspect” models of similarity and choice

Various recent works have developed feature or aspect models of similarity and preference. These models are more concerned with the fine detail of the judgment process than were prior models, but nevertheless they have not in general developed an underlying stochastic process compatible with the assumed structure. In this paper, we show that a particular class of multivariate stochastic processes, namely those associated with the Marshall-Olkin multivariate exponential distribution, generates several of these models. In particular, such stochastic processes (appropriately interpreted) yield Tversky's elimination by aspects model, Edgell and Geisler's (normal) additive random aspects model, and Shepard and Arabie's additive cluster model.This work was supported by Natural Science and Engineering Research Council of Canada Grant A8124 to A.A.J. Marley.     

Language Processing Differences Between Blind and Sighted Individuals and the Abstract Versus Concrete Concept Difference

In the property listing task (PLT), participants are asked to list properties for a concept (e.g., for the concept dog, “barks,” and “is a pet” may be produced). In conceptual property norming (CPNs) studies, participants are asked to list properties for large sets of concepts. Here, we use a mathematical model of the property listing process to explore two longstanding issues: characterizing the difference between concrete and abstract concepts, and characterizing semantic knowledge in the blind versus sighted population. When we apply our mathematical model to a large CPN reporting properties listed by sighted and blind participants, the model uncovers significant differences between concrete and abstract concepts. Though we also find that blind individuals show many of the same processing differences between abstract and concrete concepts found in sighted individuals, our model shows that those differences are noticeably less pronounced than in sighted individuals. We discuss our results vis-a-vis theories attempting to characterize abstract concepts.     

Psychological distance as a means of evaluation

The psychological distance of objects (e.g., things, places, other people) affects how we think about them. Research suggests that psychological proximity and distance might be also related to positive and negative evaluations, respectively. In this study, we examined whether we can infer how children aged 13–16 years evaluate objects based on their statements regarding the psychological distance between themselves and these objects. Using a mixed-methods design, we verified the relationship between evaluations of objects and whether they are perceived as psychologically close or distant, in a sample of secondary school students. School subjects were predominantly used as evaluation objects. Students used a worksheet that allowed them to visually demonstrate perceived psychological distance between themselves and objects, and then they were asked to explain their choice. Results suggested a strong association between psychological distance and positive or negative evaluation. Thus, the implications of our findings may be relevant for psychodiagnostics.     

Crafting Mosaics: Person-Centered Religious Influence and Selection in Adolescent Friendships

This research addresses the intersection of two key domains of adolescents’ lives: religion and peer networks. Religion scholars argue that religion is multi-faceted and better understood by focusing on combinations of indicators (i.e., mosaics), versus a variable-centered approach. We adopt this framework and investigate the interplay between religion and peer networks, both in how religious mosaics are shaped by friends and how religious profiles affect friend selection dynamics. With data from two schools in the National Longitudinal Study of Adolescent Health, we estimate religious mosaics using latent class analysis (LCA) to identify profiles consisting of combinations of commonly available survey-based measures of religious attitudes, behaviors, and identities. Finding evidence of theoretically expected profiles, we then use stochastic actor–based models (SABMs) to investigate network dynamics for these LCA-based religious profiles. We demonstrate how the profile data can be integrated within the SABM framework to evaluate processes of friend selection and influence. Results show evidence of adolescents influencing one another's religious mosaics, but not selecting friends on that basis.     

The relevance of Rawls' principle of justice for research on cognitively impaired patients

An ethical conflict arises when we must performresearch in the interest of future patients,but that this may occasionally injure theinterests of today's patients.In the case of cognitively impaired persons, thequestion arises whether it is compatible withhumane healthcare not only to treat, but alsoto use these patients for research purposes.Some bioethicists and theologians haveformulated a general duty of solidarity, alsopertaining to cognitively impaired persons, as ajustification for research on these persons. Ifone examines this thesis from the theory ofjustice according to John Rawls, it is revealedthat such a duty of solidarity cannotnecessarily be extrapolated from Rawls'conception of justice. This is at least true ofRawls' difference principle, because accordingto the difference principle only those measuresare justifiable which serve the interest of therespective least well off. Those measures whichwould engender additional injury for the leastwell off could not be balanced by any utilityaccording to Rawls.However, John Rawls' difference principleis subordinate to the first principle,which is that each person has an equalright to the most extensive basic libertycompatible with the same liberty for others.These primary goods are determined by thefreedom and integrity of the person.This integrity of decisionally impaired personswould be in danger if one would abstain fromresearch and thus forego the increase inknowledge related to their disease. Thus onecould conclude, at least from Rawls' firstprinciple, that society must take on a duty toguarantee the degrees of freedom forcognitively impaired persons and thus alsosupport the efforts for their healing.     

Checking the Assumptions of Rasch's Model for Speed Tests

Two new tests for a model for the response times on pure speed tests by Rasch (1960) are proposed. The model is based on the assumption that the test response times are approximately gamma distributed, with known index parameters and unknown rate parameters. The rate parameters are decomposed in a subject ability parameter and a test difficulty parameter. By treating the ability as a gamma distributed random variable, maximum marginal likelihood (MML) estimators for the test difficulty parameters and the parameters of the ability distribution are easily derived. Also the model tests proposed here pertain to the framework of MML. Two tests or modification indices are proposed. The first one is focused on the assumption of local stochastic independence, the second one on the assumption of the test characteristic functions. The tests are based on Lagrange multiplier statistics, and can therefore be computed using the parameter estimates under the null model. Therefore, model violations for all items and pairs of items can be assessed as a by-product of one single estimation run. Power studies and applications to real data are included as numerical examples.