Observed-score equating as a test assembly problem

A set of linear conditions on item response functions is derived that guarantees identical observed-score distributions on two test forms. The conditions can be added as constraints to a linear programming model for test assembly that assembles a new test form to have an observed-score distribution optimally equated to the distribution on an old form. For a well-designed item pool and items fitting the IRT model, use of the model results into observed-score pre-equating and prevents the necessity ofpost hoc equating by a conventional observed-score equating method. An empirical example illustrates the use of the model for an item pool from the Law School Admission Test.The authors are most indebted to Norman D. Verhelst for suggesting Proposition 4 and its proof, to the Law School Admission Council (LSAC) for making available the data set, and to Wim M. M. Tielen for his computational assistance.     

D-optimal design for the Rasch counts model with multiple binary predictors

In this paper we derive optimal designs for the Rasch Poisson counts model and its extended version of the (generalized) negative binomial counts model incorporating several binary predictors for the difficulty parameter. To efficiently estimate the regression coefficients of the predictors, locally D-optimal designs are developed. After an introduction to the Rasch Poisson counts model and its extension, we will specify these models as particular generalized linear models. Based on this embedding, optimal designs for both models including several binary explanatory variables will be presented. Therefore, we will derive conditions on the effect sizes for certain designs to be locally D-optimal. Finally, it is pointed out that the results derived for the Rasch Poisson models can be applied for more general Poisson regression models which should receive more attention in future psychological research.     

On what we can ensure

The Conjunction Principle says, roughly, that if the truth of a conjunction can be brought about, then the truth of each conjunct can be brought about. The current essay argues that this principle is not valid. After a clarification of the principle, it is shown how a proper understanding of the involved notions falsify the principle. As a corollary, a recent attack on van Inwagen’s Consequence Argument will be rebutted, because it relies on the invalid conjunction principle.     

The Post-Movement Beta Rebound and Motor-Related Mu Suppression in Children

Abstract

Age-related EEG activity change is a prominent feature that reflects the functional development of the brain. The current study investigated the beta and mu rhythms of 16 children (7.7 ± 1.5 years, 5 to 9.6 years) and 13 adults when a self-determining arm motion was performed. The results indicated that mu power was decreased during movement and returned to baseline level after the movement for both children and adults. However, although a decrease in beta power was observed for both children and adults during movement, the post-movement beta power rebound (PMBR) was observed in adults but not in children. These results suggest that motor-related mu suppression develops early in children; PMBR develops later and may be associated with a more prolonged motor development process.     

A latent trait theory via a stochastic learning theory for a knowledge space

To capture the cognitive organization of a set of questions or problems pertaining to a body of information, Doignon and Falmagne have proposed, and analyzed in a number of papers, the concept of aknowledge space, that is, a distinguished collection of subsets of questions, representing the possibleknowledge states. This collection of sets is assumed to satisfy a number of conditions. Since this concept is a deterministic one, the problem of empirical testing arises. A stochastic version of a knowledge space is developed in this paper, in which the knowledge states are considered as possible epochs in a subject's learning history. The knowledge space is decomposed as a union of a number of possible learning paths, calledgradations. The model specifies how a subject is channelled through and progresses along a gradation. A probabilistic axiom of the local indepencence type relates the knowledge states to the observable responses. The predictions of this model are worked out in details in the case of parametric assumptions involving gamma distributions. An application of the model to artificial data is described, based on maximum likelihood methods. The statistical analysis is shown to be capable of revealing the combinatoric core of the model.This work was supported by NSF grant IST-8418860 and ARI grant DAAG29-84-G-0083 to New York University. I am grateful to Jean-Paul Doignon, Mathieu Koppen, Geoff Iverson and Michael Landy for their reactions to previous drafts of this paper, to Michael Villano for carrying out the computer simulation and the analysis of the simulated data, and especially to one referee for his very useful comments.     

Note on two generalizations of coefficient alpha

An important relationship is given for two generalizations of coefficient alpha, Rajaratnam, Cronbach and Gleser's generalizability formula for stratified-parallel tests and Raju's coefficient beta.The author gratefully acknowledges the generous assistance given by reviewers and the editor.     

An INAR(1) negative multinomial regression model for longitudinal count data

This paper discusses a regression model for the analysis of longitudinal count data observed in a panel study. An integer-valued first-order autoregressive [INAR(1)] Poisson process is adapted to represent time-dependent correlations among the counts. By combining the INAR(1)-representation with a random effects approach, a new negative multinomial distribution is derived that includes the bivariate negative binomial distribution proposed by Edwards and Gurland (1961) and Subrahmaniam (1966) as a special case. A detailed analysis of the relationship between personality factors and daily emotion experiences illustrates the approach.This research was partially supported by NSF grant SBR-9409531. The author is grateful to Ulrich Schimmack and Ed Diener for providing the data set used in the application section and for helpful comments on this research.     

Latent change classes in dichotomous data

Changes in dichotomous data caused by treatments can be analyzed by means of the so-called linear logistic model with relaxed assumptions (LLRA). The LLRA does not require observable criteria representing a single underlying latent trait, but it postulates the generalizability of the treatment effects over criteria and subjects. To test this latter crucial assumption, the mixture LLRA was proposed that allows directly unobservable types of subjects to have different treatment effects. As the earlier methods for estimating the parameters of the mixture LLRA have specific drawbacks, a further method based on the conditional maximum likelihood principle will be presented here. In contrast to the earlier conditional methods, it uses all of the dichotomous change data while having fewer parameters. Further, its goodness-of-fit tests become more sensitive to a falsely specified number of change-types even though the treatment effects are biased. For typically occurring small to moderate sample sizes, however, parametric bootstrapping of the distributions of the fit statistics is recommended for performing hypotheses tests. Finally, three applications of the new method to empirical data are described: first, about the effect of the so-called Trager psychophysical integration, second, about the effect of autogenic therapy on patients with psychosomatic symptoms, and, third, about the effect of religious education on the attitude towards sects. The mixture LLRA is implemented in the menu-driven program MIXLLRA which can be obtained from Ivo Ponocny via e-mail (ivo.ponocny@univie.ac.at).     

Composition of brain oscillations and their functions in the maintenance of auditory,visual and audio–visual speech percepts: an exploratory study

In the present exploratory study based on 7 subjects, we examined the composition of magnetoencephalographic (MEG) brain oscillations induced by the presentation of an auditory, visual, and audio-visual stimulus (a talking face) using an oddball paradigm. The composition of brain oscillations were assessed here by analyzing the probability-classification of short-term MEG spectral patterns. The probability index for particular brain oscillations being elicited was dependent on the type and the modality of the sensory percept. The maintenance of the integrated audio-visual percept was accompanied by the unique composition of distributed brain oscillations typical of auditory and visual modality, and the contribution of brain oscillations characteristic for visual modality was dominant. Oscillations around 20 Hz were characteristic for the maintenance of integrated audio-visual percept. Identifying the actual composition of brain oscillations allowed us (1) to distinguish two subjectively/consciously identical mental percepts, and (2) to characterize the types of brain functions involved in the maintenance of the multi-sensory percept.