Loglinear Rasch model tests

Existing statistical tests for the fit of the Rasch model have been criticized, because they are only sensitive to specific violations of its assumptions. Contingency table methods using loglinear models have been used to test various psychometric models. In this paper, the assumptions of the Rasch model are discussed and the Rasch model is reformulated as a quasi-independence model. The model is a quasi-loglinear model for the incomplete subgroup × score × item 1 × item 2 × ... × itemk contingency table. Using ordinary contingency table methods the Rasch model can be tested generally or against less restrictive quasi-loglinear models to investigate specific violations of its assumptions.     

Quasi-dynamic choice models: Melioration and ratio invariance

There is continuing controversy about the behavioral process or processes that underlie the major regularities of free-operant choice such as molar matching and systematic deviations therefrom. A recent interchange between Vaughan and Silberberg and Ziriax concerned the relative merits of melioration, and a computer simulation of molecular maximizing. There are difficulties in evaluating theories expressed as computer programs because many arbitrary decisions must often be made in order to get the programs to operate. I therefore propose an alternative form of model that I term quasi-dynamic as a useful intermediate form of theory appropriate to our current state of knowledge about free-operant choice. Quasi-dynamic models resemble the game-theoretic analyses now commonplace in biology in that they can predict stable and unstable equilibria but not dynamic properties such as learning curves. It is possible to interpret melioration as a quasi-dynamic model. An alternative quasi-dynamic model for probabilistic choice, ratio invariance, has been proposed by Horner and Staddon. The present paper compares the predictions of melioration and ratio invariance for five experimental situations: concurrent variable-interval variable-interval schedules, concurrent variable-interval variable-ratio schedules, the two-armed bandit (concurrent random-ratio schedules), and two types of frequency-dependent schedule. Neither approach easily explains all the data, but ratio invariance seems to provide a better picture of pigeons' response to probabilistic choice procedures. Ratio invariance is also more adaptive (less susceptible to “traps”) and closer to the original expression of the law of effect than pure hill-climbing processes such as momentary maximizing and melioration, although such processes may come in to play on more complex procedures that provide opportunities for temporal discrimination.     

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.     

Tail-measurability in monotone latent variable models

We consider latent variable models for an infinite sequence (or universe) of manifest (observable) variables that may be discrete, continuous or some combination of these. The main theorem is a general characterization by empirical conditions of when it is possible to construct latent variable models that satisfy unidimensionality, monotonicity, conditional independence, andtail-measurability. Tail-measurability means that the latent variable can be estimated consistently from the sequence of manifest variables even though an arbitrary finite subsequence has been removed. The characterizing,necessary and sufficient, conditions that the manifest variables must satisfy for these models are conditional association and vanishing conditional dependence (as one conditions upon successively more other manifest variables). Our main theorem considerably generalizes and sharpens earlier results of Ellis and van den Wollenberg (1993), Holland and Rosenbaum (1986), and Junker (1993). It is also related to the work of Stout (1990).The main theorem is preceded by many results for latent variable modelsin general—not necessarily unidimensional and monotone. They pertain to the uniqueness of latent variables and are connected with the conditional independence theorem of Suppes and Zanotti (1981). We discuss new definitions of the concepts of true-score and subpopulation, which generalize these notions from the stochastic subject, random sampling, and domain sampling formulations of latent variable models (e.g., Holland, 1990; Lord & Novick, 1968). These definitions do not require the a priori specification of a latent variable model.The authors made equivalent contributions to the results of this article. Ellis' research was supported by the Dutch Interuniversitary Graduate School of Psychometrics and Sociometrics. Junker's research was supported by ONR Grant N00014-87-K-0277, NIMH Grant MH15758, and a Carnegie Mellon University Faculty Development Grant. In addition Junker would like to acknowledge the hospitality of the Nijmegen Institute for Cognition and Information during his visit to the University of Nijmegen in August 5–10, 1993.     

A note on the use of rank-ordered logit models for ordered response categories

Models for rankings have been shown to produce more efficient estimators than comparable models for first/top choices. The discussions and applications of these models typically only consider unordered alternatives. But these models can be usefully adapted to the case where a respondent ranks a set of ordered alternatives that are ordered response categories. This paper proposes eliciting a rank order that is consistent with the ordering of the response categories, and then modelling the observed rankings using a variant of the rank ordered logit model where the distribution of rankings has been truncated to the set of admissible rankings. This results in lower standard errors in comparison to when only a single top category is selected by the respondents. And the restrictions on the set of admissible rankings reduces the number of decisions needed to be made by respondents in comparison to ranking a set of unordered alternatives. Simulation studies and application examples featuring models based on a stereotype regression model and a rating scale item response model are provided to demonstrate the utility of this approach.     

Optimal selection of E‐learning websites using multiattribute decision‐making approaches

A computational quantitative model based on weighted Euclidean distance‐based approximation and complex proportional assessment has been developed for the evaluation, selection, and ranking of various E‐learning websites in ascending or descending order based on their Euclidean distance value from the optimal website. The E‐learning website with rank 1 is considered the optimal selection on the particular dataset under consideration. The problem of the E‐learning website Selection, Evaluation and Ranking is modeled as a multiattribute decision‐making problem in which various interrelated attributes collectively termed as ranking criteria are identified to make the evaluation of available alternatives. In this research, 5 most popular E‐learning websites related to the C programming language for the software development have been considered to show the utility of developed model. Further, the concept of methodology validation strengthens this research by comparing the obtained results with the existing multiattribute decision‐making approach as analytical hierarchy process method.     

Reactions to Different Types of Forced Distribution Performance Evaluation Systems

Purpose  We isolate and describe four key elements that distinguish different forms of forced distribution systems (FDS). These key elements are the consequences for low performers, differentiation of rewards for top performers, frequency of feedback, and comparison group size. We examine how these elements influence respondents’ attraction to FDS. Design/methodology/approach  Undergraduate students (n = 163) completed a policy capturing study designed to determine how these four FDS elements influence their attraction to FDS. We examine the relative importance of these elements that most influence attraction to different FDS, as well as individual attributes (i.e., cognitive ability, gender, and major) that may affect those preferences. Findings  Respondents were most attracted to systems with less stringent treatment of low performers, high differentiation of rewards, frequent feedback and large comparison groups. Consequences for low performers were nearly twice as influential as any other element. Respondents with higher cognitive ability favored high reward differentiation and males were less affected by stringent consequences for low performers. Implications  Before practitioners implement FDS, it would be prudent to consider all four elements examined in this study—with the treatment of low performers being the most salient issue. Future accounts of FDS should clarify the nature of these elements when reporting on FDS. Such precision will be useful in generating a knowledge base on FDS. Originality/value   We add precision to the discussion of FDS by identifying four key elements. This is one of the first studies to examine perceptions of FDS from a ratee perspective.

EMERGENCE OF TACTS FOLLOWING MAND TRAINING IN YOUNG CHILDREN WITH AUTISM

This study sought to examine the effects of training mands on the emergence of tacts with the same response forms. Results indicated that training adjective sets as mands resulted in the emergence of adjective sets as tacts under modified, but not standard, antecedent conditions. The findings suggested that the apparent functional independence of mands and tacts may be explained by a lack of appropriate antecedent control over responding.