The Dutch Identity: A new tool for the study of item response models

The Dutch Identity is a useful way to reexpress the basic equations of item response models that relate the manifest probabilities to the item response functions (IRFs) and the latent trait distribution. The identity may be exploited in several ways. For example: (a) to suggest how item response models behave for large numbers of items—they are approximate submodels of second-order loglinear models for 2 ^J tables; (b) to suggest new ways to assess the dimensionality of the latent trait—principle components analysis of matrices composed of second-order interactions from loglinear models; (c) to give insight into the structure of latent class models; and (d) to illuminate the problem of identifying the IRFs and the latent trait distribution from sample data.This research was supported in part by contract number N00014-87-K-0730 from the Cognitive Science Program of the Office of Naval Research. I realized the usefulness of the identity in Theorem 1 while lecturing in the Netherlands during October, 1986. Because this was in no small part due to the stimulating psychometric atmosphere there, I call the result the Dutch Identity.     

Latent class models for nonmonotone dichotomous items

Starting from perfectly discriminating nonmonotone dichotomous items, a class of probabilistic models with or without response errors and with or without intrinsically unscalable respondents is described. All these models can be understood as simply restricted latent class analysis. Thus, the estimation and identifiability of the parameters (class sizes and item latent probabilities) as well as the chi-squared goodness-of-fit tests (Pearson and likelihood-ratio) are free of the problems. The applicability of the proposed variants of latent class models is demonstrated on real attitudinal data.This research was supported by the Kulturamt der Stadt Wien, Magistratsabteilung 7.The author wishes to thank the editor, Ivo W. Molenaar, as well as Clifford C. Clogg and the anonymous reviewers for their valuable comments on the earlier drafts of this paper.     

Explicit candecomp/parafac solutions for a contrived 2 × 2 × 2 array of rank three

Kruskal, Harshman and Lundy have contrived a special 2 × 2 × 2 array to examine formal properties of degenerate Candecomp/Parafac solutions. It is shown that for this array the Candecomp/Parafac loss has an infimum of 1. In addition, the array will be used to challenge the tradition of fitting Indscal and related models by means of the Candecomp/Parafac process.     

Comparing item characteristic curves

Test items are often evaluated and compared by contrasting the shapes of their item characteristics curves (ICC's) or surfaces. The current paper develops and applies three general (i.e., nonparametric) comparisons of the shapes of two item characteristic surfaces: (i) proportional latent odds, (ii) uniform relative difficulty, and (iii) item sensitivity. Two items may be compared in these ways while making no assumption about the shapes of item characteristic surfaces for other items, and no assumption about the dimensionality of the latent variable. Also studied is a method for comparing the relative shapes of two item characteristic curves in two examinee populations.The author is grateful to Paul Holland, Robert Mislevy, Tue Tjur, Rebecca Zwick, the editor and reviewers for valuable comments on the subject of this paper, to Mari A. Pearlman for advice on the pairing of items in the examples, and to Dorothy Thayer for assistance with computing.     

The rank of reduced dispersion matrices

Psychometricians working in factor analysis and econometricians working in regression with measurement error in all variables are both interested in the rank of dispersion matrices under variation of the diagonal elements. Psychometricians concentrate on cases in which low rank can be attained, preferably rank one, the Spearman case. Econometricians cocentrate on cases in which the rank cannot be reduced below the number of variables minus one, the Frisch case. In this paper we give an extensive historial discussion of both fields, we prove the two key results in a more satisfactory and uniform way, we point out various small errors and misunderstandings, and we present a methodological comparison of factor analysis and regression on the basis of our results.Financial support by the Netherlands Organization for the Advancement of Pure Research (ZWO) is gratefully acknowledged.     

态度及其与行为模式述评

态度一直是社会心理学的核心问题,态度对于预测行为具有重要作用。本文阐述了态度的界定、态度的结构模型及态度预测行为模型的各种理论,在这些理论的基础上,提出了态度预测行为的另一模型。     

Cross-Sectional Analysis of Longitudinal Mediation Processes

Statistical mediation analysis can help to identify and explain the mechanisms behind psychological processes. Examining a set of variables for mediation effects is a ubiquitous process in the social sciences literature; however, despite evidence suggesting that cross-sectional data can misrepresent the mediation of longitudinal processes, cross-sectional analyses continue to be used in this manner. Alternative longitudinal mediation models, including those rooted in a structural equation modeling framework (cross-lagged panel, latent growth curve, and latent difference score models) are currently available and may provide a better representation of mediation processes for longitudinal data. The purpose of this paper is twofold: first, we provide a comparison of cross-sectional and longitudinal mediation models; second, we advocate using models to evaluate mediation effects that capture the temporal sequence of the process under study. Two separate empirical examples are presented to illustrate differences in the conclusions drawn from cross-sectional and longitudinal mediation analyses. Findings from these examples yielded substantial differences in interpretations between the cross-sectional and longitudinal mediation models considered here. Based on these observations, researchers should use caution when attempting to use cross-sectional data in place of longitudinal data for mediation analyses.     

Sellars's Two Images as a Philosopher's Tool

The distinction between the manifest and the scientific image of man‐in‐the‐world is widely seen as crucial to Wilfrid Sellars's philosophical work. The present essay agrees with this view. It contends, however, that precisely because the distinction is important, we should not hurry to a quick and superficial understanding of it. The essay identifies several oversimplifications that can be found in the literature on the topic and argues that they are at least partly rooted in too rigid a view of the role that the two‐image distinction plays in Sellars's philosophy. It shows that this rigid approach is quite common in the secondary literature, either explicitly or by implication. It then presents a more cautious, flexible approach to the problem of the two images and explains why this approach is fruitful on the basis of textual evidence, along with the overall advantages of interpreting Sellars's thought as a whole.