A Creation Narrative for the Psychometric Society and <Emphasis Type="Italic">Psychometrika</Emphasis>: In the Beginning There Was Paul Horst

A review is provided for the creation of the Psychometric Society in 1935, and the establishment of its journal, Psychometrika, in 1936. This document is part of the 80th anniversary celebration for Psychometrika’s founding, held during the annual meeting of the Psychometric Society in July of 2016 in Asheville, NC.     

How to Measure and Explain Achievement Change in Large-Scale Assessments: A Rejoinder

In this rejoinder, we discuss substantive and methodological validity issues of large-scale assessments of trends in student achievement, commenting on the discussion paper by Van den Heuvel-Panhuizen, Robitzsch, Treffers, and Köller (2009). We focus on methodological challenges in deciding what to measure, how to measure it, and how to foster stability. Next, we discuss what to do with trends that are found. Finally, we reflect on how the research findings were received.     

Interpreting degenerate solutions in unfolding by use of the vector model and the compensatory distance model

In this paper, we reconsider the merits of unfolding solutions based on loss functions involving a normalization on the variance per subject. In the literature, solutions based on Stress-2 are often diagnosed to be degenerate in the majority of cases. Here, the focus lies on two frequently occurring types of degeneracies. The first type typically locates some subject points far away from a compact cluster of the other points. In the second type of solution, the object points lie on a circle. In this paper, we argue that these degenerate solutions are well fitting and informative. To reveal the information, we introduce mixtures of plots based on the ideal point model of unfolding, the vector model, and on the signed distance model. In addition to a different representation, we provide a new iterative majorization algorithm to optimize the average squared correlation between the distances in the configuration and the transformed data per individual. It is shown that this approach is equivalent to minimizing Kruskal’s Stress-2.This revised article was published online in August 2005 with the PDF paginated correctly.     

Analysis of asymmetry by a slide-vector

The slide-vector scaling model attempts to account for the asymmetry of a proximity matrix by a uniform shift in a fixed direction imposed on a symmetric Euclidean representation of the scaled objects. Although no method for fitting the slide-vector model seems available in the literature, the model can be viewed as a constrained version of the unfolding model, which does suggest one possible algorithm. The slide-vector model is generalized to handle three-way data, and two examples from market structure analysis are presented.     

A Latent Class Multidimensional Scaling Model for Two-Way One-Mode Continuous Rating Dissimilarity Data

In this paper, we propose a cluster-MDS model for two-way one-mode continuous rating dissimilarity data. The model aims at partitioning the objects into classes and simultaneously representing the cluster centers in a low-dimensional space. Under the normal distribution assumption, a latent class model is developed in terms of the set of dissimilarities in a maximum likelihood framework. In each iteration, the probability that a dissimilarity belongs to each of the blocks conforming to a partition of the original dissimilarity matrix, and the rest of parameters, are estimated in a simulated annealing based algorithm. A model selection strategy is used to test the number of latent classes and the dimensionality of the problem. Both simulated and classical dissimilarity data are analyzed to illustrate the model.     

A Model-Free Diagnostic for Single-Peakedness of Item Responses Using Ordered Conditional Means

In this article we propose a model-free diagnostic for single-peakedness (unimodality) of item responses. Presuming a unidimensional unfolding scale and a given item ordering, we approximate item response functions of all items based on ordered conditional means (OCM). The proposed OCM methodology is based on Thurstone &; Chave's (1929) Thurstone, L. L. and Chave, E. J. 1929. The measurement of attitude: A psychophysical method and some experiments with a scale for measuring attitude toward the church. Chicago, IL: University of Chicago Press.. [Crossref] , [Google Scholar] criterion of irrelevance, which is a graphical, exploratory method for evaluating the “relevance” of dichotomous attitude items. We generalized this criterion to graded response items and quantified the relevance by fitting a unimodal smoother. The resulting goodness-of-fit was used to determine item fit and aggregated scale fit. Based on a simulation procedure, cutoff values were proposed for the measures of item fit. These cutoff values showed high power rates and acceptable Type I error rates. We present 2 applications of the OCM method. First, we apply the OCM method to personality data from the Developmental Profile; second, we analyze attitude data collected by Roberts and Laughlin (1996) Roberts, J. S. and Laughlin, J. E. 1996. A unidimensional item response model for unfolding responses from a graded disagree-agree response scale. Applied Psychological Measurement, 20: 231–255. [Crossref], [Web of Science ®] , [Google Scholar] concerning opinions of capital punishment.     

A latent class distance association model for cross‐classified data with a categorical response variable

In this paper we propose a latent class distance association model for clustering in the predictor space of large contingency tables with a categorical response variable. The rows of such a table are characterized as profiles of a set of explanatory variables, while the columns represent a single outcome variable. In many cases such tables are sparse, with many zero entries, which makes traditional models problematic. By clustering the row profiles into a few specific classes and representing these together with the categories of the response variable in a low‐dimensional Euclidean space using a distance association model, a parsimonious prediction model can be obtained. A generalized EM algorithm is proposed to estimate the model parameters and the adjusted Bayesian information criterion statistic is employed to test the number of mixture components and the dimensionality of the representation. An empirical example highlighting the advantages of the new approach and comparing it with traditional approaches is presented.