Models for Paired Comparison Data: A Review with Emphasis on Dependent Data

Thurstonian and Bradley-Terry models are the most commonly applied models in the analysis of paired comparison data. Since their introduction, numerous developments have been proposed in different areas. This paper provides an updated overview of these extensions, including how to account for object- and subject-specific covariates and how to deal with ordinal paired comparison data. Special emphasis is given to models for dependent comparisons. Although these models are more realistic, their use is complicated by numerical difficulties. We therefore concentrate on implementation issues. In particular, a pairwise likelihood approach is explored for models for dependent paired comparison data, and a simulation study is carried out to compare the performance of maximum pairwise likelihood with other limited information estimation methods. The methodology is illustrated throughout using a real data set about university paired comparisons performed by students.Comment: Published in at http://dx.doi.org/10.1214/12-STS396 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Modeling faking in the multidimensional forced-choice format: the faking mixture model

The multidimensional forced-choice (MFC) format has been proposed to reduce faking because items within blocks can be matched on desirability. However, the desirability of individual items might not transfer to the item blocks. The aim of this paper is to propose a mixture item response theory model for faking in the MFC format that allows to estimate the fakability of MFC blocks, termed the Faking Mixture model. Given current computing capabilities, within-subject data from both high- and low-stakes contexts are needed to estimate the model. A simulation showed good parameter recovery under various conditions. An empirical validation showed that matching was necessary but not sufficient to create an MFC questionnaire that can reduce faking. The Faking Mixture model can be used to reduce fakability during test construction. SUPPLEMENTARY INFORMATION: The online version supplementary material available at 10.1007/s11336-021-09818-6

Modeling Preference Data

We provide a gentle overview of modeling choice data, with an emphasis on statistical models that allow treating both observed and unobserved effects due to the decision makers and choice options. We first consider the situation when decision makers express their preferences in the form of liking judgments or purchase intentions (as in conjoint studies).Then, we consider applications that involve partial and/or incomplete ranking data -including paired comparisons and first choices. In this case, we assume that choice outcomes are a result of a maximization process, i.e., decision makers are assumed to select or choose options that have the highest utility among the considered options.Preference data, Random utility models

Asking the Right Questions: Increasing Fairness and Accuracy of Personality Assessments with Computerised Adaptive Testing

Personality assessments are frequently used in real-life applications to predict important outcomes. For such assessments, the forced choice (FC) response format has been shown to reduce response biases and distortions, and computerised adaptive testing (CAT) has been shown to improve measurement efficiency. This research developed FC CAT methodologies under the framework of the Thurstonian item response theory (TIRT) model. It is structured into a logical sequence of three areas of investigation, where the findings from each area inform key decisions in the next one. First, the feasibility of FC CAT is tested empirically. Analysis of large historical samples provides support for item parameter invariance when an item appears in different FC blocks, with person score estimation remaining very stable despite minor violations. Remedies for minimising the risk of assumption violations are also developed. Second, the design of the FC CAT algorithm is optimised. Current CAT methodologies are reviewed and adapted for TIRT-based FC assessments, and intensive simulation studies condense the design options to a small number of practical recommendations. Third, the practicality and usefulness of FC CAT is examined. An adaptive FC assessment measuring the HEXACO model of personality is developed and trialled empirically. In conclusion, this research mapped out a blueprint for developing FC CAT that use the TIRT model, highlighting the benefits, limitations, and key directions for further research

Testing the Foundations of Signal Detection Theory in Recognition Memory

Signal detection theory (SDT) plays a central role in the characterization of human judgments in a wide range of domains, most prominently in recognition memory. But despite its success, many of its fundamental properties are often misunderstood, especially when it comes to its testability. The present work examines five main properties that are characteristic of existing SDT models of recognition memory: (a) random-scale representation, (b) latent-variable independence, (c) likelihood-ratio monotonicity, (d) ROC function asymmetry, and (e) nonthreshold representation. In each case, we establish testable consequences and test them against data collected in the appropriately designed recognition-memory experiment. We also discuss the connection between yes–no, forced-choice, and ranking judgments. This connection introduces additional behavioral constraints and yields an alternative method of reconstructing yes–no ROC functions. Overall, the reported results provide a strong empirical foundation for SDT modeling in recognition memory. (PsycInfo Database Record (c) 2021 APA, all rights reserved

Euclidean distance geometry and applications

Euclidean distance geometry is the study of Euclidean geometry based on the concept of distance. This is useful in several applications where the input data consists of an incomplete set of distances, and the output is a set of points in Euclidean space that realizes the given distances. We survey some of the theory of Euclidean distance geometry and some of the most important applications: molecular conformation, localization of sensor networks and statics.Comment: 64 pages, 21 figure