Extending exploratory diagnostic classification models: Inferring the effect of covariates

Diagnostic models provide a statistical framework for designing formative assessments by classifying student knowledge profiles according to a collection of fine-grained attributes. The context and ecosystem in which students learn may play an important role in skill mastery, and it is therefore important to develop methods for incorporating student covariates into diagnostic models. Including covariates may provide researchers and practitioners with the ability to evaluate novel interventions or understand the role of background knowledge in attribute mastery. Existing research is designed to include covariates in confirmatory diagnostic models, which are also known as restricted latent class models. We propose new methods for including covariates in exploratory RLCMs that jointly infer the latent structure and evaluate the role of covariates on performance and skill mastery. We present a novel Bayesian formulation and report a Markov chain Monte Carlo algorithm using a Metropolis-within-Gibbs algorithm for approximating the model parameter posterior distribution. We report Monte Carlo simulation evidence regarding the accuracy of our new methods and present results from an application that examines the role of student background knowledge on the mastery of a probability data set.     

Ambiguity attitudes in qualitative contexts: The role of prior beliefs

Most studies of ambiguity aversion rely on experimental paradigms involving monetary bets. Thus, the extent to which ambiguity aversion occurs outside of such contexts is much less understood, particularly when the situation cannot easily be reduced to numerical terms. The present work seeks to understand whether people prefer to avoid ambiguous decisions in a variety of different qualitative domains (e.g., work, family, love, friendship, exercise, study, and health), and, if so, to determine the role played by prior beliefs in those domains. Across three studies, we presented participants with 24 vignettes and measured the degree to which they preferred risk to ambiguity in each. We also asked them for their prior probability estimates about the likely outcomes in the ambiguous events. Ambiguity aversion was observed in the vast majority of vignettes, but at different magnitudes. It was predicted by whether the vignette involved gain or loss as well as by people's prior beliefs; however, the heterogeneity between people meant that the role of prior beliefs was only evident in an individual-level analysis (i.e., not at the group level). Our results suggest that the desire to avoid ambiguity occurs in a wide variety of qualitative contexts but to different degrees for different people and may be partially driven by unfavorable prior estimates of the likely outcomes of the ambiguous events.     

The Fallacy Fallacy: From the Owl of Minerva to the Lark of Arete

The fallacy fallacy is either the misdiagnosis of fallacy or the supposition that the conclusion of a fallacy must be a falsehood. This paper explores the relevance of these and related errors of reasoning for the appraisal of arguments, especially within virtue theories of argumentation. In particular, the fallacy fallacy exemplifies the Owl of Minerva problem, whereby tools devised to understand a norm make possible new ways of violating the norm. Fallacies are such tools and so are vices. Hence a similar problem arises with argumentative vices. Fortunately, both instances of the problem have a common remedy.