Some remarks on Scheiblechner's treatment of isop models

Scheiblechner (1995) proposes a probabilistic axiomatization of measurement called ISOP (isotonic ordinal probabilistic models) that replaces Rasch's (1980) specific objectivity assumptions with two interesting ordinal assumptions. Special cases of Scheiblechner's model include standard unidimensional factor analysis models in which the loadings are held constant, and the Rasch model for binary item responses. Closely related are the doubly-monotone item response models of Mokken (1971; see also Mokken & Lewis, 1982; Sijtsma, 1988; Molenaar, 1991; Sijtsma & Junker, 1996; and Sijtsma & Hemker, in press). More generally, strictly unidimensional latent variable models have been considered in some detail by Holland and Rosenbaum (1986), Ellis and van den Wollenberg (1993), and Junker (1990, 1993). The purpose of this note is to provide connections with current research in foundations and nonparametric latent variable and item response modeling that are missing from Scheiblechner's (1995) paper, and to point out important related work by Hemker, Sijtsma, Molenaar, & Junker (1996, 1997), Ellis and Junker (in press) and Junker and Ellis (1997). We also discuss counterexamples to three major theorems in the paper. By carrying out these three tasks, we hope to provide researchers interested in the foundations of measurement and item response modeling the opportunity to give the ISOP approach the careful attention it deserves. This research was supported by the National Science Foundation, Grant DMS-94.04438. I thank the Editor and three anonymous referees for careful readings that improved the completeness of this note.     

A Propositional Dynamic Logic with Qualitative Probabilities

This paper presents an -completeness theorem for a new propositional probabilistic logic, namely, the dynamic propositional logic of qualitative probabilities (D Q P), which has been introduced by the author as a dynamic extension of the logic of qualitative probabilities (Q P) introduced by Segerberg.     

Reasonable Doubt: A Note on ‘Neutral’ Illatives and Arguments

George Bowles and Thomas Gilbert claim that illatives such as so, therefore, and hence convey the meaning that the premise confers upon the conclusion a probability greater than 1/2. This claim is false, for there are straightforward uses of these illatives that do not convey the meaning that the probability is greater than 1/2. In addition, because Bowles' and Gilbert's claim is false, a revision of their definition of argument is required.     

The probabilistic import of illatives

It is not only overtly probabilistic illatives like makes it certain that but also apparently non-probabilistic ones like therefore that have probabilistic import. Illatives like therefore convey the meaning that the premise confers on the conclusion a probability not only greater than 0 but also greater than 1/2. But because they do not say whether that probability is equal to or less than 1, these illatives are appropriately called neutral.     

Improving Accuracy on Bayesian Inference Problems Using a Brief Tutorial

Research suggests that most people struggle when asked to interpret the outcomes of diagnostic tests such as those presented as Bayesian inference problems. To help people interpret these difficult problems, we created a brief tutorial, requiring less than 10 minutes, that guided participants through the creation of an aid (either graph or table) based on an example inference problem and then showed the correct way to calculate the positive predictive value of the problem (i.e., likelihood that positive tests correctly indicate presence of condition). Approximately 70% of those in each training condition found the correct response on at least one problem in the format for which they were trained. Just under 55% of those in the control condition (i.e., no training) were able to find the correct response on at least one table or graph problem. We demonstrated a relationship between numeracy and performance on both problem formats, although we did not find evidence for a relationship between graph literacy and performance for either problem format. Potential improvements to and applications of the tutorial are discussed. Copyright © 2016 John Wiley & Sons, Ltd.     

Preparing for retirement: how self-efficacy and resource threats contribute to retirees’ satisfaction,depression, and losses

The resource-based dynamic perspective has been applied in this study to explore retirees’ satisfaction, depression, and actual loss of resources. A three-wave design with Spanish workers who were in transition to retirement (N = 286) was used with the aim of investigating correlations between pre-retirement variables and post-retirement well-being. Participants were working at Time 1 and Time 2 but at Time 3, they had retired in the past year. Individual attributes (age), access to resources (life satisfaction and depression), situational characteristics (job stress, job tenure, and retirement transition quality), and psychological disposition (general self-efficacy and positive retirement expectations) at the first wave, correlated with the threat of loss at the second wave. Moreover, these predictors explained how people adjust to retirement at the third wave, assessed both directly (actual loss of resources) and indirectly (satisfaction with retirement and depression), via their effects on Time 2 variables. The results revealed that threat of loss had a positive relationship on loss of resources after retirement, and also both on retirement satisfaction and depression after retirement. Hence, this suggested several avenues for intervention targeting expectations and, in turn, increasing retirees’ well-being, which are discussed.     

Fallacies in probability judgments for conjunctions and disjunctions of everyday events

The conjunction fallacy occurs when people judge a conjunction B‐and‐A as more probable than a constituent B, contrary to probability theory's ‘conjunction rule’ that a conjunction cannot be more probable than either constituent. Many studies have demonstrated this fallacy in people's reasoning about various experimental materials. Gigerenzer objects that from a ‘frequentist’ standpoint probability theory is not valid for these materials, and so failure to follow the conjunction rule is not a fallacy. This paper describes three experiments showing that the conjunction fallacy occurs as consistently for conjunctions where frequentist probability theory is valid (conjunctions of everyday weather events) as for other conjunctions. These experiments also demonstrate a reliable correlation between the occurrence of the conjunction fallacy and the disjunction fallacy (which arises when a disjunction B‐or‐A is judged less probable than a constituent B). This supports a probability theory + random variation account of probabilistic reasoning. Copyright © 2008 John Wiley & Sons, Ltd.     

Recovering a Probabilistic Knowledge Structure by Constraining its Parameter Space

In the Basic Local Independence Model (BLIM) of Doignon and Falmagne (Knowledge Spaces, Springer, Berlin, 1999), the probabilistic relationship between the latent knowledge states and the observable response patterns is established by the introduction of a pair of parameters for each of the problems: a lucky guess probability and a careless error probability. In estimating the parameters of the BLIM with an empirical data set, it is desirable that such probabilities remain reasonably small. A special case of the BLIM is proposed where the parameter space of such probabilities is constrained. A simulation study shows that the constrained BLIM is more effective than the unconstrained one, in recovering a probabilistic knowledge structure.     

统计认知理论及应用研究

长期以来大家认为人类认知尽管可以看成是非确定的推理计算过程,但它的知识表达、模型结构、及计算方法和概率统计理论在本质上是不同的,因此认知科学和概率统计方法存在巨大的鸿沟,过去两者基本上独立发展。近年来随着Bayesian概率统计模型研究的一系列突破性工作和认知过程本质的不断被发现和挖掘,两者的相关性和互补性逐渐突显出来。许多研究者认为认知是近似遵循概率统计推理原则的,一些研究工作显示两者的结合有可能对人工智能发展产生深远的影响。本文对当前统计认知理论及应用研究的现状进行系统的梳理,并结合自身的研究对它今后的发展提出自己的看法。