Testing the actual equivalence of automatically generated items

If the automatic item generation is used for generating test items, the question of how the equivalence among different instances may be tested is fundamental to assure an accurate assessment. In the present research, the question was dealt by using the knowledge space theory framework. Two different ways of considering the equivalence among instances are proposed: The former is at a deterministic level and it requires that all the instances of an item template must belong to exactly the same knowledge states; the latter adds a probabilistic level to the deterministic one. The former type of equivalence can be modeled by using the BLIM with a knowledge structure assuming equally informative instances; the latter can be modeled by a constrained BLIM. This model assumes equality constraints among the error parameters of the equivalent instances. An approach is proposed for testing the equivalence among instances, which is based on a series of model comparisons. A simulation study and an empirical application show the viability of the approach.     

On Some Generalizations of the Concept of Partition

There are well-known isomorphisms between the complete lattice of all partitions of a given set A and the lattice of all equivalence relations on A. In the paper the notion of partition is generalized in order to work correctly for wider classes of binary relations than equivalence ones such as quasiorders or tolerance relations. Some others classes of binary relations and corresponding counterparts of partitions are considered.     

Action Emulation between Canonical Models

In this paper we investigate Kripke models, used to model knowledge or belief in a static situation, and action models, used to model communicative actions that change this knowledge or belief. The appropriate notion for structural equivalence between modal structures such as Kripke models is bisimulation: Kripke models that are bisimilar are modally equivalent. We would like to find a structural relation that can play the same role for the action models that play a prominent role in information updating. Two action models are equivalent if they yield the same results when updating Kripke models. More precisely, two action models are equivalent if it holds for all Kripke models that the result of updating with one action model is bisimilar to the result of updating with the other action model. We propose a new notion of action emulation that characterizes the structural equivalence of the important class of canonical action models. Since every action model has an equivalent canonical action model, this gives a method to decide the equivalence of any pair of action models. We also give a partial result that holds for the class of all action models. Our results extend the work in van Eijck et al. (Synthese 185(1):131–151, 2012).     

Remarks on the identifiability of thurstonian ranking models: Case V, case III, or neither?

It is well-known that the representations of the Thurstonian Case III and Case V models for paired comparison data are not unique. Similarly, when analyzing ranking data, other equivalent covariance structures can substitute for those given by Thurstone in these cases. That is, we may more broadly define the family of covariance structures satisfying Case III and Case V conditions. This paper introduces the notion of equivalence classes which defines a more meaningful partition of the covariance structures of the Thurstonian ranking models. In addition, the equivalence classes of Case V and Case III are completely characterized.     

A characterization of the concept of independence in knowledge structures

In knowledge space theory a knowledge structure provides a deterministic representation of the implications among the items in a given set Q. Concrete procedures for the efficient assessment of knowledge by means of a knowledge structure have been proposed by Doignon and Falmagne [Falmagne, J.-C., & Doignon, J.-P. (1988a). A class of stochastic procedures for the assessment of knowledge. British Journal of Mathematical and Statistical Psychology, 41, 1-23; Falmagne, J.-C., & Doignon, J.-P. (1988b). A markovian procedure for assessing the state of a system. Journal of Mathematical Psychology, 32, 232-258]. The primitive idea at the core of such procedures is that the (correct or wrong) answers of a student to a subset A⊆Q of items could be inferred from the answers to a subset B⊆Q of items that were previously presented to that student. Since B provides information about A, from the viewpoint of the teacher these two subsets are not independent. This idea of dependence vs. independence is formalized in this paper in terms of an independence relation on the power set of Q. A nice characterization of this relation allows to express an arbitrary knowledge structure as the combination of a number of substructures each of which is independent of each other. An algorithm is then proposed which checks for independence in a knowledge structure and decomposes this last into a collection of independent substructures.     

Monadic MV-algebras are Equivalent to Monadic ?-groups with Strong Unit

In this paper we extend Mundici??s functor ?? to the category of monadic MV-algebras. More precisely, we define monadic ?-groups and we establish a natural equivalence between the category of monadic MV-algebras and the category of monadic ?-groups with strong unit. Some applications are given thereof.     

Epistemic justification and premise acceptability

In this paper, we want to explore the connection between premises' being acceptable and their being in some sense justified. The equivalence of premise acceptability and justification seems intuitively correct. But to argue for such a connection, we need to analyze the concepts of acceptability and justification. Such an analysis also seems necessary if this equivalence is to advance our understanding of premise acceptability. Following L. J. Cohen, we may say S believes that p when S is disposed to feel it true that p, while S accepts that p when S takes that p as a premise for further deliberation or action. Reasons for belief are reasons for acceptance, and epistemological (as opposed to pragmatic) reasons for acceptance are reason for belief. Following William P. Alston, we may explicate being a justifying reason for belief through the notion of an adequate ground on which the belief is based. In turn, adequacy of ground means that the mechanism grounding the belief is reliable. Given these notions, we may define a concept of justification in terms of presumptive adequacy.     

Blocking the Vagueness Block - A New Restricted Answer to the Special Composition Question

The vagueness objection seems to block any moderate answer to the Special Composition Question leaving us with the two extreme alternatives that there either is no composite object or that any set of things compose an object. In this technical paper I introduce the notion of causal objects and a definition of a predicate that permits the set of all parts to be divided into equivalence classes. On this view we can use equivalence classes of parts to define the notion of composite objects why vagueness is blocked. The block works in a hypothetical domain where all parts have a cause so the aim is not to suggest empirically detectable parts and composites, nor to claim any kind of existence of the things being defined, but to present a consistent account of a possible moderate answer to the Special Composition Question that avoids the vagueness objection. The underlying idea is that an object, as such, is not caused whereas its parts are. For example, if we have three caused parts A, B and C constituting the composite D, we have three things that are caused (A, B and C) whereas the composite D has no cause over and above the three causes of A, B and C.

     

Abduction: A categorical characterization

Scientific knowledge is gained by the informed (on the basis of theoretic ideas and criteria) examination of data. This can be easily seen in the context of quantitative data, handled with statistical methods. Here we are interested in other forms of data analysis, although with the same goal of extracting meaningful information. The idea is that data should guide the construction of suitable models, which later may lead to the development of new theories. This kind of inference is called abduction and constitutes a central procedure called Peircean qualitative induction. In this paper we will present a category-theoretic representation of abduction based on the notion of adjunction, which highlights the fundamental fact that an abduction is the most efficient way of capturing the information obtained from a large body of evidence.     

Bayesian power equivalence in latent growth curve models

Longitudinal studies are the gold standard for research on time-dependent phenomena in the social sciences. However, they often entail high costs due to multiple measurement occasions and a long overall study duration. It is therefore useful to optimize these design factors while maintaining a high informativeness of the design. Von Oertzen and Brandmaier (2013,Psychology and Aging, 28, 414) applied power equivalence to show that Latent Growth Curve Models (LGCMs) with different design factors can have the same power for likelihood-ratio tests on the latent structure. In this paper, we show that the notion of power equivalence can be extended to Bayesian hypothesis tests of the latent structure constants. Specifically, we show that the results of a Bayes factor design analysis (BFDA; Schönbrodt & Wagenmakers (2018,Psychonomic Bulletin and Review, 25, 128) of two power equivalent LGCMs are equivalent. This will be useful for researchers who aim to plan for compelling evidence instead of frequentist power and provides a contribution towards more efficient procedures for BFDA.     

Considerations on a <Emphasis Type="Italic">Phronetic</Emphasis> Proposal: a Bakhtinian Reply

The present text is a Bakhtinian reply to Eugene Matusov’s conceptual elaborations on the Aristotelic notion of phronesis, related to contemporary teaching activity and to his research-on-teaching proposal, carried out to involve pre-service practitioners in the educational field. Following his line of reasoning, some of the arguments raised in his search to define the specificities of teaching and researching in education are taken as fruitful ground for discussing the possibilities and limits of the concept of phronesis, and the educational implications of his phronetic proposal. The comments are circumscribed to two main focuses: 1. the notion of phronesis and the specificity of teaching/researching; and 2. the need for knowledge and research on teaching in contemporary world. An analysis of the implied conceptual assumptions with regards to Aristotle’s four ways of knowing leads to an inquiry about the need and the pertinence of bringing the concept of phronesis to define the personal dimension of teaching and of learning to teach. The Bakhtinian reply attempts to situate Matusov’s conceptual and practical work among the polemical issues that cross this uneasy field nowadays, highlighting the heuristic value of his conceptual elaborations to the present debates, also pointing to his positioning and specific contributions to teacher education and research activity.     

IRT-related factor analytic procedures for testing the equivalence of paper-and-pencil and Internet-administered questionnaires

This article describes a general item response theory-based factor analytic procedure that allows assessment of the equivalence between 2 administrative modes of a questionnaire: paper and pencil, and Internet based. The theoretical relations between the present procedure and other methods used in previous empirical research are shown, and the advantages of the procedure are discussed. An empirical application based on 2 personality questionnaires is given, and the results are compared with the results of using traditional procedures for assessing equivalence. The substantive implications of the results, as well as suggestions for further research and methodology, are discussed.     

The good lives model of offender rehabilitation: Clinical implications

The major aim of the current paper is to expand on the practice elements of the Good Lives Model-Comprehensive (GLM-C) of offender rehabilitation and to provide a detailed examination of its assessment and treatment implications. First we discuss the notion of rehabilitation and the qualities a good theory of rehabilitation should possess. Second, the principles, etiological assumptions, and general treatment implications of the GLM-C are briefly described. Third, we outline in considerable detail the application of this novel perspective to the assessment and treatment of sexual offenders. Finally, we conclude the paper with a summary of the major benefits we envisage the GLM-C bringing to the rehabilitation of sexual offenders.     

Bisimulation for Conditional Modalities

We give a definition of bisimulation for conditional modalities interpreted on selection functions and prove the correspondence between bisimilarity and modal equivalence, generalizing the Hennessy–Milner Theorem to a wide class of conditional operators. We further investigate the operators and semantics to which these results apply. First, we show how to derive a solid notion of bisimulation for conditional belief, behaving as desired both on plausibility models and on evidence models. These novel definitions of bisimulations are exploited in a series of undefinability results. Second, we treat relativized common knowledge, underlining how the same results still hold for a different modality in a different semantics. Third, we show the flexibility of the approach by generalizing it to multi-agent systems, encompassing the case of multi-agent plausibility models.     

Representative co-design: Utilising a source of experiential knowledge for athlete development and performance preparation

Contemporary models for athlete development and performance preparation in sport have advocated a role re-conceptualisation for coaches grounded as learning environment designers. Within this re-conceptualisation, expert practitioners are encouraged to draw upon their experiential knowledge to design representative and meaningful learning activities that place the performer-environment interaction at its core. However, we propose that, currently, a critical source of experiential knowledge is often overlooked within the process of learning design – that of performers. Specifically, practitioner-performer interactions could enrich the design of learning environments by promoting the utilisation of soliciting affordances and encouraging the psychological engagement of performers. This paper introduces the concept of representative co-design – a notion which builds on existing research by framing how the insights and experiences of performers can be negotiated within the design of practice tasks that seek to faithfully simulate interacting constraints of competition to enrich learning environments. We frame the notion of representative co-design, and contend its importance within more contemporary athlete development and performance preparation models, at two levels: (i) that of enriching physical education curricula to develop thought provoking, ‘intelligent’ child/adolescent learners, and (ii) that of enriching contemporary athlete preparation models in high-performance sport to enhance learning and engagement, and to develop ‘next generation’ coaches within current athletes. To bring this conceptualisation to life, we present two exemplars demonstrating the notion of representative co-design, while concurrently highlighting areas for future research.     

Justified Judging

Traditional approaches to epistemology have sought, unsuccessfully, to define knowledge in terms of justification. I follow Timothy Williamson in arguing that this is misconceived and that we should take knowledge as our fundamental epistemological notion. We can then characterise justification as a certain sort of approximation to knowledge. A judgement is justified if and only if the reason (if there is one) for a failure to know is to be found outside the subject's mental states; that is, justified judging is possible knowing (where one world accessible from another if and only if they are identical with regard to a subject's antecedent mental states and judgement forming processes). This view is explained and defended.     

Loss aversion and perceptual risk aversion

We prove that, in cumulative prospect theory, the weak loss aversion for S-shaped value functions is equivalent to a notion of risk aversion that we define from the perceptual point of view. No additional assumption or condition on the probability distortion is needed. It is demonstrated that a power S-shaped value function does not satisfy weak loss aversion, i.e., a decision maker is risk seeking with respect to some mixed sign lotteries.     

The Five Factor Model in personnel selection: Measurement equivalence between applicant and non-applicant groups

This study investigates the measurement equivalence of a Five Factor measure of personality between applicant and non-applicant samples. The Big Five Questionnaire-2 was administered in two samples: A group of volunteers (n = 903), who completed the test for research purposes, and a group applying for jobs, who completed the test during hiring procedures (n = 401). Multiple-group confirmatory factor analysis on item composites was conducted to test for the equivalence of factor covariance and mean structures of twenty facets of the Five Factors. Item-level analyses were carried out through analysis of variance to further examine the issue of measurement invariance. Findings suggested that personality facets have the same measurement unit across applicants and non-applicants, while a lack of equivalence was found in the origin of the scales. Similar results were found at the item-level. Implications for personality assessment are advanced and discussed.     

A test of the discrimination account in equivalence class formation

An equivalence class is typically established when a subject is taught a set of interrelated conditional discriminations with physically unrelated stimuli and additional, untaught, conditional discriminations are then demonstrated. Interestingly, and perhaps counter-intuitively, the relations among the stimuli within such a class are not necessarily equal. Rather, some members of the class are differentially related to other class members. There are two opposing theories of why relations among stimuli are unequal: nodal and discrimination accounts. The former suggests that delayed emergence is due to nodal distance (i.e. the number of intervening stimuli) while the latter suggests that delayed emergence is an artifact of the training procedure itself. The current paper reports on the first empirical study that directly compares these theories. Forty participants were given training designed to establish two 5-member equivalence classes. Participants’ response speed supported the nodal account, thus suggesting that unequal relations among equivalence class members is not an artifact of the training procedure.     

Co‐Hyperintensionality

Co‐hyperintensionality, or hyperintensional equivalence, is a relation holding between two or more contents that can be substituted in a hyperintensional context salva veritate. I argue that two strategies used to provide criteria for co‐hyperintensionality (appeal to some form of impossible worlds, or to structural or procedural equivalence of propositions) fail. I argue that there is no generalized notion of co‐hyperintensionality that meets plausible desiderata, by showing that the opposite thesis leads to falsity. As a conclusion, I suggest to take co‐hyperintensionality as a primitive and I provide a general criterion of co‐hyperintensionality whose content depends on each hyperintensional notion we aim to formalize.