Some neglected problems in IRT

The paper addresses three neglected questions from IRT. In section 1, the properties of the “measurement” of ability or trait parameters and item difficulty parameters in the Rasch model are discussed. It is shown that the solution to this problem is rather complex and depends both on general assumptions about properties of the item response functions and on assumptions about the available item universe. Section 2 deals with the measurement of individual change or “modifiability” based on a Rasch test. A conditional likelihood approach is presented that yields (a) an ML estimator of modifiability for given item parameters, (b) allows one to test hypotheses about change by means of a Clopper-Pearson confidence interval for the modifiability parameter, or (c) to estimate modifiability jointly with the item parameters. Uniqueness results for all three methods are also presented. In section 3, the Mantel-Haenszel method for detecting DIF is discussed under a novel perspective: What is the most general framework within which the Mantel-Haenszel method correctly detects DIF of a studied item? The answer is that this is a 2PL model where, however, all discrimination parameters are known and the studied item has the same discrimination in both populations. Since these requirements would hardly be satisfied in practical applications, the case of constant discrimination parameters, that is, the Rasch model, is the only realistic framework. A simple Pearsonx ² test for DIF of one studied item is proposed as an alternative to the Mantel-Haenszel test; moreover, this test is generalized to the case of two items simultaneously studied for DIF.     

Matching behavior: Some methodological problems

Two classes of problems associated with specifying the controlling stimuli in matching experiments were discussed. The first class-control of matching behavior by cues other than the standard stimuli-was demonstrated by the results of a pseudomatching experiment. The second class related to the “effective” sample or standard stimulus set and to changes in the S’s matching strategy that may occur in a matching experiment.     

Some neglected contributions of Wilhelm Wundt to the psychology of memory

Wilhelm Wundt, whose name is rarely associated with the scientific study of memory, conducted a number of memory experiments that appear to have escaped the awareness of modern cognitive psychologists. Aspects of Wundt's system are reviewed, particularly with respect to his experimental work on memory. Wundt investigated phenomena that would fall under the modern headings of iconic memory, short-term memory, and the enactment and generation effects, but this research has been neglected. Revisiting the Wundtian perspective may provide insight into some of the reasons behind the historical course of memory research and in general into the progress of science in psychology.     

Some problems concerning language and physics

We discuss three problems concerning the use of formal languages in theoretical physics: (i) the definability of time and spacetime in classical physical theories; (ii) how to cope with indistinguishable elementary particles in quantum mechanics without labeling them; and (iii) how to get a formal picture of quantum states jumping.     

Categories and causality: the neglected direction

The standard approach guiding research on the relationship between categories and causality views categories as reflecting causal relations in the world. We provide evidence that the opposite direction also holds: categories that have been acquired in previous learning contexts may influence subsequent causal learning. In three experiments we show that identical causal learning input yields different attributions of causal capacity depending on the pre-existing categories to which the learning exemplars are assigned. There is a strong tendency to continue to use old conceptual schemes rather than switch to new ones even when the old categories are not optimal for predicting the new effect, and when they were motivated by goals that differed from the present context of causal discovery. However, we also found that the use of prior categories is dependent on the match between categories and causal effect. Whenever the category labels suggest natural kinds which can be plausibly related to the causal effects, transfer was observed. When the categories were arbitrary, or could not be plausibly related to the causal effect learners abandoned the categories, and used different categories to predict the causal effect.     

The principle of reversibility: Some problems of interpretation

Summary and conclusion In summary, the question of how to construe the procedure called reversibility cannot be given an absolute answer. No one moral interpretation of the principle is universally applicable, that is, applicable to all moral issues. The decision concerning which to apply cannot be made a priori, but only in context - that is, only when we are faced with a particular moral problem. Moreover, there appears to be no rule which would enable us to choose which version is correct in a particular case. It is a matter of judgment.That the various versions represent a moral progression from lower to higher constructions is debatable. We have seen that the altruism of reversibility₃ - the ethic of care - may recommend itself in some personal relations to the point of making either version of reversibility₄ irrelevant. Similarly, it is not clear that reversibility₃ is always higher than reversibility₂. For example, parents in trying to decide what is morally best for a young child should often - in the spirit of the second construction - substitute the judgment of their mature selves for the judgment of the immature self of the child. Moreover, this substitution may not be justifiable in terms of either utility or autonomy.If I seem to have ignored reversibility₁ in this discussion that is because I consider it outside morality: it is, if anything, a principle of self-interested calculation. If Baier is correct in holding that we teach children to think morally when we get them to take the standpoint of others, that requires, I believe, getting them beyond the stage of crude reciprocity. If Piaget and Kohlberg are correct in their developmental claims, we cannot immediately teach children reversibility₄ but must help them progress through the other two versions. There is some basis for thinking that children can transcend egoism and sympathize with others much earlier than Kohlberg allows - an important consideration in the development of a system of moral education. That point has been pursued by Michael Pritchard in his critique of Kohlberg. My point is a different one: even granting Kohlberg's theory of development (which asserts, for example, that a particular cognitive ability is required to think like a Kantian), it does not follow that the moral thinking which accompanies the highest cognitive stage is morally superior to the moral thinking which accompanies the lesser cognitive stages. That it is cognitively easier to master reversibility₃ than reversibility₄ does not settle the question of which is morally superior.Rather than arguing about which moral version of reversibility is morally best- a pointless debate if the desirability of a version is understood as contingent upon appropriateness with respect to context - we should instead celebrate the richness of the concept of reversibility. In teaching students the moral point of view by getting them to put themselves in another's place, we would not be asking them to master a rigid formula, but rather to be sensitive to the decisional context and to make a thoughtful judgment about which version of reversibility is most appropriate to that context. We would not be teaching them either moral relativism or moral absolutism, but the complexity of trying to make a moral decision by applying an ancient and philosophically rich ethical principle.

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Some problems in forensic assessment

The establishing of facts in criminal cases calls for the marshalling of evidence, from every angle and without bias, in strict compliance with the law. The findings of the court in respect of criminal accountability must likewise be established beyond doubt; probability is inadequate as a basis for conviction. The highest degree is inadequate as a basis for conviction. The highest degree of forensic competence in matters psychiatric and psychological must be assured. Expert opinion must proceed from an evaluation of the accused person's capacity to distinguish between right and wrong, taking account of the nature of the offense. Part of this evaluation consists in the determination of the combined effect of the principal determining factors. Greater depth of knowledge is required respecting the part played by alcohol in the capacity to distinguish right from wrong compared with impulse, mental deficiency, grave abnormal development, etc. In the interests of securing a sound judgment of criminal accountability, further research is desirable into the complexus of determining factors, for example, into the multifunctional contribution of deranged physiological structures and processes which take a mental and/or psychopathological course.     

Some problems of Wilson's disease

The Leipzig Center for Wilson's Disease in the GDR is charged with the registration and diagnosis of all homozygous Wilson gene carriers, the clarification of all suspected cases, including the heterozygote test, and the co-ordination of long-term treatment. At present, there are 78 recorded Wilson gene carriers living. On the basis of our own comprehensive observations and investigations over prolonged periods of time, questions concerning pathogenesis, genetics, diagnosis and therapeutic measures, including their side-effects, are dealt with.     

Some representation problems for semiorders

Suppose we have a number representation of a semiorder 〈A, P〉 such that aPb iff f(a)+δ(a) < f(b), for all a, b ∈ A, where δ is a nonnegative function describing the variable jnd. Such an f (here called a closed representation) may not preserve the simple order relation $\text{R}{}^1$ generated by 〈A, P〉, i.e., $\text{aR}{}^1\text{b}$ but f(a) > f(b) for some f, δ and a, b ∈ A. We show that this “paradox” can be eliminated for closed and closed interval representations. For interval representations it appears to be impossible. That is why we introduce a new type of representation (an R-representation) which is of the most general form for number representations that preserve the linear structure of the represented semiorders. The necessary and sufficient condition for an R-representation is given. We also give some independent results on the semiorder structure. Theorems are proved for semiorders of arbitrary cardinality. The Axiom of Choice is used in the proofs.     

Some problems for Gibbard's norm-expressivism

Conclusion I conclude that Gibbard fails to solve several of the traditional problems for expressivism. He solves some of these problems, but his solutions to them in effect give up expressivism. Of course, one might respond that it does not really matter whether his theory is expressivist. In some ways, I agree. Gibbard says many fascinating things about morality which have at most indirect connections to his expressivist analysis. I am thinking especially of his later discussions of hyperscepticism (180), parochialism (203 ff.), and indirect pragmatism (224). These views could still be developed even if he gave up expressivism. All I have tried to show here is that he does need to give up expressivism unless he can solve the problems that I have raised.