Evaluating Equating Transformations in IRT Observed-Score and Kernel Equating Methods

Test equating is a statistical procedure to ensure that scores from different test forms can be used interchangeably. There are several methodologies available to perform equating, some of which are based on the Classical Test Theory (CTT) framework and others are based on the Item Response Theory (IRT) framework. This article compares equating transformations originated from three different frameworks, namely IRT Observed-Score Equating (IRTOSE), Kernel Equating (KE), and IRT Kernel Equating (IRTKE). The comparisons were made under different data-generating scenarios, which include the development of a novel data-generation procedure that allows the simulation of test data without relying on IRT parameters while still providing control over some test score properties such as distribution skewness and item difficulty. Our results suggest that IRT methods tend to provide better results than KE even when the data are not generated from IRT processes. KE might be able to provide satisfactory results if a proper pre-smoothing solution can be found, while also being much faster than IRT methods. For daily applications, we recommend observing the sensibility of the results to the equating method, minding the importance of good model fit and meeting the assumptions of the framework

eXeRCISeS FOR PAReTIC UPPeR LIMb AFTeR STROKe: A COMbINeD VIRTUAL-ReALITY AND TeLeMeDICINe APPROACH

Objective: Telerehabilitation enables a remotely controlled programme to be used to treat motor deficits in post-stroke patients. The effects of this telerehabilitation approach were compared with traditional motor rehabilitation methods. Design: Randomized single-blind controlled trial. Patients: A total of 36 patients with mild arm motor impairments due to ischaemic stroke in the region of the middle cerebral artery. Methods: The experimental treatment was a virtual realitybased system delivered via the Internet, which provided motor tasks to the patients from a remote rehabilitation facility. The control group underwent traditional physical therapy for the upper limb. Both treatments were of 4 weeks duration. All patients were assessed one month prior to therapy, at the commencement and termination of therapies and one month post-therapy, with the Fugl-Meyer Upper Extremity, the ABILHAND and the Ashworth scales. Results: Both rehabilitative therapies significantly improved all outcome scores after treatment, but only the Fugl-Meyer Upper Extremity scale showed differences in the comparison between groups. Conclusion: Both strategies were effective, but the experimental approach induced better outcomes in motor performance. These results may favour early discharge from hospital sustained by a telerehabilitation programme, with potential beneficial effects on the use of available resources

On the exercise of American quanto options

American option pricing is an important and engaging area of financial economics, particularly so in the presence of negative interest rates. Quanto options offer major international hedging/investment opportunities. We provide a comprehensive description of the optimal exercise policies associated with American quanto options. We show that a non-standard exercise policy characterized by a double continuation region may be optimal in the presence of non-positive domestic interest rates. We study empirical examples of finite-maturity American quanto options for which a double continuation region surrounding a non-empty early exercise region exists even if the infinite-maturity early exercise region is empty and the value of the infinite maturity option is unbounded. Under the assumptions underpinning such empirical examples, we carefully characterize the existence, the monotonicity properties and the close-to-maturity behaviour of the upper and lower critical prices

Risk tolerance levels for insurance companies

We describe two procedures that assist insurance firms in determining shareholders' risk tolerance thresholds and in using such thresholds within the decision-making process. The first procedure is based on parsimonious measures of the risk/return tradeoff such as the Sharpe Ratio; the second procedure makes a direct use of expected utility theory

Optimal exercise of American put options near maturity: A new economic perspective

The critical price S∗(t) of an American put option is the underlying stock price level that triggers its immediate optimal exercise. We provide a new perspective on the determination of the critical price near the option maturity T when the jump-adjusted dividend yield of the underlying stock is either greater than or weakly smaller than the riskfree rate. Firstly, we prove that S∗(t) coincides with the critical price of the covered American put (a portfolio that is long in the put as well as in the stock). Secondly, we show that the stock price that represents the indifference point between exercising the covered put and waiting until T is the European-put critical price, at which the European put is worth its intrinsic value. Finally, we prove that the indifference point’s behavior at T equals S∗(t) ’s behavior at T when the stock price is either a geometric Brownian motion or a jump-diffusion. Our results provide a thorough economic analysis of S∗(t) and rigorously show the correspondence of an American option problem to an easier European option problem at maturity

Applying modern psychometric techniques to melodic discrimination testing: Item response theory, computerised adaptive testing, and automatic item generation

Modern psychometric theory provides many useful tools for ability testing, such as item response theory, computerised adaptive testing, and automatic item generation. However, these techniques have yet to be integrated into mainstream psychological practice. This is unfortunate, because modern psychometric techniques can bring many benefits, including sophisticated reliability measures, improved construct validity, avoidance of exposure effects, and improved efficiency. In the present research we therefore use these techniques to develop a new test of a well-studied psychological capacity: melodic discrimination, the ability to detect differences between melodies. We calibrate and validate this test in a series of studies. Studies 1 and 2 respectively calibrate and validate an initial test version, while Studies 3 and 4 calibrate and validate an updated test version incorporating additional easy items. The results support the new test’s viability, with evidence for strong reliability and construct validity. We discuss how these modern psychometric techniques may also be profitably applied to other areas of music psychology and psychological science in general

IRT Test Equating in Complex Linkage Plans

Linkage plans can be rather complex, including many forms, several links, and the connection of forms through different paths. This article studies item response theory equating methods for complex linkage plans when the common-item nonequivalent group design is used. An efficient way to average equating coefficients that link the same two forms through different paths will be presented and the asymptotic standard errors of indirect and average equating coefficients are derived. The methodology is illustrated using simulations studies and a real data example