FACULTY OF

MATHEMATICS

The main aim of the present project is the development of optimal designs for Thurstonian IRT modes in the case of metric, binary, or ordinal responses which provide a sufficiently good estimation of the trait scores. In addition, binary paired comparisons will be considered which are derived from ranking more than two alternatives. In the present situation, optimal designs are characterized by combinations of those values of item parameters, factor loadings and intercepts which optimize prior determined criteria, as correlation between estimated and true trait scores. In order to apply these models in the selection of personnel, only positive factor loadings are admitted. This condition is supported by simulation studies and requires the development of novel types of optimal designs. Beyond properties of optimal designs developed in the literature so far, three more requirements have to be particularly taken into account: (a) the specific form of the non-linearity, (b) the restriction of the design region, and © the constraint that alternatives have to load on mutually distinct factors, respectively. To implement the findings of the project in practical applications, a user-friendly program in R is to be developed using a shiny app.

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Grant number: NIHRDH-PB-PG-0817-20031. Osteoarthritis (OA) is a common, debilitating and painful condition, particularly when patients move the affected joint. Core-management approaches (exercise and weight control) reduce pain and improve function, but exercise-induced pain creates anxiety and confusion about such self-management. Common, unhelpful, misconceptions about OA exist and currently professionals do not have the language to explain OA in a way that reflects current scientific understanding. The overarching aim of the project is to improve OA explanations through the development and implementation of a multimedia Patient Explanation Package (PEP-OA). A partial-profile conjoint analysis study with patients will estimate the extent to which new, prioritised, explanation statements are preferred over currently used/available statements. Suitable OA explanations identified in this study will be used in the further development of the multimedia package. The corresponding work package requires the development of an efficient experimental design for the choice experiment which will be carried out at the University of Magdeburg.

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Bestimmte neurologische Erkrankungen beeinträchtigen die Gehfähigkeit der betroffenen Individuen. In diesem Projekt werden Verfahren der funktionalen Datenanalyse entwickelt, um Daten zu analysieren, die mit Hilfe bildgebender Verfahren in einem Ganglabor bei Kindern und Jugendlichen erhoben werden. Im angewandten Teil des Projekts wird unter anderem untersucht, wie sich bestimmte medizinische Hilfsmittel (Orthesen) auf das Gehverhalten auswirken.

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Generalized linear models with fixed and random effects offer an elegant way to model dependent observations. When estimating the model parameters, it is usually assumed that the random parameters have a multivariate normal distribution. In this project, an alternative approach is considered that is particularly suitable for small sample sizes, in which, as usual, the conditional distribution of the dependent variable belongs to the exponential family for given values of the random parameters, but the distribution of the random effects is derived from randomization considerations. An estimation algorithm is developed for the resulting semi-parametric model. Furthermore, simulation studies are used to numerically investigate how violations of the normal distribution assumption affect the estimates.
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