Item-response theory forms a theoretical framework for scaling latent person characteristics. The most widely known representative of item-response theory is the Rasch model for measuring performance and competencies, but also attitudes. The central characteristic of the Rasch model, the specific objectivity of the measurements, allows objective and fair comparisons between subjects, as long as the assumptions underlying the model hold - which is, however, not necessarily the case in practice. If you consider, for example, a test designed for measuring mathematical competency, a verbally stated test item can be harder to solve for students for whom the test language is a second language, even if they have the same mathematical competency. Such a test item, that shows so called differential item functioning, can lead to biased test results and does not permit fair comparisons between the students. Therefore, in our workgroup statistical methods for identifying test items with differential item functioning as well as the affected groups are developed. These methods are based on modern approaches from parametric statistics and machine learning, such as mixture distribution models and recursive partitioning. By means of these methods problematic items can be excluded or modified by means of the additional information on the affected groups already in the test construction phase.
When scaling preferences, that are investigated in paired comparison experiments, there can also be systematic differences between various groups of subjects, that can be of great interest for psychological research but also, e.g., for marketing purposes. In this context, too, both the stimuli affected by the different preferences as well as the description of the groups by means of psychological or sociodemographic characteristics or latent classes is relevant. From a methodological point of view, a particular challenge here is the separation of groups based on cutpoints in continuous variables, such as the separation of "younger" and "older" subjects based on their age. If this separation is, however, based on an arbitrarily chosen value, important information from the data is lost and possible group differences between other age groups may be overlooked. Therefore, special statistical procedures are necessary, that allow for the selection of an optimal cutpoint for separating the groups without increasing the statistical risk for a type 1 error.
In many areas among the social and life sciences the amount of data available for research has rapidly increased within the past years, for example due to the automatic recording of user data on the internet and the decreasing costs for evaluating genetic information. The resulting high-dimensional datasets pose a great challenge to classical statistical methods. In particular, traditional parametric models cannot be employed when the number of variables of interest is highter than the number of available observations - which is the case, e.g., when information on the expression of several thousands of genes is available for only a few hundred subjects. To address this problem, many new statistical methods have been developed in recent years, that are inspired by machine learning approaches from computer sciences and can detect hidden information, e.g. on the causes of psychological or physiological diseases, even in large amounts of data. However, the statistical properties of these methods are still largely unknown, which in some cases can lead to severe misinterpretations.
In our workgroup, such methods are therefore investigated with respect to their statistical properties and improved in a way that allows for a reliable application and interpretation of the resulting research findings. In this process many fundamental methodological questions are touched, such as die measurement of the importance of a predictor variable in models with several potentially correlated and interacting variables as well as the effects of randomly and non-randomly missing values on the importance of a variable. Some of the methods developed in international cooperations are already being widely applied in a variety of research areas, such as genetic association studies on the causes of diseases in humans and animals as well as the analysis of forest inventory data.