The identification of the current state in the business cycle and the forecast of the next quarters do not only receive a lot of attention in the public, they are also of prime importance for the plans of firms and the government. The most important leading indicator for the German economy is the ifo Business Climate Index that is based on a monthly business survey with more than 7,000 respondents. Due to the large number of firms, the results can be analysed at a disaggregate level for the different sectors, firms and response categories. Thus, it is possible to use a panel of sector-specific survey indices in order to forecast the sectoral gross value added or to examine whether they are leading important aggregate variables like total gross value added or gross domestic product (GDP).

• Are there sectors or firms that have stable leading properties to the target series?
• Are there interactions between sectors or firms that attenuate or intensify the original signal?
• What is the delay with which firms react to macroeconomic impulses? Which explanations can be found?

Due to the large number of possible lead-lag relationships and the additional difficulty of time-varying structures it seems necessary to pre-select factors that are relevant for the question of interest. Modern selection methods such as parametric and nonparametric boosting or random forests will be adapted to the problem at hand.

The modelling of sojourn time is crucial for grasping the dynamics of response behavior in panel surveys. Particularly the Ifo Business Survey, which is conducted monthly among 7,000 participating firms, is an excellent basis for the analysis of nonresponse behaviour in business surveys because it can build on an enormous data set. The main research tasks that can be answered by means of business surveys concern nonresponse behavior and expectations at the firm level. Nonresponse considerably influences the stability of the data and can create a bias in the results. While severals analyses of the issue are available for individual and houshold surveys, there is little research on processes and sources of compliance in business surveys. The main factors responsible for "panel fatigue", i.e. a decreasing compliance over time, can be used to improve the quality and uncover present selectivity. At the firm level, the analysis of expectations is of special interest, particularly because current macroeconomic models emphasize the importance of expectations to explain business cycle dynamics. However, it often turns out empirically that the standard assumption of rational expectations does not hold. Since the surveys of the Ifo Institute also contain expectational categories, they allow a deeper analysis of the process of expectation formation. An interesting question is in how far current expectations correlate and interact with previous expectations and other response categories, especially with future realizations.

Methodological problems for the Ifo data arise from the fact that the responses of the enterprises are given in categorical form (e.g., “better”, “unchanged”, “worse”). In the corresponding competing risk approaches, the question needs to be evaluated whether the monthly survey allows for discrete or continuous modelling. In general, the empirical analysis of sojourn time data often shows that the effect of influencing variables varies over time. Ignoring these effects often results in artificial effect sizes and reduced prediction accuracy. In order to model these variations adequately, it is necessary to incorporate time-varying effects in nonparametric form. This leads to severe selection problems: which variables should be modelled parametrically to be time-constant and which nonparametrically to be time-varying? The selection problems are to be solved by means of modern selection techniques like the Lasso and Boosting. Especially the generalization to multi-state models and the modelling of heterogeneity are of substantial interest for the intended analysis of the Ifo business survey as well as other econometric and sociological surveys.

Item Response Theory (IRT) is one of last century's most important achievements of psychological diagnosis and empirical educational research: It allows for an objective measurement of latent person characteristics by means of separating item and person parameters. Moreover, as opposed to the classical psychological measurement theory, IRT provides the opportunity to statistically test the model assumptions. The Rasch model, which has been used in the PISA-study, is the most well-known IRT model.

In an intervention study on the effectiveness of competence-supporting learning environments the Rasch model was emplyed to measure mathematical comptetency for using diagrams and models in statistical contexts. In this study, both the objective measurement of the students' competencies and the modelling of the treatment effects is of major interest. Methodological challenges arise from the heterogeneity of the sample: The data have a hierarchical structure, because students are grouped in classes, classes in schools and so forth. Moreover it is necessary to check whether the measures are comparable for students from different groups, or if differential item functioning occurs.

The aim of the project is to develop and apply new IRT Methods to account for the sample heterogeneity: For the diagnosis of differential item functioning methods from machine learning will be used in combination with latent-class-approaches. The hierarchical data structure will be accounted for by means of mixed models.