P1-4 Scaling Problems in Model Choice and Variable Selection
PhD student: Benjamin Säfken
Thesis Committee: Prof. Thomas Kneib, Prof. Tatyana Krivobokova, Dr. Christoph Scherber
Graduation Date: 3/2015
Thesis: online publication
This PhD project is concerned with developing methods, for model choice and variable selection in hierarchical models which allow data to be measured on different scales. Mixed models in particular have been widely used for analyzing this kind of data. Since regularity conditions are violated in these models standard methods known from likelihood based inference cannot be applied.
This also has an effect on the use of the Akaike Information Criteria (AIC) which is a measure for model selection. In linear mixed models there are two versions of the AIC. One is based on the marginal likelihood and the other based on the conditional likelihood. Since the first version is a biased estimator due to the open parameter space, the AIC based on the conditional likelihood is preferable. In specific models with normally distributed responses the conditional AIC can be derived analytically. The goal of this PhD project is to develop a conditional AIC for a broader class of models. In generalized linear mixed models the response is not necessarily normally distributed.
Therefore new methods have to be developed to obtain the conditional AIC in generalized linear mixed models without being too computationally expensive. For example bootstrap based methods for the estimation of the equivalent degrees of freedom.
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