Selektieren und Kombinieren von Modellen unter Berücksichtigung der Problematik fehlender Daten (English shop)

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In recent years, model averaging procedures have become established as an alternative to model selection. Instead of restricting oneself to a single winning model, several competing models are considered and their parameter estimators are combined in a weighted fashion. The main focus is usually on the construction of the weights as well as on the optimality of the resulting weighted parameter estimation.

The present work explains various concepts of frequentist model averaging (FMA) and highlights their strengths and weaknesses compared with a large number of traditional model selection methods. The emphasis lies on the construction and discussion of different strategies for the use of FMA methods while taking into account the problem of missing data. Two core concepts are proposed for this purpose: the first approach constructs weights for an FMA estimator on the basis of a criterion adjusted for missing data, which stems from the current literature in the field of model selection and which employs the principle of inverse probability weighting known from the context of missing values; the second approach replaces the missing values by imputations in order to construct suitable estimates on this basis using established model averaging approaches. To this end, a recursive imputation algorithm is also presented that generalises the common idea of a regression imputation using generalised additive models.

The work reveals the peculiarities, strengths and weaknesses of the presented approaches in the context of linear and logistic regression analyses by means of extensive Monte Carlo simulations and discusses, using the example of factor analysis, possible extensions and generalisations of the estimators presented to further multivariate statistical methods of analysis. All procedures are illustrated on real data sets.

It turns out that in many situations both concepts presented are preferable to discarding the incomplete observations, that the strategy of model averaging after imputation as a rule achieves better results than the use of an FMA estimator that employs weights based on a criterion adjusted for missing data, and that in particular the technically less demanding model averaging procedures lead to better estimates than those resulting from classical model selection.