Effect Separation in Regression Models with Multiple Scales
von Hauke Thaden
Datum der mündl. Prüfung:2017-05-17
Betreuer:Prof. Dr. Thomas Kneib
Gutachter:Prof. Dr. Thomas Kneib
EnglischConfounding problems in regression analysis arise when one or more third variables are simultaneously associated with both the covariates and the response variables under consideration. Even when these confounders are included in the modeling process, standard regression models usually fail at separating the corresponding effects due to the complex correlation structure. Third variables inducing similar spatial structure within covariates and responses constitute the special case of spatial confounding, which is at the core of this dissertation. Existing methods for alleviating the resulting estimation bias are based on the orthogonalization of spatial and covariate information. Using this approach, the effect of the covariate of interest is clearly identified, but the estimates for the spatial components are restricted and thus hard to interpret. Adapted from the framework of simultaneous equation models, this dissertation provides a fully interpretable model class for dealing with spatial confounding. Besides its applicability in spatial statistics, additional flexibility of the methodology presented here is achieved by incorporating alternative effect types such as nonlinear or cluster-specific random effects. These extensions further enhance the applicability of the newly introduced model class which is illustrated for various research fields such as economics, health and ecology.
Keywords: Structural Equation Models; Spatial Statistics; Spatial Confounding; Statistical Identification; Semiparametric SEM