Extended feature models enable the expression of complex cross-tree constraints involving feature attributes. The inclusion of attributes in cross-tree relations not only enriches the constraints, but also engenders an extended type of variability that involves attributes. In this article, we elaborate on the effects of this new variability type on feature models. We start by analyzing the nature of the variability involving attributes and extend the definitions of the configuration and the product to suit the emerging requirements. Next, we propose classifications for the features, configurations, and products to identify and formalize the ramifications that arise due to the new type of variability. Then, we provide a semantic foundation grounded on constraint satisfaction for our proposal. We introduce an ordering relation between configurations and show that the set of all the configurations represented by a feature model forms a semilattice. This is followed by a demonstration of how the feature model analyses will be affected using illustrative examples selected from existing and novel analysis operations. Finally, we summarize our experiences, gained from a commercial research and development project that employs an extended feature model.