We present a novel data-driven Parametric Linear Blend Skinning (PLBS) model meticulously crafted for generalized 3D garment dressing and animation. Previous data-driven methods are impeded by certain challenges including overreliance on human body modeling and limited adaptability across different garment shapes. Our method resolves these challenges via two goals: 1) Develop a model based on garment modeling rather than human body modeling. 2) Separately construct low-dimensional sub-spaces for modeling in-plane deformation (such as variation in garment shape and size) and out-of-plane deformation (such as deformation due to varied body size and motion). Therefore, we formulate garment deformation as a PLBS model controlled by canonical 3D garment mesh, vertex-based skinning weights and associated local patch transformation. Unlike traditional LBS models specialized for individual objects, PLBS model is capable of uniformly expressing varied garments and bodies, the in-plane deformation is encoded on the canonical 3D garment and the out-of-plane deformation is controlled by the local patch transformation. Besides, we propose novel 3D garment registration and skinning weight decomposition strategies to obtain adequate data to build PLBS model under different garment categories. Furthermore, we employ dynamic fine-tuning to complement high-frequency signals missing from LBS for unseen testing data. Experiments illustrate that our method is capable of modeling dynamics for loose-fitting garments, outperforming previous data-driven modeling methods using different sub-space modeling strategies. We showcase that our method can factorize and be generalized for varied body sizes, garment shapes, garment sizes and human motions under different garment categories.