In design of advanced heterogeneous materials system, microstructures play an important role as a link between processing and material properties. An accurate and efficient representation of material microstructures is necessary. Our prior work applied a supervised ranking algorithm to identify key microstructure descriptors, however the approach falls short in identifying redundancy in descriptors and is not reliable when the training sample size is small. In this paper, we propose a Structural Equation Modeling (SEM) based approach to identify significant microstructure descriptors based on either correlation functions (CF) or material properties, or both. By building a reflective structural model, we are able to deal with high correlations among all candidate descriptors, gain more insights into their relations, and identify latent factors for categorizing microstructure features. The proposed approach begins with an Exploratory Factor Analysis (EFA) for grouping and reducing descriptors to determine the proper structure of microstructure descriptors as indicators of latent factors. The SEM analysis is then applied to identify the key descriptors using the Partial Least Squares (PLS) algorithm. The nanodielectric system with epoxy-nanosilica is used as an example to illustrate and validate the proposed approach. The potential use of identified key microstructure descriptors for optimal design of microstructural materials is discussed.