Gaining a deep insight into the factors that influence product competition is essential for a company to maintain its competitiveness in the market. While many studies have been conducted on competition analysis of various products, existing work often has oversight of market heterogeneity. This makes the analysis of product competition less accurate, which could significantly influence many downstream product design decisions. To address this issue, this paper presents a network mining approach to support product competition analysis for engineering design. The approach investigates product competition (represented by co-consideration relations) networks at three different levels, including macro (competition within the entire market), meso (competitions happening between a small group of products), and micro (competitiveness of individual products) levels. In this approach, we first develop a network motif-based representation of individual products' competitiveness. Then, we use the Exponential Random Graph Model (ERGM) to study how the inclusion of such competitiveness measurement would influence products' co-consideration relations and improve the model's goodness-of-fit. This network mining approach is demonstrated in a case study on the household vacuum cleaner market, where heterogeneous customer preferences are pervasive. A multilevel network analysis of product competition provides a new way to quantify the competitiveness of a product in a heterogeneous market. It also helps quantify the importance of different competitive roles (e.g., competition within a brand or across brands) in forming co-consideration relations in the market.