Wireless systems exhibit a wide range of configurable parameters (factors), each with a number of values (levels), that may influence performance. Exhaustively analyzing all factor interactions is typically not feasible in experimental systems due to the large design space. We propose a method for determining which factors play a significant role in wireless network performance with multiple performance metrics (response variables). Such screening can be used to reduce the set of factors in subsequent experimental testing, whether for modelling or optimization. Our method accounts for pairwise interactions between the factors when deciding significance, because interactions play a significant role in real-world systems. We utilize locating arrays to design the experiment because they guarantee that each pairwise interaction impacts a distinct set of tests. We formulate the analysis as a problem in compressive sensing that we solve using a variation of orthogonal matching pursuit, together with statistical methods to determine which factors are significant. We evaluate the method using data collected from the w-iLab.t Zwijnaarde wireless network testbed and construct a new experiment based on the first analysis to validate the results. We find that the analysis exhibits robustness to noise and to missing data.