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This study develops a computationally efficient and statistically consistent learning algorithm for large-scale Gaussian linear structural equation models with equal error variances. The novelty of the proposed algorithm is that it applies a hypothesis test rather than a score when recovering the directions of the edges. Specifically, the proposed algorithm estimates the topological layers using a Z-test. Subsequently, it estimates the parents of each node using a consistent conditional independence test. This study proves that the proposed topological layer estimation approach is asymptotically consistent. It further shows that the proposed method is computationally more efficient than existing score-based algorithms for Gaussian linear SEMs by comparing the computational complexities. It is confirmed through synthetic and real-world data that the proposed algorithm is consistent and computationally much faster than the state-of-the-art large-scale Gaussian linear SEM learning algorithms, such as the USF, USB, TD, and HGSM algorithms.  Supplementary materials  for this article are available online.

Computationally Efficient Learning of Gaussian Linear Structural Equation Models with Equal Error Variances