Structural Equation Modeling using Computation Graphs
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Structural equation modeling (SEM) is evolving as available data is becoming more complex, reaching the limits of what traditional estimation approaches can achieve. As SEM expands to ever larger, more complex applications, the estimation challenge grows and currently available methods will be insufficient. To overcome this challenge in SEM, we see an opportunity to use existing solutions from the field of deep learning, which has been pioneering methods for estimation of complex models for decades. To this end, this paper introduces computation graphs, a flexible method of specifying objective functions. When combined with state-of-the-art optimizers, we argue that our computation graph approach is capable not only of estimating SEM models, but also of rapidly extending them -- without the need of bespoke software development for each new extension. We show that several SEM improvements follow naturally from our approach; not only existing extensions such as least absolute deviation estimation and penalized regression models, but also novel extensions such as spike-and-slab penalties for sparse factor analysis. By applying computation graphs to SEM, we hope to greatly accelerate the process of developing SEM techniques, paving the way for novel applications. The accompanying R package tensorsem is under active development.
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