We used a large convenience sample (n=22,228) from the Simons Powering Autism Research (SPARK) dataset to causal, explanatory theories of autism positing a key role of imitation ability within the same, large sample. We used a highly theory-constrained approach, formalizing statistical models based on the proposals of Ornitz & Ritvo (1968), Rogers & Pennington (1991) and Mostofsky & Ewen (2011). Results disconfirmatory for the accounts of Rogers & Pennington and Mostofsky & Ewen, however limitations of the convenience sample affected the strength of the inference. While the results did not disconfirm the tested portions of Ornitz & Ritvo’s model linking sensory-motor function with social engagement and language, they did entail that other mechanisms must also be in play.