“Models of data have a deep inﬂuence on the kinds of theorising that researchers do. A structural equation model with latent variables named Shifting, Updating, and Inhibition (Miyake et al. 2000) might suggest a view of the mind as inter-connected Gaussian distributed variables. These statistical constructs are driven by correlations between variables, rather than by the underlying cognitive processes […]. Davelaar and Cooper (2010) argued, using a more cognitive-process-based mathematical model of the Stop Signal task and the Stroop task, that the inhibition part of the statistical model does not actually model inhibition, but rather models the strength of the pre-potent response channel. Returning to the older example introduced earlier of g (Spearman 1904), although the scores from a variety of tasks are positively correlated, this need not imply that the correlations are generated by a single cognitive (or social, or genetic, or whatever) process. The dynamical model proposed by van der Mass et al. (2006) shows that correlations can emerge due to mutually beneﬁcial interactions between quite distinct processes.”
Fugard, A. J. B & Stenning, K. (2013). Statistical models as cognitive models of individual differences in reasoning. Argument & Computation, 4, 89–102.