As can be seen from the expression above, a model with a smaller AIC is preferable: we want the fit to be optimal at little cost in complexity. Notice that the number of dimensions, or independent parameters, in the model increases the AIC and thereby lowers the eligibility of the model: if two models achieve the same maximum likelihood for the sample, then the model with fewer parameters will be preferred. For this reason, statistical model selection by the AIC can be seen as an independent motivation for preferring simple models over more complex ones (Sober and Forster 1994). But this result also invites some critical remarks. For one, we might impose other criteria than merely the unbiasedness on the estimation of the proximity to the truth, and this will lead to different expressions for the approximation. Moreover, it is not always clearcut what the dimensions of the model under scrutiny really are. For curve fitting this may seem simple, but for more complicated models or different conceptualizations of the space of models, things do not look so easy (cf. Myung et al 2001, Kieseppa 2001). 