Ivancevic_Applied-Diff-Geom

324 Applied Differential Geometry: A Modern IntroductionThis is obtained by maximizing the log–likelihood of the observed data:m∑loglik (w) = ln f(y i |w).i=1By maximizing either the likelihood or the log–likelihood, the same solutionis obtained because the two are monotonically related to each other.In practice, the log–likelihood is preferred for computational ease. The parametersthat minimize the sum of squares error or the log–likelihood arecalled the LSE or MLE estimates, respectively.For normally distributed data with constant variance, LSE and MLEare equivalent in the sense that both methods yield the same parameterestimates. For non–normal data such as proportions and response times,however, LSE estimates tend to differ from MLE estimates. Although LSEis often the ‘de facto’ method of estimation in cognitive psychology, MLEis a preferred method of estimation in statistics, especially for non–normaldata. In particular, MLE is well–suited for statistical inference in hypothesistesting and model selection. Finding LSE or MLE estimates generallyrequires use of a numerical optimization procedure.3.11.4.2 Model Evaluation and TestingQualitative CriteriaA model satisfies the explanatory adequacy criterion if its assumptionsare plausible and consistent with established findings, and importantly, thetheoretical account is reasonable for the cognitive process of interest. Inother words, the model must be able to do more than redescribe observeddata. The model must also be interpretable in the sense that the modelmakes sense and is understandable. Importantly, the components of themodel, especially, its parameters, must be linked to psychological processesand constructs. Finally, the model is said to be faithful to the extent thatthe model’s ability to capture the underlying mental process originatesfrom the theoretical principles embodied in the model, rather than fromthe choices made in its computational instantiation.3.11.4.3 Quantitative CriteriaFalsifiabilityThis is a necessary condition for testing a model or theory, refers towhether there exist potential observations that a model cannot describe [Pop-