Model selection is a complicated matter in science, and psychology is no exception. In particular, the high variance in the object of study (i.e., humans) prevents the use of Popper’s falsification principle (which is the norm in other sciences). Therefore, the desirability of quantitative psychological models must be assessed by measuring the capacity of the model to fit empirical data. In the present paper, an error measure (likelihood), as well as five methods to compare model fits (the likelihood ratio test, Akaike’s information criterion, the Bayesian information criterion, bootstrapping and cross-validation), are presented. The use of each method is illustrated by an example, and the advantages and weaknesses of each method are also discussed.