The present paper discusses the relationship between the traditional factor analytic model and stochastic models of test behaviour for the case of dichotomous manifest variables. It is shown that the factor loadings can be interpreted as parameters of item trace lines. Furthermore, by comparing a linear and a nonlinear model of item characteristics, it is suggested that the assumption of a small number of latent dimensions or factors (small in comparison to the number of manifest variables) always requires the estimation of communalities making the explicit conceptualization of specific factors unnecessary. In addition, it is indicated that, because of the arbitrariness of criteria for the number of common factors, the general tendency among researchers to extract a small number of latent dimensions will, for a given data set, lead to quite similar results regardless of the trace line model chosen.