This paper deals with multidimensional ICA and its performance analysis, applied to cosmological observations. Our purpose is the separation of the cosmic microwave background radiation from the Galactic emission, in a noise-free setup, using a model of correlated sources. Since the Galactic emission does not obey this model, we propose a method to select the effective model order. As there are more detectors than signal-space dimensions, a dimension reduction scheme is derived. Our simulations show a good match between the closed-form analytical expression for the error and its empirical counterpart. This analytical expression is compact and involves inversions only of small matrices. Therefore, it can serve as a reliable predictor of the separation error without resorting to exhaustive Monte-Carlo trials.