We perform multi-photon direct laser writing as a function of laser repetition rate over many orders of magnitude and otherwise unchanged experimental conditions. These new data serve as basis for investigating the influence of different proposed mechanisms involved in the photopolymerization: two-photon absorption, photoionization, avalanche ionization and heat accumulation. We find different non-linearities for high and low repetition rates consistent with different initiation processes being involved. The scaling of the resulting linewidths, however, is neither expected nor found to depend on repetition rate or non-linearity.