  Trees are a special sub-class of networks with unique properties, such as the
level distribution which has often been overlooked. We analyse a general tree
growth model proposed by Klemm {\em et. al.} (2005) to explain the growth of
user-generated directory structures in computers. The model has a single
parameter $q$ which interpolates between preferential attachment and random
growth. Our analysis results in three contributions: First, we propose a more
efficient estimation method for $q$ based on the degree distribution, which is
one specific representation of the model. Next, we introduce the concept of a
level distribution and analytically solve the model for this representation.
This allows for an alternative and independent measure of $q$. We argue that,
to capture real growth processes, the $q$ estimations from the degree and the
level distributions should coincide. Thus, we finally apply both
representations to validate the model with synthetically generated tree
structures, as well as with collected data of user directories. In the case of
real directory structures, we show that $q$ measured from the level
distribution are incompatible with $q$ measured from the degree distribution.
In contrast to this, we find perfect agreement in the case of simulated data.
Thus, we conclude that the model is an incomplete description of the growth of
real directory structures as it fails to reproduce the level distribution. This
insight can be generalised to point out the importance of the level
distribution for modeling tree growth.
