Is it a good idea to use log scale on scree plots for PCA/ICA/FA? I always found the concept of determining the "ideal" number of components/factors for an ICA/PCA/FA via a scree plot useful and quick, but also a bit shaky.
In an effort to try to make the scree plot "elbow" more obvious (and without trying to fit a function to the scree plot data points). I was thinking whether plotting on log-scale coordinates might help shed some light.
 
The non-log plot (first from the left) is pretty bunched up, but it's as "obvious" as it gets with scree plots that the third factor is the elbow (and thus my ideal number of factors should be 3).
Now, it also seems that whether my log scale is in base 2 or 10 makes little difference for the plot appearance - which I guess is good.
Lastly, I find that the X/Y log plots show the most quaintness for the 3rd factor, making it the point where 2 types of "curves" in the plot meet. I also think this feature stands out better here than in the first (linear) plot.
Is it safe to assume this is always the case? Is it worth recommending to use X/Y log coordinates for scree plots? 
 A: Summary: I think that converting y-axis to log scale often works the best, in your example as well.
Continuing what has already been said in the comments above: The main idea of looking at the spectrum (also known as scree plot, but I am not used to factor analysis and am not a big fan of its terminology) to identify the number of significant components, is to see how many eigenvalues "stand out" of the "bulk". Therefore, for example, looking at your first plot, I would definitely conclude that the answer is two, and not three.
Does it make sense to transform the spectrum in any way? I would say yes, but only if it helps achieving the above goal, i.e. makes it more obvious which eigenvalues stand out. The first (untransformed) plot is suboptimal, because one simply cannot see anything starting with the third eigenvalue, so there is definitely room for improvement.
Looking at your plots, I would say that transforming eigenvalues (y-axis) to log scale works the best, and in particular better than the log-log plot, mainly because the "bulk" of the spectrum becomes nicely linear, and makes it easy to see how many eigenvalues are strongly above this linear trend (answer: two definitely, but maybe three).
Interestingly, linear trend on a log-plot corresponds to exponential decay, and this is something I have observed myself in many different datasets. The reason for this is not entirely clear to me; please check my answer in Eigenvalues of correlation matrices exhibit exponential decay -- there is an expression for the spectrum of a random covariance matrix, but it is not given by an exponential and I am not exactly sure why exponential function gives such a good approximation. Still, it seems to be the case.
