Here I think you misread my earlier post. What I actually asked was: I guess now what I'd love to know now is how Olive arrived at each of the formulae defining each of the parameters. Did he use a kind of intuitive trial and error? Did he design an algorithm that did it (I presume not)? Was some other process involved?
Ah, apologies. English is hard
The paper states the
weights were obtained through
Principal Component Analysis (PCA). However, the variables used (NBD, SM, etc.), and, to a lesser extent, the curves used, seem somewhat arbitrary. My best guess is that Olive just designed a few metrics on his own and then ran PCA on them. That's fine as long as the model works, but I definitely wish he had spent a bit more time refining the variables. Besides the weirdness of SM, there are a few other things that are eyebrow-raising, such as NBD using arbitrary, fixed 1/2 octave-band averages instead of something like a smooth moving average (detrending).
Given steepness of slope positively affects SM_PIR while negatively affecting NBD_PIR, surely this would imply a maximum possible preference rating that is in fact below 10. Which seems particularly counter-intuitive given that the preference rating is "out of" 10.
Perhaps you could share the formulae? Presumably the maximum rating can be deduced from the relationship between the formulae (although I'm almost certainly not the person to work out mathematically what it is).
One would be hard pressed to figure out exactly how NBD_PIR and SM_PIR interact together: the first variable is an average of averages defined over non-continuous arbitrary ranges and uses absolute deviation; SM_PIR is a ratio of a sum of squares, one of which is from a least-squares linear regression, defined over a slightly different frequency range. Good luck trying to model how they interact without running simulations or something. This is why the PIR model variables are so head-banging when it comes to interpretation.
Actually
@napilopez, I just remembered that Olive gives the target slopes for the top-rated speakers from the sample in the study. [...] it was these target slope values that the model was based upon in the first place.
The model was not "based upon" these target slopes. The target slopes are only used to define the SL variable. SL didn't make it into the final model after Olive ran PCA. The target slope values are not relevant to the final model. That doesn't mean these numbers aren't useful for discussion though.
If you plug the slope values for NBD_PIR, SM_PIR and NBD_ON from the "All Tests" column into the equation on the right and ignore LFX, you should end up with a the slopes that achieve the best possible rating
You can't "plug the slope values into the equation on the right". That equation is supposed to represent the best-fit linear regression line on the data.
a and
b are
outputs of the linear regression process, not inputs. Once the regression line is fitted,
then its
b is compared to the target
b, and the distance between the two is defined as SL.
In another thread
@MZKM and I just had a
detailed debate on how SL,
b and slope values work.
But I cannot follow the discussion, because the whole apparatus of formulas is hidden behind the counter of AES. Would You mind to link a free source for the formulas?
In addition to the AES paper, the model is also described in
this patent which has a freely available PDF. It doesn't quite use the same phrasing and it's slightly more confusing than the paper because it uses lawyery patent language, but it's pretty close.
