Clutch Hits - True Talent Levels (January 22, 2004)
I make yet another post in the PECOTA thread, this time regarding a term that I define as "true talent".
--posted by TangoTiger at 10:05 PM EDT
Posted 4:11 p.m.,
January 24, 2004
(#1) -
Ed
So technically this is another thread, right?
On the test score theory, one thing you should note is that the standard setup (as presented on the PSU page) makes an assumption of one-dimensionality. That is, the "latent trait" or the "true ability" or whatever is only one-dimensional. Tango is introducting another dimension, which would leave one with something like:
Xi1, Xi2 instead of just the Xi.
To deal with those types of models, psychometricians typically use the more modern technique of Item Response Theory (IRT), which can much more easily accomodate multiple dimensions. Implicit in what you are arguing, I think, is an IRT model with covariates, whether the covariates capture the "context" that affects the IRT scores. But I really don't think you want more than one dimension.
Posted 4:38 p.m.,
January 24, 2004
(#2) -
tangotiger
(I usually block these threads, when I reference other threads. Not sure how this one slipped by me!)
***
Just to be clear, are you saying that I'm saying that:
1 - there is only one true talent level per player/student, given the exact context
2 - there is multiple talent levels per player/student, given the exact context
3 - there is multiple talent levels per player/student, given multiple contexts
The answer is #1 and #3.
Are you saying that I'm saying:
1 - We can measure the whole distribution of true talent levels of ALL Players, as a single true talent level per player, given the single same context
2 - We can measure the whole distribution of true talent levels of ALL Players, as a single true talent level per player, given the single different contexts
3 - We can measure the whole distribution of true talent levels of ALL players, as multiple true talent levels per player, given the multiple contexts
The answer is #1.
If you agree that this is what I'm saying, then you can proceed with whatever assumptions you have about what I'm saying.
If you don't agree with my answers, then you do not know what I'm saying. Therefore, proceed with whatever you have to say, without referencing what I'm saying.