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I have changed my modelling technique. Instead of continuing with logistic regression, I am going with a total least squares approach instead. For those serious number crunchers out there, see: (http://en.wikipedia.org/wiki/Total_least_squares).

Why change the approach? Well, I am a bit worried about the error in this model. In particular, this should satisfy those who belive in the potential sub-levels theory since it allows for error in both the response and dependent variables. I can now drop that assumption from my (long) list of assumptions. It is certainly more complex but that is another story.

In any case, in order to program this I had to go back to my university days and re-learn non-linear programming. This allowed me to put certain constraints on the model parameters (so, for example, no coefficient becomes negative, which I was having a problem with under logistic regression).

I would still like to put additional constraints but I think I have reached the limit of my skills. If anyone knows anything about non-linear programming, and in particular how to program it in SAS, please contact me.

Sorry for the long-winded details, I will be less technical in the future. ;-)

Now, I bet you are all wondering how this new approach changes the model. To be honest: not much. I mean, the parameters change and I must admit that the model now seems to do a better job in general. But shockingly, the outside defense contribution is still zero! Same goes for driving, it is not contributing anything to capping in the current model (although that is not necessarily a surprise, since it is linked to handling and handling is now contributing more).

The other parameters have a bit more of a contribution now, most notably passing and handling.

While I like this approach a lot more, it still needs the data to do a good job. So please continue to send data. ;-)

of which by far the biggest, in my view, is that the cap coefficients are the same independent of position.

I am putting position in the model (as a class varible) but as I said before (I think I said it, anyways), the effect is pretty small, so I drop it from the final model. But I will keep testing it. If and when I get enough data I should be able to determine if indeed the formula needs to be split (like you did for salary) or if it still remains insignificant enough to be left off the final model.

Anyhow, a couple of people have mentioned that I should consult with you while I do this. I sort of assumed you would be reading and would comment as necessary. So please do - I welcome any suggestions you might have.

I have a little question: What about the possibility of decimal in the potential? I don't know if it's the case, but the question deserves to be asked

Why just ask this about potential? Why not also ask the question for skills?

Anyhow, I will answer the question myself. ;-) The reason why Joseph Ka's salary analysis worked is because he knew that the salary value was (basically) correct. However, he also knew that there was error in the skill component (because of sub-levels). But that is not an issue with a regression model (like the one he used). You can accept error in the dependent variables. It may mean that it takes more data to get to the end result. But his error coefficients were pretty good, so he was comfortable that he was not missing the data.

So, if I could know or assume that there is no error in the potential value, I could be quite comfortable using a regression model. And that is where I started with my analysis. But because of the results so far, and because of people like you who keep bringing up the possibility of sub-levels in potential, I looked around for other options. And I think I might be on to something here: (155261.24). This "total least squares" approach lets you model with errors in both your response variable (in this case, potential) and also in your explanatory variables (in this case, skills).

Now, what I would like to be able to do is limit the error for potential. I think we can all agree that, even if there are sub-levels, allstar potential is probably going to fall somewhere between 6-7 (or maybe 5-6, I don't know). But like I said, that is beyond my programming knowledge at the moment. So all I can model is for some type of error in potential, but what kind of error, I can't specify without some help on the programming side.

I have a little question: What about the possibility of decimal in the potential? I don't know if it's the case, but the question deserves to be asked :)

I guess that's what he's referring to when saying "potential sublevels" for the new model.

It is an unsolved question about potentials :/

Last edited by Zero, the Magi. at 9/1/2010 2:59:25 PM

Now - if someone knows of an easier way to go about this, I would really love to hear different options.

That would make it too easy, you don't want all the formulas and calculations given to you or else everyone would just be doing the same thing.

Having a lot of factors largely unknown (or leaving it up to the community to work out) leaves things open to individual interpretation which means everyone can have different ideas and tactics etc