JoeyDVivre
New member
- Jun 18, 2026
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OK I've been playing with this data a bit and here's the plan. I thought I would do an analysis of the data in a pedagogical way because it's data and results that everyone cares about and maybe we can learn some statistics that would be useful for other things.
The goals:
1) Determine the MPS
2) See how much we can improve on 40/60/80
3) Give everyone a fancy calculator for their score
4) See if we can come up with some insights useful for studying
5) See if we can find any evidence that ethics is more important than its points would indicate for borderlines.
The Plan:
First the score on the sections are highly correlated. Just a correlation of 1's, 2's, and 3's yields correlations that are all positive and are almost 0.5 for equity analysis and FSA. Obviously, the 1-2-3 transformation is not especially justified.
We are going to assume that the percentage in each section is a beta r.v.. Betas are quite useful for this kind of thing and wikipedia has a fine entry about beta r.v.'s. However, unlike the normal distribution there is not an obvious generalization of the beta into a multivariate distribution (except Dirichlet which is inappropriate here because it would mean the scores are negatively correlated). So in keeping with what's chic in finance these days, we'll estimate a Gaussian copula. I haven't tried estimating the marginals and the copula simultaneously yet, but I'm going to try. It looks a little numerically tricky because the data are binned and it's just a tough numerical problem (if you don't think so, I would like to hear from you). If this doesn't work we'll do the marginals first and then the copula which is totally easy. We're going to try using the trusty EM algorithm to solve the likelihood equations.
If you think about what that does, we will have a multivariate distribution. You then take your binned scores and find the highest likelihood point on this distribution function and that's your maximum likelihood score. That means, for example, that if you got in the mid range on FSA your estimated FSA score would be higher if you aced equity analysis than if you bombed it.
However, we will use everyone's score to find the MLE of the MPS. Thus, when you find an estimate of your score it will be the maximum likelihood point in the pass/fail region based on the estimate of the MPS.
That covers goals 1)- 3), I think.
For 4), I'm going to think about some kind of principal components analysis and compare the weights given by CFAI with the PCA weights. I don't quite have this worked out.
For 5), I'll bet we need a mountain of data to come up with anything. In the framweork above it means there is a "kink" in the MPS in the ethics dimension. We'll see how hard this is when we get there.
Suggestions? Cool, huh?
The goals:
1) Determine the MPS
2) See how much we can improve on 40/60/80
3) Give everyone a fancy calculator for their score
4) See if we can come up with some insights useful for studying
5) See if we can find any evidence that ethics is more important than its points would indicate for borderlines.
The Plan:
First the score on the sections are highly correlated. Just a correlation of 1's, 2's, and 3's yields correlations that are all positive and are almost 0.5 for equity analysis and FSA. Obviously, the 1-2-3 transformation is not especially justified.
We are going to assume that the percentage in each section is a beta r.v.. Betas are quite useful for this kind of thing and wikipedia has a fine entry about beta r.v.'s. However, unlike the normal distribution there is not an obvious generalization of the beta into a multivariate distribution (except Dirichlet which is inappropriate here because it would mean the scores are negatively correlated). So in keeping with what's chic in finance these days, we'll estimate a Gaussian copula. I haven't tried estimating the marginals and the copula simultaneously yet, but I'm going to try. It looks a little numerically tricky because the data are binned and it's just a tough numerical problem (if you don't think so, I would like to hear from you). If this doesn't work we'll do the marginals first and then the copula which is totally easy. We're going to try using the trusty EM algorithm to solve the likelihood equations.
If you think about what that does, we will have a multivariate distribution. You then take your binned scores and find the highest likelihood point on this distribution function and that's your maximum likelihood score. That means, for example, that if you got in the mid range on FSA your estimated FSA score would be higher if you aced equity analysis than if you bombed it.
However, we will use everyone's score to find the MLE of the MPS. Thus, when you find an estimate of your score it will be the maximum likelihood point in the pass/fail region based on the estimate of the MPS.
That covers goals 1)- 3), I think.
For 4), I'm going to think about some kind of principal components analysis and compare the weights given by CFAI with the PCA weights. I don't quite have this worked out.
For 5), I'll bet we need a mountain of data to come up with anything. In the framweork above it means there is a "kink" in the MPS in the ethics dimension. We'll see how hard this is when we get there.
Suggestions? Cool, huh?