Quote:
Originally Posted by wgardner
And yes, given this, the standard errors I compute are the variations of the OPR estimates if they fit the model, all of which assumes that there is not variation in the way individual teams perform other than their mean contribution. Obviously, this final assumption is suspect.
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I think this assumption can be restated a different way. We might assume that the contribution of each team is normally distributed with a certain mean and variance. If the variance is fixed and assumed to be the same for each team, then the maximum likelihood estimate of the means of the distributions should be the same as the least squares estimate as in usual OPR. This assumes that there is some hidden distribution of the contribution of each team which is normal and that the variance of each distribution is the same.