Llprior #56
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Llprior #56
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added 8 commits
November 7, 2016 11:42
Seems to work in ideal cases, but does not pass tests yet. In particular, need to modify the na-checking code. Will do in future commit.
Previously when dropna=True user was warned that NAs would be dropped, but they never actually got dropped. This also fixes the LL prior implementation for slope-only models.
Not 79 because fuck 79.
Also removes the calls to pd.stats.ols that were giving unsightly warnings during model building.
We now numerically approximate the 2nd derivative manually rather than using GLM.hessian() from statsmodels.
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This changes the implementation of the default priors so that they are based entirely on the log-likelihood function, never referencing the multiple regressions of Y and X on the covariates as in the previous implementation. For Normal response models, the results are essentially the same as before, but not exactly, as the new implementation relies on a quadratic approximation to the log-likelihood function (which is close but not perfect). Non-normal response models are now handled exactly the same as Normal response models now. However, the quadratic approximation to the log-likelihood is not as good for non-Normal response models, so the interpretation of the priors in terms of the standard deviation of the implied partial correlation should be considered a fairly rough approximation. Nevertheless, the default priors for non-Normal models are now much more intuitively sensible than before. This same implementation should also work almost entirely "as-is" for other link functions / response distributions that we have not explicitly implemented; all we really need to do is point to the appropriate statsmodels distribution family in priors.py.
We might be able to upgrade the quadratic approximation to a quartic approximation, which should give even better results. But I have not worked this out yet. In any case, for now this is ready for production.