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corrected a typo: hierarchial -> hierarchical (#194)
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examples/generalized_linear_models/GLM-hierarchical.ipynb

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" * individual/non-hierarchical model: 0.13\n",
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" * hierarchical model: 0.08\n",
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"\n",
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"As can be seen above the hierarchical model performs better than the non-hierarchical model in predicting the radon values. Following this, we'll plot some examples of county's showing the actual radon measurements, the hierarchial predictions and the non-hierarchical predictions. "
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"As can be seen above the hierarchical model performs better than the non-hierarchical model in predicting the radon values. Following this, we'll plot some examples of county's showing the actual radon measurements, the hierarchical predictions and the non-hierarchical predictions. "
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"In the shrinkage plot above we show the coefficients of each county's non-hierarchical posterior mean (blue) and the hierarchical posterior mean (red). To show the effect of shrinkage on a single coefficient-pair (alpha and beta) we connect the blue and red points belonging to the same county by an arrow. Some non-hierarchical posteriors are so far out that we couldn't display them in this plot (it makes the axes too wide). Interestingly, all hierarchical posteriors of the floor-measure seem to be around -0.6 indicating that having a basement in almost all county's is a clear indicator for heightened radon levels. The intercept (which we take for type of soil) appears to differ among countys. This information would have been difficult to find if we had only used the non-hierarchial model.\n",
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"In the shrinkage plot above we show the coefficients of each county's non-hierarchical posterior mean (blue) and the hierarchical posterior mean (red). To show the effect of shrinkage on a single coefficient-pair (alpha and beta) we connect the blue and red points belonging to the same county by an arrow. Some non-hierarchical posteriors are so far out that we couldn't display them in this plot (it makes the axes too wide). Interestingly, all hierarchical posteriors of the floor-measure seem to be around -0.6 indicating that having a basement in almost all county's is a clear indicator for heightened radon levels. The intercept (which we take for type of soil) appears to differ among countys. This information would have been difficult to find if we had only used the non-hierarchical model.\n",
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"\n",
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"Critically, many effects that look quite large and significant in the non-hiearchical model actually turn out to be much smaller when we take the group distribution into account (this point can also well be seen in plot `In[12]` in [Chris' NB](http://nbviewer.ipython.org/github/fonnesbeck/multilevel_modeling/blob/master/multilevel_modeling.ipynb)). Shrinkage can thus be viewed as a form of smart regularization that helps reduce false-positives!"
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.8.6"
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"version": "3.8.3"
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},
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"latex_envs": {
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"bibliofile": "biblio.bib",

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