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Ordinal regression docs #719

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merged 13 commits into from
Sep 28, 2023
Merged

Ordinal regression docs #719

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edbfa6b
ordinal model with cumulative link notebook
GStechschulte Sep 13, 2023
6d89eb4
ordinal model with cumulative link function
GStechschulte Sep 13, 2023
a2167bc
unified explanation for cumulative and sequential models
Sep 14, 2023
7f9b118
sratio model and data
GStechschulte Sep 15, 2023
3dffcce
code review changes
GStechschulte Sep 18, 2023
f7a1826
remove intercept in models
GStechschulte Sep 19, 2023
e27194f
zero mu vector prior for sratio family
GStechschulte Sep 22, 2023
6f357f2
code review and add section on default priors
GStechschulte Sep 22, 2023
0521b01
explicit explanation of K and k and added summary section
GStechschulte Sep 25, 2023
32e49fd
Zero inflated docs (#725)
GStechschulte Sep 28, 2023
ff9c044
ordinal model with cumulative link function
GStechschulte Sep 13, 2023
d7acdeb
use plot_ppc_discrete for posterior predictive samples
GStechschulte Sep 26, 2023
075f537
add plots explaining the ordinal outcome of the dataset
GStechschulte Sep 28, 2023
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2 changes: 1 addition & 1 deletion bambi/priors/scaler.py
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Original file line number Diff line number Diff line change
Expand Up @@ -114,7 +114,7 @@ def scale_threshold(self):
threshold = self.model.components["threshold"]
if isinstance(threshold, ConstantComponent) and threshold.prior.auto_scale:
response_level_n = len(np.unique(self.response_component.response_term.data))
mu = np.round(np.linspace(-2, 2, num=response_level_n - 1), 2)
mu = np.zeros(response_level_n - 1)
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@GStechschulte GStechschulte Sep 25, 2023 •
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If sequential models assume that for every response level there is a latent continuous variable $Z_k$, then wouldn't we need each response level? Thus, mu should be mu = response_level_n and not response_level_n - 1?

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@tomicapretto tomicapretto Sep 25, 2023 •
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Ohh, I think you're right!

I'm thinking why the current approach is working and not failing. Is it because it's not considering the probability of Y being larger than the largest observed category? I think it would make sense for the years example, but I'm not sure if it would make sense for cases where there is a pre-specified set of categories.

I wrote that as I was looking at this visualization from the ordinal tutorial by Bürkner and Vuorre:

image

and I wonder: Do we always have a Pr(Y > K)? (as in the Y > 3 in the figure)

@GStechschulte if you make that modification and run the example, does it work?

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@GStechschulte GStechschulte Sep 26, 2023 •
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If I remove the -1, I get ValueError: Incompatible Elemwise input shapes [(35,), (36,)].

This makes sense as I stated in the docs because the sequential model is a product of probabilities, i.e., the probability that $Y$ is equal to category $k$ is equal to the probability that it did not fall in one of the former categories $1: k-1$ multiplied by the probability that the sequential process stopped at $k$.

In the case of the attrition dataset, there are 36 response categories. Because of the statement above, this makes sense why the probability of category 36 is 1. There is no category after 36, so once you multiply all of the previous probabilities with the current category, you get 1. Thus, you don't need a parameter (threshold) for it.

threshold.prior = Prior("Normal", mu=mu, sigma=1)

def scale(self):
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