How to manually overwrite the link ratios?

[contenrico]

Hello,

I'm trying to manually overwrite the link ratios calculated through triangle.link_ratio.

As triangle.link_ratio is also a Triangle object, I'm guessing I can use .loc[] to substitute specific link ratios with my manual inputs. However, I can't find a way to maintain these all the down the pipeline.

For example, when I subsequently use cl.Development().fit(triangle), it goes back to using the original link ratios. However, I'd like to be able to use all the functionalities of cl.Development and cl.Chainladder() with my modified link ratios. Is it possible to do that?

Thanks!

[jbogaardt]

Hi @contenrico. Neither the Development estimator nor the Triangle supports modifying the link ratios directly. The Triangle assumes link ratios to be a function of the underlying data and Development estimator allows for various options of selecting a pattern from link ratios, but not in a way that modifies them.

To achieve the functionality you're looking for, I could suggest doing the modification outside of an estimator and using DevelopmentConstant to get it back into a chainladder-compliant format.

For example:

import chainladder as cl
import numpy as np

raa = cl.load_sample('raa')

# Modify link ratios however you want. Here I am naively limiting the low and high of my link ratios directly 
limited_link_ratios = np.maximum(np.minimum(raa.link_ratio, 5), 1.0)

# Convert link ratios into a selected pattern stored as a dictionary of (age,  ldf) pairs.
selected_patterns = dict(
    zip(raa.development[:-1], 
        limited_link_ratios.mean().to_frame().iloc[0])
)

# Use DevelopmentConstant to leverage your custom patterns in a compliant way
pipe = cl.Pipeline([
    ('dev', cl.DevelopmentConstant(patterns=selected_patterns, style='ldf')),
    ('model', cl.Chainladder())]
)

# Fit a chainladder model to your selected patterns and explore its properties.
pipe.fit(raa).named_steps.model.ibnr_

[contenrico]

Hi @jbogaardt

Many thanks for your reply.

This approach could work, however I was wondering if there an easy way to have more control over how the LDFs are calculated? I'm referring to this snippet:

limited_link_ratios.mean().to_frame().iloc[0]

This is just calculating the simple mean for all origins - is there a way to control the type of average (i.e. select the volume average option) and the number of periods considered? Or would I have to create a custom function for that?

Thanks!

[jbogaardt]

The Development estimator is a pretty flexible estimator for selecting various development patterns. However, it does NOT support modifying the age-to-age factors of the underlying Triangle itself. I probably don't I understand your use case fully. Does the Development estimator not provide enough flexibility in selecting patterns? Or can you describe the use case that requires modifying the underlying link ratios directly before selecting patterns?

[contenrico]

My specific use case would involve Nth-root smoothing of the age-to-age factors.

What I would like to do, for example, is take three LDFs in an origin year (let's say 1.5, 3, 1.25) and replace them with the cube root of (1.5 * 3 * 1.25). In this case, I would replace 1.5, 3, 1.25 with 1.78, 1.78, 1.78.

I don't think the Development estimator can do that, so I was trying to find a way to replace link ratios directly, however I would like to maintain the functionalities of the Development estimator (such as the volume average). Is there potentially another way to achieve the same type of smoothing?

[jbogaardt]

I see. This is geometric averaging which has been requested in #272. I think this is a worthwhile enhancement. Still, it doesn't do you much good until implemented. However, similar to my example above, you can probably get pretty creative with what currently exists along the lines I mention above. In the case of a 3-year geometric average, you could do this:

import chainladder as cl
import numpy as np

raa = cl.load_sample('raa')
n = 3

# Modify link ratios however you want. Here is he cubed-root 3 year most recent average
link_ratios = cl.Development(n_periods=n).fit_transform(raa).link_ratio.prod(axis=2) ** (1/n)


# Convert link ratios into a selected pattern stored as a dictionary of (age,  ldf) pairs.
selected_patterns = dict(
    zip(raa.development[:-1], link_ratios.to_frame().iloc[0])
)

# Use DevelopmentConstant to leverage your custom patterns in a compliant way
pipe = cl.Pipeline([
    ('dev', cl.DevelopmentConstant(patterns=selected_patterns, style='ldf')),
    ('model', cl.Chainladder())]
)

# Fit a chainladder model to your selected patterns and explore its properties.
pipe.fit(raa).named_steps.model.ibnr_

[contenrico]

Thanks @jbogaardt.

Just for clarity, my request is not exactly the same as #272. My understanding is that this request is asking for a geometric mean across the columns, whereas my request is about a geometric mean across a row (which results in the smoothing of a pattern for a given origin year).

So starting from a triangle like this:

I would like to be able to replace sets of factors with their geometric mean like so (red boxes):