zero-inflated asymmetric laplace distribution

[pauljeco]

Many data sets e.g. rainfall data contain numerous zero's. By adding this functionality this would open a whole new dimension to analysing climate and other data. zero-inflated asymmetric laplace distribution is specifically mentioned to the potential for quantile regression. This would provide mechanisms to making sense of the inherent variance in time series climate data - I believe this would be useful to many climate scientists.

[HaydenTWilson]

Thats a great idea. Please do. this is exactly what we need.

[paul-buerkner]

Has someone written about this distribution yet? Do we understand its properties?

[pauljeco]

Hi Paul, Thanks for your quick response. I'm not aware of documentation of the 'zero-inflated asymmetric laplace distribution'. The alternative quantile regression probability distribution for climate data with many zero's may be through implementation of quantile functionality with your hurdle_gamma distribution? Although I'm not sure of the technicalities in implementing this it would certainly be useful.

[paul-buerkner]

I am wondering whether it could make sense to work on a more methodological paper together on the zero-inflated asymmetric laplace distribution (given that noone has worked on it before, as I understand from your response) before applying it in practice. The reason is that the main parameter of the asym laplace distribution may no longer describe a given quantile once we introduce zero-inflation but this is something that needs to be worked out. Perhaps you (or someone else) has interest in leading such an endavor. I would gladly help with this but don't have the time to take the lead.

[pauljeco]

Thanks Paul. If you were able to write the function for stan in brms I would be grateful to run some tests with it using a long-term rainfall data set? A methodological paper would be a good outcome.

[paul-buerkner]

That could be a start. I will post an update once the brms family is ready.

[pauljeco]

Thanks Paul - looking forward to this - much appreciated

[paul-buerkner]

What I do wonder is why is the asymmetric laplace distribution used for rainfall data at all?

To my understanding, rainfall can only be non-negative while the asymmetric laplace distribution supports both positive and negative values. Having a zero-inflation "in the middle" of a distribution is something I have yet to see in real data.

[pauljeco]

Thanks Paul. Possibly because of this a tweedie has used more often. For the zero-inflation a compound 'poisson-gamma' (doi.org/10.1155/2018/1012647) appears to be a good approach - from my limited experience, the math behind this is beyond me. This would be great to implement however, my interest was in quantile regression - changes in central tendency or the median are non-significant so it is more interesting to see what is happening with different quantiles. I had a really rudimentary analysis like this published (frequency of events - count data doi.org/10.1016/j.ppees.2012.09.005) but would like a better approach, if possible. Otherwise, I can perform multiple zero-inflated poisson models for classes of event frequency.

Have you had any other interest in implementing quantile regression for the (hurdle) gamma distribution? Not sure if this is possible though?

[paul-buerkner]

Quantile regression cannot just be enabled for an arbitrary family. Instead, the key feature of the asymmetric laplace distribution with parameters mu, sigma, and p (the quantile parameter) is that P(X < mu) = p, which makes the distribution usable for quantile regression in the first place. For a zero-inflated asymmetric laplace distribution to be useful, we have to preserve this key property or otherwise we won't be able to use it for quantile regression anymore.

Let's have a skype call about this issue to make sure we are on the same page and to better understand whether the zero-inflated asymmetric laplace distribution is a promising approach worth spending more time on. Do you mind writing me an email about this? I can't see your email address right now.

[pauljeco]

Have dropped you an email using this ticket header

[paul-buerkner]

Thank you! What time would work for you? For me start of next week would be ideal but I may also manage other times. In which Time zone are you?

pauljeco notifications@github.com schrieb am Do., 8. Aug. 2019, 11:04:

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[paul-buerkner]

Was ment to be send via email. Sorry :-D

Paul Buerkner paul.buerkner@gmail.com schrieb am Do., 8. Aug. 2019, 11:13:

Thank you! What time would work for you? For me start of next week would be ideal but I may also manage other times. In which Time zone are you?

pauljeco notifications@github.com schrieb am Do., 8. Aug. 2019, 11:04:

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[paul-buerkner]

An experimental version of the zero_inflated_asym_laplace distribution is now available in the github version of brms. Please note that this family is not yet documented or offically supported as we still need to get a better understanding of the properties of this distribution (and whether its generally useful).

Here is an example how to use it:

y <- rasym_laplace(1000, mu = 5)
y <- c(y, rep(0, 100))
dat <- data.frame(y, x = rnorm(1100))

fit <- brm(y ~ x, data = dat, 
           family = brmsfamily("zero_inflated_asym_laplace"))

pp_check(fit)
marginal_effects(fit)
loo(fit)

[michaelkyei66]

Hello everyone,

I am trying to model a continous outcome variable(non-integer) with excess zeros.I have four independent variables to predict the outcome variable. I have seen that people have referred to the compound poisson gamma model( https://doi.org/10.1111/2041-210X.12122) as one of the possible models to deal with such data.My questions are ;

1. What model will be most apprioprate for my data? 2.Do you have a similar r scripts that I could follow as an example?

Best wishes,

Michael Kyei

[paul-buerkner]

please ask brms related questions on https://discourse.mc-stan.org/