Zero-and-one-inflated beta regression

[Andrew Tredennick]

Hello,

I am modeling percent cover of trees in 1 hectare plots using remote sensing variables as predictors. So the data is basically proportional, but we have a zero-inflation problem. Out 896 observations, 121 have zero percent cover. I have a model working in INLA using the "beta" likelihood, but to do so required altering the data so that, if we let y=percent cover, when y=0 I reset to y=0.0001. I would much rather model tree cover as a mixture of Bernoulli and Beta distributions. Is this possible using INLA?

Best regards,
Andrew

[Elias T Krainski]

Dear Andrew,
Maybe one way to do that is following the example chapter five of
  http://www.r-inla.org/examples/tutorials/spde-tutorial
best,
Elias.

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[Andrew Tredennick]

Thanks Elias, that chapter does help. If I mix your example with the multiple likelihood section of the INLA "Tools for Manipulating..." section I get a working version. However, if we consider your example in Chapter 5, is it truly a mixture distribution with a parameter that determines the extent to which each likelihood influences the posterior distribution? What I am particularly looking for is an INLA implementation of the example outlined here, http://mbjoseph.github.io/blog/2014/02/06/beta/.

On Tuesday, July 29, 2014 1:23:12 AM UTC-6, Elias T. Krainski wrote:

Dear Andrew,
Maybe one way to do that is following the example chapter five of
  http://www.r-inla.org/examples/tutorials/spde-tutorial
best,
Elias.

On 29/07/14 00:47, Andrew Tredennick wrote:

Hello,

I am modeling percent cover of trees in 1 hectare plots using remote sensing variables as predictors. So the data is basically proportional, but we have a zero-inflation problem. Out 896 observations, 121 have zero percent cover. I have a model working in INLA using the "beta" likelihood, but to do so required altering the data so that, if we let y=percent cover, when y=0 I reset to y=0.0001. I would much rather model tree cover as a mixture of Bernoulli and Beta distributions. Is this possible using INLA?

Best regards,
Andrew

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[Adam Smith]

Andrew,

I'm in the process of doing something similar (submerged aquatic vegetation cover) and running into the same issue.  Did you get any further with this?  Also, perhaps the geostatsp package (http://www.jstatsoft.org/article/view/v063i12), which uses INLA will make the process easier?   

Thanks,
Adam

[Iosu]

Hi Andrew and Adam,
Maybe you could use this new package. https://cran.r-project.org/web/packages/zoib/zoib.pdf
you may not be able to apply spatial stats but you could check if the addition of small values does really change you conclusions

Hope its useful,