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MLE Estimation of Gamma Distribution Parameters for data with 'zeros'

6 messages · Nyasha, Bert Gunter, Peter Dalgaard +3 more

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Please how can one go about this one? I don't know how to go about it.
3 days later
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Is this homework? This list has a no-homework policy.


-- Bert
On Tue, Jan 10, 2023 at 8:13 AM Nyasha <kahuninyasha13296 at gmail.com> wrote:
8 days later
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Not necessarily homework, Bert. There's a generic issue with MLE and rounded data, in that gamma densities may be 0 at the boundary but small numbers are represented as 0, making the log-likelihood -Inf. 

The cleanest way out is to switch to a discretized distribution in the likelihood, so that instead of log(dgamma(0,...)) you use log(pgamma(.005,..) - pgamma(0,...)) == pgamma(.005,..., log=TRUE). (For data rounded to nearest .01, that is). Cruder techniques would be to just add, like, .0025 to all the zeros. 

-pd

  
    
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Beware of adding a constant... the magnitude of the constant used can have an outsized impact on the answer obtained. See e.g. https://gist.github.com/jdnewmil/99301a88de702ad2fcbaef33326b08b4
On January 19, 2023 3:49:29 AM PST, peter dalgaard <pdalgd at gmail.com> wrote:

  
    
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There's at least one package that can do zero-inflated gamma regression
(Rfast2::zigamma).  I'm not sure it's ML, though.


On Thu, Jan 19, 2023 at 10:17 AM Jeff Newmiller <jdnewmil at dcn.davis.ca.us>
wrote:

  
  
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Another situation for the presence of 0 is about dosage when 
concentration is below the detection limit. It is not necessary to 
discretize the data. We propose a method here:
Salvat-Leal I, Cort?s-G?mez AA, Romero D, Girondot M (2022) New method 
for imputation of unquanti?able values using Bayesian statistics for a 
mixture of censored or truncated distributions: Application to trace 
elements measured in blood of olive ridley sea turtles from mexico. 
Animals 2022: 2919 doi 10.3390/ani12212919
with R code.
If the data has "true" 0, the gamma distribution is not the best choice 
as 0 is impossible with gamma distribution.

Marc

Le 19/01/2023 ? 12:49, peter dalgaard a ?crit?: