[R-sig-eco] Continuous distribution for zero or positive values (in GLM or GLMM)

[Ben Bolker]

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On 11-05-18 11:54 AM, Pavel Goldstein wrote:
> Hello Fred,
> You can use Zerro Inflated Poisson or Negative binomial models.
> 
> Pavel

  That doesn't work very well because Fred's data are continuously
distributed.  This is a common problem, and not one with an easy solution.

  1) One could add a small constant, as Fred suggests.  That's
problematic if there are more than a few zeros, because the constant is
arbitrary and the answer may depend on it.

  2) One could treat the zeros as censoring, i.e. values below a
particular detection limit.  This is sensible in some cases but fairly
difficult to fit into generalized software that handles G(A|L)M(M)s.

  3) One can split the problem into two parts, i.e. analyze the
zero/non-zero distribution as a binary variable and analyze the
conditional (non-zero) data as Gamma/log-normal/whatever (this is
similar to the way that hurdle models work, except that in this case the
non-zero part of the data is continuous rather than a truncated discrete
distribution).

  4) The Tweedie distribution has a point mass at zero plus a
continuously distributed component, and some modeling capabilities exist
in R (library("sos"); findFn("tweedie")), but see the comment in #2 above.

> 
> On Wed, May 18, 2011 at 6:46 PM, Fred Takahashi <fredtaka at gmail.com> wrote:
> 
>> Hello, just a basic question: what distribution I should use to
>> analyze continuous data which can had zero or positive values (eg.
>> mass of grasses in plots assuming that zero mass is meaningful)? My
>> expected analysis is in the framework of GLM or GLMM (or
>> alternatively, GAM / GAMM).
>>
>> One idea I had is to add 0.0001 to all values and use family=Gamma.
>> That is a good approach?
>>
>> If a better choice is to use a different distribution, suggestions of
>> packages to do that are welcome.
>>
>> Thanks,
>> Fred Takahashi
>> Universidade de Brasília - Brasil
>>
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> 
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