[R-sig-ME] Deviations from normality in MCMC models

Ben Bolker bbolker at gmail.com
Fri Jun 2 03:47:08 CEST 2017

 In my experience it's *usually* the case that a log-Normal (i.e.,
log-transforming the variable and treating it as Normal) should be an
adequate substitute for a Gamma.  They have the same general qualitative
range of shapes. If the log-Normal is problematic/your log-transformed
data are far from Normal, then you're likely to have had similar
troubles with a Gamma. As one example, you have observations that are
exactly zero, then you can't log transform them -- but these don't work
with the Gamma either, as it has a log-likelihood density that is either
negative infinite, if the shape parameter is >1, or infinite, if the
shape parameter is <1.

On 17-06-01 02:29 PM, landon hurley wrote:
> On 01/06/2017 10:04, Christopher Robinson wrote:
>> The MCMCglmm package in R allows users to specify the distribution 
>> family for each variable. Unfortunately, I cannot fit a gamma	
>> distribution to my data because MCMCglmm currently does not support 
>> this family. My question is how sensitive to deviations from 
>> normality is MCMC? That is, if I apply a gaussian distribution to 
>> this variable, will my results be strongly affected?
> Chris,
> Why not fit the normal model, cross-validate, and then decide if its
> adequate? Depending upon the sample size of course, it may not make a
> large difference in terms of choice of the prior, beyond support
> constraints introduced for the variable being modelled if you used
> something other than Gaussian.
> If negative predicted responses are of a concern (assuming it's
> truncated at zero), it looks like you could potentially use the censored
> Gaussian family options, which would at least restrict you to the same
> support as a Gamma distribution.

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