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I am very new to statistical modeling. We are working on the effect of the disease on the heritability and repeatability of milk yield. Based on my understanding, milk yield is continuous data (family = Gaussian). However, when we look at the distribution of our data, it is not normally distributed. It follows negative binomial distribution. I am using MCMCglmm and the package does not support negative binomial. And I have read somewhere that we can use "family = "poisson"" for overdispersed continuous data, but I can't help but think that Poisson can only be used for count data. I would appreciate it if anyone could suggest me something.

I really appreciate any help you can provide.

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  • $\begingroup$ See stats.stackexchange.com/a/38588/7071. You will need to use heteroskedastic SEs to handle overdispersion. $\endgroup$
    – dimitriy
    Commented Aug 22 at 1:43
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    $\begingroup$ How about a Gamma distribution, or log-normal, or another positive continuous distribution? Continuous data cannot be negative binomial distributed, as the NB distribution is integer valued $\endgroup$
    – Alex J
    Commented Aug 22 at 1:58
  • $\begingroup$ Family = "gamma" is not supported by MCMCglmm. It is somewhat confusing because some references mentioned that we can use Poisson for non-normally distributed continuous data and some said that we can't. $\endgroup$
    – d22e003
    Commented Aug 22 at 5:00

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You are making the mistake of assuming that the distribution applies to your entire data where in actuality it applies to each observation. A single observation of milk yield, if that's what you are modelling, cannot be negative so the observations cannot be distributed Gaussian as this distribution allows for 0 and negative values, none of which would be admissible for milk yield^1.

Yield cannot be distributed negative binomial either as that allows 0s, but also this distribution has support on the set of non-negative integers, 0, 1, 2, etc. Milk yield values are continuous, not discrete.

The same issue means it can't be Poisson. And the Poisson is not even used to model overdispersed counts so I don't see how it could be useful for overdispersed anything...

Logical choices for the conditional distribution of $y_i$ then are continuous distributions with support on the positive reals. The gamma and log-normal distributions would be common choices to start modelling with.

That MCMCglmm doesn't support the gamma distribution shouldn't stop you modelling these data. Did you need this for the phylogenetic random effects it allows? If so, the brms package can fit these kinds of phylogenies and it has the gamma and log-normal distributions. It also estimates model parameters using a flavour of MCMC using the Stan probabilistic programming language. brms provides a user-friendly formula-based interface to specifying models.

See this vignette for info on the phylogenetic capabilities in brms to see if it meets your specific needs: https://cran.r-project.org/web/packages/brms/vignettes/brms_phylogenetics.html

[1:] unless you are modelling milk/no milk and milk yield given the cow gave milk via a hurdle model. In general 0s are not allowed because you cannot possibly differentiate from 0 milk and a trivially small amount of milk. In other words, below some positive amount of milk (the detection limit) you don't actually know what the value was. This would require a hurdle model (detect / no-detect hurdle followed by a gamma or log normal for milk yield given a detection), or a censored model.

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  • $\begingroup$ Thanks a lot for a very detailed explanation. What if I need to use the MCMCglmm model to incorporate pedigree record to estimate the heritability and repeatability of the trait? $\endgroup$
    – d22e003
    Commented Aug 22 at 8:11
  • $\begingroup$ I'm not familiar with pedigrees; a quick Google search found this: discourse.mc-stan.org/t/… and the links to related discussions suggest that a pedigree is ~= a phylogeny and you can get heritability out of the phylogenetic model. You should probably ask that as another questions after you've done some basic investigations yourslef to figure this out. $\endgroup$
    – Gavin Simpson
    Commented Aug 22 at 8:22

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