[R-sig-ME] Zero-truncated Poisson distribution in glmmTMB

[Mollie Brooks]

The poilogMLE function is fitting a Poisson-lognormal which is equivalent to a Poisson with an observation level random effect (OLRE) to account for overdispersion. So to make the models similar, you probably need to add
df_01$obs = row.names(df_01)
and then add (1|obs) to your model formulas. 
  
Here is a reference about OLREs https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4194460/ <https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4194460/>

cheers,
Mollie

> On 25Apr 2020, at 9:24, Erik Solbu <erik.solbu using nibio.no> wrote:
> 
> Hi everyone,
> 
> I'm trying to replace a package called 'poilog' with glmmTMB, but the results differ in such a way that I'm not sure how to interpret the results from glmmTMB.  I've written a short example below:
> 
> #### Start of code ####
> 
> # Required packages
> library(poilog)
> library(glmmTMB)
> 
> # Simulate using the 'poilog' package
> # sim_01 <- rpoilog(S = 1000, mu = 0, sig = 2, keep0 = TRUE)
> # This is the same as
> sim_01 <- rpois(n = 1000, lambda = exp(rnorm(n = 1000, mean = 0, sd = 2)))
> 
> # estimate the parameters
> # using the 'poilog' package, assume regular Poisson distribution
> est_01 <- poilogMLE(n = sim_01, zTrunc = FALSE)
> # using the 'poilog' package, assume zero truncated Poisson distribution
> est_02 <- poilogMLE(n = sim_01[sim_01>0], zTrunc = TRUE)
> 
> # make data.frame for glmmTMB estimation
> df_01 <- data.frame(abundance = sim_01,
>                   species = 1:length(sim_01))
> 
> # using the 'glmmTMB' package, assume regular Poisson distribution
> est_03 <- glmmTMB(abundance ~ (1 | species),
>                      family = poisson(link = "log"),
>                      data = df_01)
> # using the 'glmmTMB' package, assume zero truncated Poisson distribution
> est_04 <- glmmTMB(abundance ~ (1 | species),
>                      family = truncated_poisson(link = "log"),
>                      data = df_01[df_01$abundance>0, ])
> 
> # Compare estimates
> est_df <- data.frame(method = rep(c("poilog", "glmmmTMB"), each = 2),
>                     assumptions = rep(c("poisson", "truncated_poisson"), 2),
>                     mu = c(est_01$par[1], est_02$par[1],
>                            est_03$fit$par[1], est_04$fit$par[1]),
>                     sigma = c(est_01$par[2], est_02$par[2],
>                               exp(c(est_03$fit$par[2], est_04$fit$par[2]))))
> 
> est_df
> 
> #### End of code ####
> 
> When I fit the truncated_poisson model in glmmTMB, the mean increases and the standard deviation decreases, which is similar to what happens if you ignore the zeros and fit a regular poisson distribution, but it doesn't seem to be doing quite that either.
> 
> So, I'm hoping anyone knew how to interpret the mean and standard deviation from the truncated_poisson output and how they relate to the mean and standard deviation of a regular poisson model?
> 
> Thank you very much for reading this and any response is much appreciated.
> 
> Best regards,
> 
> Erik
> 
> 
> 
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