Short summary of the problem

I am currently studying the effects of exposure on horn length in female bovids; however, some species have females that lack horns completely. I need to run a phylogenetic analyses that takes in account the zero inflation in my continuous horn length data. I used the function “brm” from the package “brms” where I could specify the “family” function to use a hurdle model, and it successfully ran. However, I am not sure what are the differences between the hurdle model options (i.e. hurdle_gamma vs hurdle_poisson).

In the output below, I used “hurdle_gamma”. If that happens to be a correct way to analyze this data, I wanted to see if it be possible to help me understand the results correctly. It seems there is a significant effect of expo (exposure score) on horn length, but I am not sure if hurdle_gamma was the correct family choice.

```
fit1 <- brm(horn~expo + (1|gr(phylo, cov = Horn)) + (1|Binomial), data = HornGamma, family = hurdle_gamma(), data2 = list(Horn = Horn), control = list(adapt_delta = 0.99), iter = 4000)
summary(fit1)
Family: hurdle_gamma
Links: mu = log; shape = identity; hu = identity
Formula: horn ~ expo + (1 | gr(phylo, cov = Horn)) + (1 | Binomial)
Data: HornGamma (Number of observations: 89)
Draws: 4 chains, each with iter = 4000; warmup = 2000; thin = 1;
total post-warmup draws = 8000
Group-Level Effects:
~Binomial (Number of levels: 89)
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept) 0.09 0.05 0.01 0.18 1.00 663 1501
~phylo (Number of levels: 89)
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept) 0.05 0.02 0.02 0.09 1.01 1285 1594
Population-Level Effects:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept 0.68 0.15 0.40 0.98 1.00 3559 4086
expo 0.18 0.06 0.07 0.30 1.00 4116 5245
Family Specific Parameters:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
shape 73.94 59.24 23.83 234.87 1.01 496 803
hu 0.35 0.05 0.26 0.45 1.00 15527 5044
Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).
```