Difficulty fitting lognormal model

Modeling
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1

Hi, I’m new to posting here and need help fitting a lognormal model (or potentially a different distribution?). I’m trying to model differences in brain region size (length, measured in mm) by wetland type (reference vs tile wetlands). I’m using RStudio 1.3.959 on macOS Sierra (version 10.12.6).

Background of experiment:
We collected frogs from reference and tile wetlands (6 sites total) to determine if there were differences in the size of specific brain regions. We have previously confirmed tile wetlands have pesticide concentrations ~2.5 times higher than reference wetlands, many of which are known to be neurotoxic, hence the idea that tile wetlands could contribute to abnormal brain morphology. To control for differences in body length, I divided brain region length by total body length.

I can’t share the data, but the standardized length of this specific brain region ranges from 0.06 - 0.34mm. Average standardized brain length was ~0.02 mm longer at reference wetlands compared to tile wetlands.

Here is my most recent model:

bo6 <- brm(Length_mm_STD ~ 0 + Wetland_type + (1|Site), data = bo, 
           family = lognormal(link = "identity"), 
           prior=c(prior(normal(-1.4, 0.15), class=b, coef="Wetland_typecontrol"),
                   prior(normal(-1.6, 0.15), class = b, coef="Wetland_typetile"),
                   prior(exponential(10), class = sd),
                   prior(exponential(10), class=sigma)),
           iter = 2000 , warmup = 500, chains = 4, cores = 4,
           seed = 5, control = list(adapt_delta = 0.999), save_pars = save_pars(all=TRUE))
}

The model output looks ok, but the pp_check shows a poor-ish fit:

Group-Level Effects:
~Site (Number of levels: 6)
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept) 0.11 0.07 0.01 0.26 1.00 1393 1894

Population-Level Effects:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Wetland_typecontrol -1.48 0.08 -1.62 -1.32 1.00 2734 2856
Wetland_typetile -1.61 0.08 -1.77 -1.45 1.00 3578 3094

Family Specific Parameters:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma 0.29 0.03 0.24 0.36 1.00 2988 3861

image

I’m mainly struggling to fit the smaller peaks. I was hopeful that adding + (1|Site) to the model would do the trick, but apparently not. I’ve also tried running numerous models with a gamma distribution and a few with skew-normal, however, I still had similar issues with fitting the small peaks.

The loo-pit overlay also shows some overdispersion, but I’m not sure where its coming from.
image

Does anyone have any idea how I can improve the fit or have suggestions for a different distribution? Please let me know if more info is needed to help, I’ve never posted in this forum before. Thanks in advance!

2

maybe try to model the scaled brain part length on the log scale? It might not solve the problem but at least you’re in the realm of distributions on the reals… Accordingly change distribution to gaussian and if not satisfying, try student_t