Good morning,

I am running both linear and non-linear models in brms, and my results are quite similar. First, I am running my model using my response variable, along with two predictors and one random effect. Below are the results. I have also created a non-linear model. After extensive research, I’m not entirely certain if it’s the correct approach for a non-linear model, but I have included quadratic effects for both predictors. After doing some reading, I think the models have been executed well, but I’m not entirely sure. Could you please provide me with some assistance? Thank you very much!

Cheers,

Felix

Below are the results I obtained:

```
fit_log <- bf(Social_dist ~ 1 + X50 + Num_Unique_Healthy_Ids + (1|p|Name)) + lognormal()
fit_log <- brm(fit_log,
data = final_data,
iter = 5000,
warmup = 1000,
thin = 4,
chains = 4,
cores = corecount)
```

```
> summary(fit_log)
Family: lognormal
Links: mu = identity; sigma = identity
Formula: Social_dist ~ 1 + X50 + Num_Unique_Healthy_Ids + (1 | p | Name)
Data: final_data (Number of observations: 30538)
Draws: 4 chains, each with iter = 5000; warmup = 1000; thin = 4;
total post-warmup draws = 4000
Group-Level Effects:
~Name (Number of levels: 292)
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept) 0.30 0.01 0.27 0.33 1.00 2133 3041
Population-Level Effects:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
Intercept 1.45 0.02 1.41 1.49 1.00 1027
X50 0.10 0.01 0.08 0.12 1.00 3443
Num_Unique_Healthy_Ids -0.11 0.01 -0.12 -0.09 1.00 3532
Tail_ESS
Intercept 2006
X50 3890
Num_Unique_Healthy_Ids 3737
Family Specific Parameters:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma 0.83 0.00 0.82 0.83 1.00 4041 3974
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).
```

I have included quadratic effects for both predictors in the non-linear model.

```
fit_nonlinear <- bf(Social_dist ~ 1 + X50^2 + Num_Unique_Healthy_Ids^2 + (1|p|Name)) + lognormal()
fit_nonlinear <- brm(fit_nonlinear,
data = final_data,
iter = 5000,
warmup = 1000,
thin = 4,
chains = 4,
cores = corecount)
```

```
Family: lognormal
Links: mu = identity; sigma = identity
Formula: Social_dist ~ 1 + X50^2 + Num_Unique_Healthy_Ids^2 + (1 | p | Name)
Data: final_data (Number of observations: 30538)
Draws: 4 chains, each with iter = 5000; warmup = 1000; thin = 4;
total post-warmup draws = 4000
Group-Level Effects:
~Name (Number of levels: 292)
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept) 0.30 0.01 0.27 0.33 1.00 2033 3073
Population-Level Effects:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept 1.45 0.02 1.41 1.49 1.00 1065 2007
X50 0.10 0.01 0.08 0.12 1.00 3478 3663
Num_Unique_Healthy_Ids -0.11 0.01 -0.13 -0.09 1.00 3618 3818
Family Specific Parameters:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma 0.83 0.00 0.82 0.83 1.00 3740 3356
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).
```

This is the LOO comparison.

```
loo_compare(loo_linear, loo_nonlinear)
elpd_diff se_diff
fit_log 0.0 0.0
fit_nonlinear -1.0 0.4
```