Comparison between the ouputs of the lmer and the brm (from the brms package) functions
Note that brms does some special reparameterization magic with the intercept and uses a weakly informative prior for both the reparameterized intercept and the random effects. Also, if you look, you'll see that youR ESS is much lower for the intercept and the RE than for the other parameters. This can be indicative of the model having trouble exploring how those parameters relate and thus still having a large amount of uncertainty. In other words, the uncertainty in the random-effect of Intercept results in increased uncertainty for the fixed-effect of Intercept. Phillip
On 16/4/21 11:54 am, Vincent Bremhorst wrote:
Dear all,
I fitted the same mixed model using two different functions : lmer and brm.
The estimation of the standard deviation of the random effect and the estimation of the standard errors of the intercept differ. Both estimates are higher with the Bayesian procedure.
Since I use non-informative prior in the brm specification, I would expect similar results.
The other estimates are similar for both procedures.
Do you have any idea what's happen here?
Thanks for your help,
Vincent Bremhorst.
lmer (model assumptions are met):
res <- lmer(dTmeanoff ~ habitat + (1|week), data=trh)
Linear mixed model fit by REML. t-tests use Satterthwaite's method ['lmerModLmerTest']
Formula: dTmeanoff ~ habitat + (1 | week)
Data: trh
REML criterion at convergence: 312.5
Scaled residuals:
Min 1Q Median 3Q Max
-3.5949 -0.5149 -0.0181 0.4792 2.2995
Random effects:
Groups Name Variance Std.Dev.
week (Intercept) 0.06142 0.2478
Residual 1.93221 1.3900
Number of obs: 89, groups: week, 4
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 0.6200 0.2788 12.5997 2.224 0.0451 *
habitatu -0.8101 0.3503 83.0542 -2.312 0.0232 *
habitatw -1.6366 0.3698 83.2151 -4.425 2.9e-05 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr) habitt
habitatu -0.638
habitatw -0.605 0.481
brm (convergence of the posterior chains ok)
priors<- c(prior(normal(0,100), class="b"),
+ prior(normal(0, 100), class="Intercept"), + prior(exponential(0.1), class="sigma"), + prior(exponential(0.1), class="sd", group= "week") + + )
fit1<- brm(dTmeanoff~habitat+(1|week), data=trh,
+ prior=priors,
+ iter=4000, warmup=2000,chains=2,
+ family = gaussian(),#no logit function applied
+ file = "output.rds",
+ sample_prior = "yes",
+ control = list(adapt_delta = .9))
Family: gaussian
Links: mu = identity; sigma = identity
Formula: dTmeanoff ~ habitat + (1 | week)
Data: trh (Number of observations: 89)
Samples: 2 chains, each with iter = 4000; warmup = 2000; thin = 1;
total post-warmup samples = 4000
Group-Level Effects:
~week (Number of levels: 4)
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept) 0.50 0.48 0.02 1.82 1.00 900 1048
Population-Level Effects:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept 0.63 0.36 -0.11 1.40 1.00 1159 901
habitatu -0.82 0.35 -1.51 -0.13 1.00 2235 2581
habitatw -1.65 0.37 -2.37 -0.89 1.00 2091 2500
Family Specific Parameters:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma 1.41 0.11 1.21 1.65 1.00 2863 2199
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