[R-sig-ME] Comparison between the ouputs of the lmer and the brm (from the brms package) functions

[Phillip Alday]

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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> 
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