I’m analyzing response time data. I was expecting that using a lognormal regression should be equivalent to applying a log-transformation on the outcome variable first and then using linear regression. While I also get mostly identical results with both approaches, the group-level effect of the main predictor variable `predictor`

varies substantially. Can anyone explain me how this can happen?

```
m1 <- brm(RT ~ 1 + predictor + session + (1 + predictor + session |subject), data=df, iter=6000, family=lognormal())
m2 <- brm(log(RT) ~ 1 + predictor + session + (1 + predictor + session |subject), data=df, iter=6000)
```

```
> summary(m1)
Family: lognormal
Links: mu = identity; sigma = identity
Formula: RT ~ 1 + predictor + session + (1 + predictor + session | subject)
Data: df (Number of observations: 16293)
Draws: 4 chains, each with iter = 3000; warmup = 0; thin = 1;
total post-warmup draws = 12000
Group-Level Effects:
~subject (Number of levels: 90)
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept) 0.42 0.03 0.36 0.49 1.00 1232 2137
sd(predictor) 0.02 0.01 0.00 0.03 1.00 902 3235
sd(session2) 0.24 0.02 0.20 0.28 1.00 4096 7285
cor(Intercept,predictor) -0.22 0.33 -0.83 0.53 1.00 13474 5731
cor(Intercept,session2) -0.33 0.10 -0.51 -0.14 1.00 5050 6463
cor(predictor,session2) -0.09 0.35 -0.78 0.64 1.02 236 265
Population-Level Effects:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept 9.77 0.05 9.68 9.86 1.01 483 692
predictor -0.03 0.01 -0.04 -0.02 1.00 14287 9032
session2 -0.20 0.03 -0.25 -0.15 1.00 2900 6087
Family Specific Parameters:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma 0.49 0.00 0.49 0.50 1.00 22156 7907
Draws were sampled using sample(hmc). 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).
```

```
> summary(m2)
Family: gaussian
Links: mu = identity; sigma = identity
Formula: log(RT) ~ 1 + predictor + session + (1 + predictor + session | subject)
Data: df (Number of observations: 16293)
Draws: 4 chains, each with iter = 3000; warmup = 0; thin = 1;
total post-warmup draws = 12000
Group-Level Effects:
~subject (Number of levels: 90)
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept) 0.42 0.03 0.36 0.49 1.00 1384 3430
sd(predictor) 0.02 0.01 0.00 0.04 1.00 1146 1911
sd(session2) 0.24 0.02 0.20 0.28 1.00 5117 7220
cor(Intercept,predictor) -0.06 0.32 -0.70 0.64 1.00 11868 5376
cor(Intercept,session2) -0.33 0.10 -0.51 -0.13 1.00 4826 7512
cor(predictor,session2) -0.26 0.33 -0.84 0.49 1.02 246 337
Population-Level Effects:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept 9.76 0.04 9.68 9.85 1.01 761 1604
predictor -0.01 0.01 -0.02 0.00 1.00 13244 8814
session2 -0.20 0.03 -0.25 -0.14 1.00 4314 6346
Family Specific Parameters:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma 0.50 0.00 0.49 0.50 1.00 20260 9036
Draws were sampled using sample(hmc). 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).
```

- Operating System: Windows
- brms Version: 2.16.3