**Is the following a correct approach for sigma modelling?**

Let’s assume we have a Y variable named **hours** in lognormal scale. We would like to know how these hours changed in time (variable named **year**)

**Data**

set.seed(0)

pi <- 0

mu_log <- 2

sigma_log <- 0.99

N = 1000

hours = (1 - rbinom(N, 1, prob = pi)) * rlnorm(N, mu_log, sigma_log)

year = seq(1,10, 1)

df = data.frame(hours=hours, year=year)

**Model**

m = brm(bf(hours ~ year, sigma ~ year), data = df, family = lognormal())

**Summary**

Family: lognormal

Links: mu = identity; sigma = log

Formula: hours ~ year

sigma ~ year

Data: df (Number of observations: 1000)

Samples: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;

total post-warmup samples = 4000

```
Population-Level Effects:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept 2.06 0.07 1.92 2.19 1.00 3742 2379
sigma_Intercept -0.01 0.05 -0.10 0.09 1.00 5050 3068
year -0.01 0.01 -0.03 0.01 1.00 4144 2783
sigma_year -0.00 0.01 -0.02 0.02 1.00 5213 3302
```

**Temporal trend for mean hours**

m %>% conditional_effects()

**Temporal trend for the standard deviation of hours?**

m %>% conditional_effects(dpar = “sigma”)

**Can we say that the standard deviation of hours did not change during the observed years, meaning that variation remained unchanged?** And am I correct that these hours on the sigma plot is on the original scale of Y variable(hours)?