# Log Student-t comparing differences in scale

**URL:** <https://discourse.mc-stan.org/t/log-student-t-comparing-differences-in-scale/41729>\
**Category:** Modeling\
**Tags:** brms\
**Created:** [October 29, 2026, 8:54pm UTC](https://discourse.mc-stan.org/t/log-student-t-comparing-differences-in-scale/41729 "2026-10-29T20:54:05Z")\
**Posts on this page:** 1\
**Page:** 1

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**Author:** ![Hunter24](https://avatars.discourse-cdn.com/v4/letter/h/3ab097/32.png) [@Hunter24](https://discourse.mc-stan.org/u/Hunter24)\
**Post date:** [October 29, 2026, 8:54pm UTC](https://discourse.mc-stan.org/t/log-student-t-comparing-differences-in-scale/41729/1 "2026-10-29T20:54:05Z")

</div>

I am doing a log student t distribution. All nu values are above 2 so both mean and variance exist.  
I want to compare the log sigmas between groups, so taking the difference in the posteriors of log sigma\_group1 - log sigma\_group2.

If this was a gaussian I would take the CV to control for different means or equally for lognormal model I would first convert the sigma to the arithmetic CV sqrt(exp(log\_var) - 1), and for gamma use 1/shape .

Although I don’t believe I can apply this to a student T. So would the perferable thing to do is to take the delta of the log sd? But just not interpret it as the arithmetic CV? Cause I want to make sure that the difference I observe in the residuals isnt due to the difference in the means.

```no-highlight
brm.formula <- bf(
  log(y) ~ 0 + group +
    (1 | gr(ID, by = group)),

  sigma ~ 0 + group
)

fit <- brm(
  formula = brm.formula,
  data = dat,
  family = student()
)

```

* * *

Thanks,  
Hunter