# Sigma in lognormal

**URL:** <https://discourse.mc-stan.org/t/sigma-in-lognormal/30720>\
**Category:** Modeling\
**Tags:** brms\
**Created:** [March 14, 2023, 9:18am UTC](https://discourse.mc-stan.org/t/sigma-in-lognormal/30720 "2023-03-14T09:18:12Z")\
**Posts on this page:** 2\
**Page:** 1

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**Author:** ![Elef](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/elef/32/4280_2.png) [@Elef](https://discourse.mc-stan.org/u/Elef)\
**Post date:** [March 14, 2023, 9:18am UTC](https://discourse.mc-stan.org/t/sigma-in-lognormal/30720/1 "2023-03-14T09:18:12Z")

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Hi,

I was looking at [this](https://rpsychologist.com/GLMM-part1-lognormal) very nice post about the lognormal GLMM from K. Magnusson.

I would like to compare the sigma and the sd\_cluster\_\_Intercept but I’m confused with the units.

In this example the model looks like the below and the output has a sigma = 0.51 and a sd\_cluster\_\_Intercept = 0.64.

```plaintext
y ~ 1 + TX + (1 | cluster), 
           family = lognormal()

```

To compare the two errors I would turn them in to variances and then I would get the proportion of the one to the other like that,  
`sd_cluster__Intercept ^2/(sd_cluster__Intercept ^2 + sigma^2)`.

But since here we have lognormal, should I get the exp first?  
I’m so confused.

Thanks for your time.

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**Author:** ![LucC](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/lucc/32/4475_2.png) [@LucC](https://discourse.mc-stan.org/u/LucC)\
**Post date:** [March 20, 2023, 5:34am UTC](https://discourse.mc-stan.org/t/sigma-in-lognormal/30720/2 "2023-03-20T05:34:59Z")

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Both parameters are measures of variation on the logarithmic scale. These parameter values themselves are not logarithmic.

There is no need to exponentiate for what you are proposing. The result of what you propose will be an estimate of the relative importance of the two measures of variation (on the logarithmic scale).