# To what extent can a non-standard variance for GLMs be specified in Stan?

When using Stan functions like `bernoulli_logit`, there is a default to a scale parameter of 1 for the standard logistic distribution.

To what extent is it possible to specify a different variance for this parameter? A scale of 5 perhaps, or something less than 1?

Anything you can write down in math thatâ€™s differentiable is fair game. The definition built-in is that

``````y ~ bernoulli_logit(alpha);
``````

is equivalent to

``````y ~ bernoulli(inv_logit(alpha));
``````

You can replace `inv_logit` with another CDF and youâ€™re good to go. For example, probit regression is just

``````y ~ bernoulli(Phi(alpha));
``````

where `Phi` is the standard normal cdf.

If you want to do inverse logit with a different scale, you can just scale the value, e.g., for scale 5,

``````bernoulli_logit(y | alpha / 5.0);
``````

You can also write this directly as a cdf as follows.

``````y ~ bernoulli(logistic_cdf(alpha | 0, 5));
``````
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Sometimes youâ€™re almost too perfect, @Bob_Carpenter. Many thanks again.