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.