# How do you specify a chi-square response distribution using custom\_family()?

**URL:** https://discourse.mc-stan.org/t/how-do-you-specify-a-chi-square-response-distribution-using-custom-family/17577
**Category:** brms
**Tags:** stan
**Created:** [August 20, 2020, 6:24pm UTC](https://discourse.mc-stan.org/t/how-do-you-specify-a-chi-square-response-distribution-using-custom-family/17577 "2020-08-20T18:24:59Z")
**Posts on this page:** 2
**Page:** 1

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### Author: ![elinck](https://avatars.discourse-cdn.com/v4/letter/e/ed8c4c/32.png) [@elinck](https://discourse.mc-stan.org/u/elinck)
#### Post date: [August 20, 2020, 6:25pm UTC](https://discourse.mc-stan.org/t/how-do-you-specify-a-chi-square-response-distribution-using-custom-family/17577/1 "2020-08-20T18:25:00Z")

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Hi! I’m attempting to fit a model in brms where the response variable fits a scaled chi-square distribution—without going to deep on the specific question, we’re looking at predictors of sample variance.

My first thought was to use `family=skew_normal()`, and while it’s an OK fit it’s not great, so instead, I’d like to use the `custom_family()` to call a [chi-square distribution from Stan](https://mc-stan.org/docs/2_21/functions-reference/chi-square-distribution.html). It’s here where I’m running into trouble: while I can follow along with [this useful vignette](https://cran.r-project.org/web/packages/brms/vignettes/brms_customfamilies.html), it’s my understanding that since this distribution is already defined in Stan, I don’t need to provide any Stan functions; only define the family and make sure its name matches the prefix in Stan.

However, I think I’m missing something in my `custom_family()` syntax, as when I try to use `family=chi_square`, Stan fails to compile. I suspect I am missing something basic and apologize if I missed a similar question in the forum.

The code below is a reproducible example of my problem. Thanks in advance!

```
library(brms)

# simulate data from linear model
set.seed(7356) 
N <- 100
x <- rnorm(N)
beta <- 0.4
errors <- rchisq(100, df=1) # errors from chi-sq dist
errors <- errors - 1 # centers error distribution on 0
y <- 1 + x*beta + errors

# visualize response distribution
hist(y, breaks = 15)

# create dataframe
df <- cbind.data.frame(x, y)
colnames(df) <- c("predictor","response")

# run model with skew_normal distribution
mod1 <- brm(
  formula = bf(response ~ predictor),
  data = df, 
  family = skew_normal(), 
  iter = 10000
)

summary(mod1)
pp_check(mod1, nsamples=50) # peak off 

# define custom family
chi_square <- custom_family(
  "chi_square", dpars = c("mu", "nu"),
  type = "real"
)

# run model with chi_square distribution
mod2 <- brm(
  formula = bf(response ~ predictor),
  data = df, 
  family = chi_square,
  iter = 10000
)

# stops after "Compiling Stan program..."

```

(I’m using brms version 2.13.5 on Mac OS X 10.14.1; R version 4.0.2.)

---

<div class="post-metadata">

### Author: ![Guido\_Biele](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/guido_biele/32/3414_2.png) [@Guido\_Biele](https://discourse.mc-stan.org/u/Guido_Biele)
#### Post date: [August 23, 2020, 10:25am UTC](https://discourse.mc-stan.org/t/how-do-you-specify-a-chi-square-response-distribution-using-custom-family/17577/2 "2020-08-23T10:25:53Z")

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Hi,

I think you still need to add a stan function that calculates the likelihood.  
(

```

stan_funs <- ...
stanvars <- ...

```

)  
However, I am not entirely sure. Could you post the brms-generated Stan-code?