Hello I am trying to model a collider process from some pre generated data but when i try to subtract mu from the observed dist i get this error.

```
# collider
# generating data
np.random.seed(2025)
beta1 = 3
beta2 = 2
x = np.random.normal(loc=10, scale=3, size=100)
y = np.random.normal(loc=2, scale=3, size=100)
z = x*beta1 + y*beta2 + np.random.normal(loc=0, scale=0.1, size=100)
data = pd.DataFrame({'x':x,'z': z,'y': y})
```

```
#WRONG MODEL INCLUDING COLLIDER
with pm.Model() as include_collider_model:
x = pm.Data('x',data['x'].values)
z = pm.Data('z',data['z'].values)
y = pm.Data('y',data['y'].values)
alpha = pm.Normal('intercept',0,1)
beta_x = pm.Normal('slope_x',0,1)
beta_z = pm.Normal('slope_z',0,1)
sigma = pm.Exponential('error',lam=1)
mu = alpha + beta_x*x + beta_z*z
y_hat = pm.Normal('y_hat',0,sigma,observed=y-mu)
trace_include_collider = pm.sample(1000)
# Figure 11
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [147], in <cell line: 3>()
11 sigma = pm.Exponential('error',lam=1)
13 mu = alpha + beta_x*x + beta_z*z
---> 14 y_hat = pm.Normal('y_hat',0,sigma,observed=y-mu)
15 trace_include_collider = pm.sample(500,tune=1500,chains=2, cores=2, target_accept=0.95)
File ~\.conda\envs\pymc_env\lib\site-packages\pymc\distributions\distribution.py:271, in Distribution.__new__(cls, name, rng, dims, initval, observed, total_size, transform, *args, **kwargs)
267 if resize_shape:
268 # A batch size was specified through `dims`, or implied by `observed`.
269 rv_out = change_rv_size(rv=rv_out, new_size=resize_shape, expand=True)
--> 271 rv_out = model.register_rv(
272 rv_out,
273 name,
274 observed,
275 total_size,
276 dims=dims,
277 transform=transform,
278 initval=initval,
279 )
281 # add in pretty-printing support
282 rv_out.str_repr = types.MethodType(str_for_dist, rv_out)
File ~\.conda\envs\pymc_env\lib\site-packages\pymc\model.py:1372, in Model.register_rv(self, rv_var, name, data, total_size, dims, transform, initval)
1366 else:
1367 if (
1368 isinstance(data, Variable)
1369 and not isinstance(data, (GenTensorVariable, Minibatch))
1370 and data.owner is not None
1371 ):
-> 1372 raise TypeError(
1373 "Variables that depend on other nodes cannot be used for observed data."
1374 f"The data variable was: {data}"
1375 )
1377 # `rv_var` is potentially changed by `make_obs_var`,
1378 # for example into a new graph for imputation of missing data.
1379 rv_var = self.make_obs_var(rv_var, data, dims, transform)
TypeError: Variables that depend on other nodes cannot be used for observed data.The data variable was: Elemwise{sub,no_inplace}.0
```

Is there an alternative approach to use in pymc4? I have made this work in pymc3 b4.

Thanks!!!

-Blaise