I’m new to the world of bayesian. I’m working on a hierarchical model with quite a few variables. One of the variables is causing the model not to converge. If I use ‘numpyro’, the sampling would finish very quickly and end up with inf r_hat for every variable. When I use ‘pymc’ sampler, it won’t even run. I identified the problematic variable by elimination. 98% of the values are zero for the variable. But the rest 2% are all valid values, nothing crazy. I’m curious what are the reasons for this to happen and if there are any potential fixes if I have to include this variable in the model. Thank you very much.

# What are the Reasons for a Variable with few Non-zero Values to Cause the Model to Fail to Converge?

You have to share more details about the model. numpyro running fast just means it’s getting a 100% divergences.

Hi Ricardo, Thank you very much for your response. Here is what the code structure looks like. It’s a hierarchical model with a nested structure. At least that’s what I’m trying to do, but I’m unsure if I have everything set up correctly. The dependent variables are categorical. When I use ‘pymc’ sampler, it would give me an error saying “Initial evaluation of model at starting point failed!”. Let’s say the variable causing issue is ‘Var1_’, If I remove ‘Var1_’, the sampling process would run. But the values of ‘Var1_’ are all valid in the dataframe, except 98% of the values are 0. I hope this provides more information. I really appreciate the help!

```
coords = {
"dim1": dim1,
"dim2": dim2,
"dim3": dim3,
"Variables": Variables,
"obs": range(N),
}
with pm.Model(coords=coords) as model:
mu = pm.Normal('mu', 0, 1000, dims="Variables")
sigma = pm.HalfNormal('sigma', sigma=1000, dims="Variables")
InterceptC_M = pm.Normal("InterceptC_M", mu[Variables.index("InterceptC_M")], sigma[Variables.index("InterceptC_M")], dims=("dim1","dim3"))
InterceptL_M = pm.Normal("InterceptL_M", mu[Variables.index("InterceptL_M")], sigma[Variables.index("InterceptL_M")], dims=("dim1","dim3"))
InterceptF_M = pm.Normal("InterceptF_M", mu[Variables.index("InterceptF_M")], sigma[Variables.index("InterceptF_M")], dims=("dim1","dim3"))
Var1_ = pm.Normal("Var1_", mu[Variables.index("Var1_")], sigma[Variables.index("Var1_")], dims="dim3")
u_A = InterceptC_M[dim1_idx, dim3_idx] + Var1_[dim3_idx] * df['Var1_']
u_B = InterceptL_M[dim1_idx, dim3_idx] + Var1_[dim3_idx] * df['Var1_']
u_C = InterceptF_M[dim1_idx, dim3_idx] + Var1_[dim3_idx] * df['Var1_']
TT_stack = pm.math.stack([u_A,u_B,u_C]).T
p_TT = pm.math.softmax(TT_stack, axis=1)
like_TT = pm.Potential("like_TT", Weight*pm.logp(pm.Categorical.dist(p=p_TT),dv_TT), dims="obs")
Intercept = pm.Normal("Intercept", mu[Variables.index("Intercept")], sigma[Variables.index("Intercept")], dims=("dim1","dim3"))
v = pm.Normal("v", mu[Variables.index("v")], sigma[Variables.index("v")], dims="dim3")
Var2_ = pm.HalfNormal("Var2_", sigma=sigma[Variables.index("Var2_")], dims='dim3')
Var3_ = pm.Normal("Var3_", mu[Variables.index("Var3_")], sigma[Variables.index("Var3_")], dims='dim1')
util=[]
for i in range(len(dim1)):
exec('''u_{} = Intercept[dim1_idx, dim3_idx] \
- Var2_[dim3_idx] * df['Var2_'] \
+ Var3_[dim1_idx] * df['Var3_'] \
+ v[dim3_idx] * pm.math.log(pm.math.sum(pm.math.exp(TT_stack),axis=1))'''.format(dim1[i]))
exec("util.append(u_{})".format(dim1[i]))
model_stack=pm.math.stack(util).T
p_model = pm.math.softmax(model_stack, axis=1)
like_model = pm.Potential("like_model", Weight*pm.logp(pm.Categorical.dist(p=p_model),dv_model),dims="obs")
idata = pm.sample(draws=2000,
chains=4,
cores=4,
tune=2000,
nuts_sampler="numpyro",
idata_kwargs={"log_likelihood": False},
nuts_sampler_kwargs={"postprocessing_vectorize":"scan"},
random_seed=1301)
```