How to properly do out-of-sample prediction for hierarchical model

Questions v5
, ,
13 
num_cohort = 2

data_list = [-1.2083030673141326,
 0.5652466185040567,
 -0.7851719239971027,
 0.20513500717041422,
 0.5652466185040567,
 -0.1549766041632283,
 2.0056930638386268,
 -1.2983309701475432,
 0.745302424170878,
 1.1054140355045206,
 -0.42506031266346017,
 -0.6951440211636921,
 -1.280325389580861,
 0.6552745213374673,
 -0.7873164649263759,
 -0.6484249514565011,
 0.5817570249909609,
 2.089722028378173,
 -0.410325214079573,
 -0.8746197019645828,
 0.8198567623678892,
 -0.410325214079573,
 -1.0214478733470218,
 0.6611236041166038,
 -0.9220549344577036,
 -0.8455301825797763,
 0.24973032867305697,
 0.9193219076049202,
 -0.6111731299536243,
 0.05841844897823892]

index_list = [0,
 0,
 0,
 0,
 0,
 0,
 0,
 0,
 0,
 0,
 0,
 0,
 0,
 0,
 1,
 1,
 1,
 1,
 1,
 1,
 1,
 1,
 1,
 1,
 3,
 3,
 3,
 3,
 3,
 3]

output_list = [4,
 4,
 4,
 4,
 4,
 4,
 4,
 3,
 4,
 3,
 2,
 4,
 2,
 1,
 2,
 1,
 4,
 4,
 4,
 2,
 4,
 3,
 3,
 4,
 1,
 2,
 2,
 4,
 4,
 4]

prediction_len = 30
training_data_lite = pd.DataFrame({'in1':data_list, 'in2':data_list, 'out':output_list, 'race_idx':index_list})
testing_data_lite = pd.DataFrame({'in1':data_list[:prediction_len], 'in2':data_list[:prediction_len],'race_idx':index_list[:prediction_len]})
# Re-assign consecutive index starting from zero
training_race_idx_mapping = dict(zip(set(training_data_lite.race_idx), range(len(set(training_data_lite.race_idx)))))
training_data_lite = training_data_lite.replace({"race_idx": training_race_idx_mapping})
testing_race_idx_mapping = dict(zip(set(testing_data_lite.race_idx), range(len(set(testing_data_lite.race_idx)))))
testing_data_lite = testing_data_lite.replace({"race_idx": testing_race_idx_mapping})

temp_df = training_data_lite

idx = temp_df.race_idx
_, races_full = temp_df.race_idx.factorize(sort=True)
coords = {
    "id": races_full,
    "obs_idx": list(range(len(idx))),
}
with pm.Model(coords=coords) as olmpp_4:
    x_0 = pm.Data("x_0", temp_df['in1'].astype(float).values, mutable=True, dims=("obs_idx",))
    x_1 = pm.Data("x_1", temp_df['in2'].values, mutable=True, dims=("obs_idx",))
    y = pm.Data("y", temp_df['out'].values - 1, mutable=True, dims=("obs_idx",))

    b_mean = pm.Normal('b_mean', [-0.05, 1., 0., 0.], 4*[5.])
    b_stddev = pm.HalfNormal('b_stddev', 4*[10.])
    b0 = pm.Normal('b0', b_mean[0], b_stddev[0], dims=("id",))
    b1 = pm.Normal('b1', b_mean[1], b_stddev[1], dims=("id",))

    phi = b0[idx] * x_0\
        + b1[idx] * x_1\

    a_mean = pm.Normal('a_mean', 0., 10.)
    a_stdev = pm.HalfNormal('a_stddev', 10.)
    
    a = pm.Normal(
         'a', a_mean, a_stdev,
         transform=pm.distributions.transforms.univariate_ordered,
         shape=(len(coords['id']), 4 - 1),
         testval=len(coords['id']) * [[-2.512425133191401, -1.1671272329327658, -0.39780512413988334]],
         dims=("id",),
     )

    obs = pm.OrderedLogistic("obs", phi, a[idx], observed=y, dims=("obs_idx",))

    idata = pm.sample(10, tune=10, chains=4, return_inferencedata=True, idata_kwargs={'log_likelihood':True})

temp_df2 = testing_data_lite
idx2 = temp_df2.race_idx
_, races_full2 = temp_df2.race_idx.factorize(sort=True)
new_coords = {
    "id": races_full2,
    "obs_idx": list(range(len(idx2))),
}
with pm.Model(coords=new_coords) as olmpp_4_pre:
    x_0 = pm.Data("x_0", temp_df2['in1'].astype(float).values, mutable=True, dims=("obs_idx",))
    x_1 = pm.Data("x_1", temp_df2['in2'].values, mutable=True, dims=("obs_idx",))
    
    b_mean = pm.Normal('b_mean', [-0.05, 1., 0., 0.], 4*[5.])
    b_stddev = pm.HalfNormal('b_stddev', 4*[10.])
    new_b0 = pm.Normal('new_b0', b_mean[0], b_stddev[0], dims=("id",))
    new_b1 = pm.Normal('new_b1', b_mean[1], b_stddev[1], dims=("id",))

    phi = new_b0[idx] * x_0\
        + new_b1[idx] * x_1\

    a_mean = pm.Normal('a_mean', 0., 10.)
    a_stdev = pm.HalfNormal('a_stddev', 10.)
    
    new_a = pm.Normal(
         'new_a', a_mean, a_stdev,
         transform=pm.distributions.transforms.univariate_ordered,
         shape=(len(coords['id']), 4 - 1),
         dims=("id",),
     )
    
    obs = pm.OrderedLogistic("obs", phi, new_a[idx], dims=("obs_idx",))

    idata_pre = pm.sample_posterior_predictive(idata, var_names=["obs"], predictions=True, extend_inferencedata=False)

If prediction_len < 30, I got an error