Question about ppc and waic

I have read arviz.plot_ppc and pymc3.waic(although it is out-of-date).
I still cannot understand the usage of ppc, and this is my code.

    r_CH4_obs = r_2 + r_3 + r_4
    r_CO_obs = - r_3 - r_4 + r_1
    r_CO2_obs = - r_2 + r_4 - r_1
    ##Likelihood function
    r_CH4_likehood = pm.Normal('r_CH4_likehood',mu = r_CH4_obs, sd = sigma, observed = r0_CH4)
    r_CO_likehood = pm.Normal('r_CO_likehood',mu = r_CO_obs, sd = sigma, observed = r0_CO)
    r_CO2_likehood = pm.Normal('r_CO2_likehood',mu = r_CO2_obs, sd = sigma, observed = r0_CO2)

Here is my likelihood.

from scipy import optimize
with Tk_PL_ab_3478:
    map_estimate = pm.find_MAP()
    step = pm.NUTS()
    #prior = pm.sample_prior_predictive()
    trace_Tk_PL_ab_3478 = pm.sample(draws = 10000, tune = 10000, cores = 2, start = map_estimate, step = step)
    #posterior_predictive = pm.sample_posterior_predictive(trace_PL_in_134)
    prior_check = pm.sample_prior_predictive(samples = 500)
    ppc = pm.sample_posterior_predictive(trace_Tk_PL_ab_3478, var_names=["r_CH4_likehood","r_CO_likehood","r_CO2_likehood"])

And here is my sampling codes.

import arviz as az
az.plot_ppc(Tk_PL_ab_3478, var_names=["r_CH4_likehood","r_CO_likehood","r_CO2_likehood"],group ={'posterior'})

When I use plot_ppc,

TypeError: Data must include log_likelihood in sample_stats occurred.

How can I deal with my codes?

Another question is about waic, used for model comparison. But in this case, I cannot run waic due to multi-likelihood. How can I use waic and loo with multi-likelihood?

Finally, in old version of pymc3, model comparsion method like dic is availble but now I cannot use it. Any other model comparison methods, like Baysian factors? or anything else?

Thank you!

For insight on how to calculate WAIC and on how to deal with multiple likelihoods, I’d refer you to this really great answer by @OriolAbril.